Inverse source problems in elastodynamics
Bao, Gang; Hu, Guanghui; Kian, Yavar; Yin, Tao
2018-04-01
We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain approaches to show uniqueness in determining the spatial function from wave fields on a large sphere over a finite time interval. The stability estimate of the temporal function from the data of one receiver and the uniqueness result using partial boundary data are proved. Our arguments rely heavily on the use of the Fourier transform, which motivates inversion schemes that can be easily implemented. A Landweber iterative algorithm for recovering the spatial function and a non-iterative inversion scheme based on the uniqueness proof for recovering the temporal function are proposed. Numerical examples are demonstrated in both two and three dimensions.
Inverse source problems for eddy current equations
International Nuclear Information System (INIS)
Rodríguez, Ana Alonso; Valli, Alberto; Camaño, Jessika
2012-01-01
We study the inverse source problem for the eddy current approximation of Maxwell equations. As for the full system of Maxwell equations, we show that a volume current source cannot be uniquely identified by knowledge of the tangential components of the electromagnetic fields on the boundary, and we characterize the space of non-radiating sources. On the other hand, we prove that the inverse source problem has a unique solution if the source is supported on the boundary of a subdomain or if it is the sum of a finite number of dipoles. We address the applicability of this result for the localization of brain activity from electroencephalography and magnetoencephalography measurements. (paper)
Solution to the inversely stated transient source-receptor problem
International Nuclear Information System (INIS)
Sajo, E.; Sheff, J.R.
1995-01-01
Transient source-receptor problems are traditionally handled via the Boltzmann equation or through one of its variants. In the atmospheric transport of pollutants, meteorological uncertainties in the planetary boundary layer render only a few approximations to the Boltzmann equation useful. Often, due to the high number of unknowns, the atmospheric source-receptor problem is ill-posed. Moreover, models to estimate downwind concentration invariably assume that the source term is known. In this paper, an inverse methodology is developed, based on downwind measurement of concentration and that of meterological parameters to estimate the source term
Point source reconstruction principle of linear inverse problems
International Nuclear Information System (INIS)
Terazono, Yasushi; Matani, Ayumu; Fujimaki, Norio; Murata, Tsutomu
2010-01-01
Exact point source reconstruction for underdetermined linear inverse problems with a block-wise structure was studied. In a block-wise problem, elements of a source vector are partitioned into blocks. Accordingly, a leadfield matrix, which represents the forward observation process, is also partitioned into blocks. A point source is a source having only one nonzero block. An example of such a problem is current distribution estimation in electroencephalography and magnetoencephalography, where a source vector represents a vector field and a point source represents a single current dipole. In this study, the block-wise norm, a block-wise extension of the l p -norm, was defined as the family of cost functions of the inverse method. The main result is that a set of three conditions was found to be necessary and sufficient for block-wise norm minimization to ensure exact point source reconstruction for any leadfield matrix that admit such reconstruction. The block-wise norm that satisfies the conditions is the sum of the cost of all the observations of source blocks, or in other words, the block-wisely extended leadfield-weighted l 1 -norm. Additional results are that minimization of such a norm always provides block-wisely sparse solutions and that its solutions form cones in source space
Source localization in electromyography using the inverse potential problem
van den Doel, Kees; Ascher, Uri M.; Pai, Dinesh K.
2011-02-01
We describe an efficient method for reconstructing the activity in human muscles from an array of voltage sensors on the skin surface. MRI is used to obtain morphometric data which are segmented into muscle tissue, fat, bone and skin, from which a finite element model for volume conduction is constructed. The inverse problem of finding the current sources in the muscles is solved using a careful regularization technique which adds a priori information, yielding physically reasonable solutions from among those that satisfy the basic potential problem. Several regularization functionals are considered and numerical experiments on a 2D test model are performed to determine which performs best. The resulting scheme leads to numerical difficulties when applied to large-scale 3D problems. We clarify the nature of these difficulties and provide a method to overcome them, which is shown to perform well in the large-scale problem setting.
Source localization in electromyography using the inverse potential problem
International Nuclear Information System (INIS)
Van den Doel, Kees; Ascher, Uri M; Pai, Dinesh K
2011-01-01
We describe an efficient method for reconstructing the activity in human muscles from an array of voltage sensors on the skin surface. MRI is used to obtain morphometric data which are segmented into muscle tissue, fat, bone and skin, from which a finite element model for volume conduction is constructed. The inverse problem of finding the current sources in the muscles is solved using a careful regularization technique which adds a priori information, yielding physically reasonable solutions from among those that satisfy the basic potential problem. Several regularization functionals are considered and numerical experiments on a 2D test model are performed to determine which performs best. The resulting scheme leads to numerical difficulties when applied to large-scale 3D problems. We clarify the nature of these difficulties and provide a method to overcome them, which is shown to perform well in the large-scale problem setting
Review on solving the inverse problem in EEG source analysis
Directory of Open Access Journals (Sweden)
Fabri Simon G
2008-11-01
Full Text Available Abstract In this primer, we give a review of the inverse problem for EEG source localization. This is intended for the researchers new in the field to get insight in the state-of-the-art techniques used to find approximate solutions of the brain sources giving rise to a scalp potential recording. Furthermore, a review of the performance results of the different techniques is provided to compare these different inverse solutions. The authors also include the results of a Monte-Carlo analysis which they performed to compare four non parametric algorithms and hence contribute to what is presently recorded in the literature. An extensive list of references to the work of other researchers is also provided. This paper starts off with a mathematical description of the inverse problem and proceeds to discuss the two main categories of methods which were developed to solve the EEG inverse problem, mainly the non parametric and parametric methods. The main difference between the two is to whether a fixed number of dipoles is assumed a priori or not. Various techniques falling within these categories are described including minimum norm estimates and their generalizations, LORETA, sLORETA, VARETA, S-MAP, ST-MAP, Backus-Gilbert, LAURA, Shrinking LORETA FOCUSS (SLF, SSLOFO and ALF for non parametric methods and beamforming techniques, BESA, subspace techniques such as MUSIC and methods derived from it, FINES, simulated annealing and computational intelligence algorithms for parametric methods. From a review of the performance of these techniques as documented in the literature, one could conclude that in most cases the LORETA solution gives satisfactory results. In situations involving clusters of dipoles, higher resolution algorithms such as MUSIC or FINES are however preferred. Imposing reliable biophysical and psychological constraints, as done by LAURA has given superior results. The Monte-Carlo analysis performed, comparing WMN, LORETA, sLORETA and SLF
Direct and inverse source problems for a space fractional advection dispersion equation
Aldoghaither, Abeer; Laleg-Kirati, Taous-Meriem; Liu, Da Yan
2016-01-01
In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from final observations. We first derive the analytic
Direct and inverse source problems for a space fractional advection dispersion equation
Aldoghaither, Abeer
2016-05-15
In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the source term from final observations. We first derive the analytic solution to the direct problem which we use to prove the uniqueness and the unstability of the inverse source problem using final measurements. Finally, we illustrate the results with a numerical example.
On rational approximation methods for inverse source problems
Rundell, William
2011-02-01
The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Such is the ubiquity of these problems, the underlying model can lead to a partial differential equation of any of the major types, but here we focus on the case of steady-state electrostatic or thermal imaging and consider boundary value problems for Laplace\\'s equation. Our inclusions are interior forces with compact support and our data consists of a single measurement of (say) voltage/current or temperature/heat flux on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler "equivalent point source" problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2011 American Institute of Mathematical Sciences.
On rational approximation methods for inverse source problems
Rundell, William; Hanke, Martin
2011-01-01
The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Such is the ubiquity of these problems, the underlying model can lead to a partial differential equation of any of the major types, but here we focus on the case of steady-state electrostatic or thermal imaging and consider boundary value problems for Laplace's equation. Our inclusions are interior forces with compact support and our data consists of a single measurement of (say) voltage/current or temperature/heat flux on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler "equivalent point source" problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2011 American Institute of Mathematical Sciences.
On an inverse source problem for enhanced oil recovery by wave motion maximization in reservoirs
Karve, Pranav M.; Kucukcoban, Sezgin; Kallivokas, Loukas F.
2014-01-01
to increase the mobility of otherwise entrapped oil. The goal is to arrive at the spatial and temporal description of surface sources that are capable of maximizing mobility in the target reservoir. The focusing problem is posed as an inverse source problem
An inverse source problem of the Poisson equation with Cauchy data
Directory of Open Access Journals (Sweden)
Ji-Chuan Liu
2017-05-01
Full Text Available In this article, we study an inverse source problem of the Poisson equation with Cauchy data. We want to find iterative algorithms to detect the hidden source within a body from measurements on the boundary. Our goal is to reconstruct the location, the size and the shape of the hidden source. This problem is ill-posed, regularization techniques should be employed to obtain the regularized solution. Numerical examples show that our proposed algorithms are valid and effective.
Inverse problems of geophysics
International Nuclear Information System (INIS)
Yanovskaya, T.B.
2003-07-01
This report gives an overview and the mathematical formulation of geophysical inverse problems. General principles of statistical estimation are explained. The maximum likelihood and least square fit methods, the Backus-Gilbert method and general approaches for solving inverse problems are discussed. General formulations of linearized inverse problems, singular value decomposition and properties of pseudo-inverse solutions are given
Iterative and range test methods for an inverse source problem for acoustic waves
International Nuclear Information System (INIS)
Alves, Carlos; Kress, Rainer; Serranho, Pedro
2009-01-01
We propose two methods for solving an inverse source problem for time-harmonic acoustic waves. Based on the reciprocity gap principle a nonlinear equation is presented for the locations and intensities of the point sources that can be solved via Newton iterations. To provide an initial guess for this iteration we suggest a range test algorithm for approximating the source locations. We give a mathematical foundation for the range test and exhibit its feasibility in connection with the iteration method by some numerical examples
Definition of the form of coal spontaneous combustion source as the inverse problem of geoelectrics
Directory of Open Access Journals (Sweden)
Sirota Dmitry
2017-01-01
Full Text Available The paper reviews the method of determining the shape and size of the coal self-heating source on coal pit benches and in coal piles during mining of coal by the open method. The method is based on the regularity found in the 1970s of the previous century and related to the distribution of potential of the natural electrical field arising from the temperature in the vicinity of the center of self-heating. The problem is reduced to the solution of inverse ill-posed problem of mathematical physics. The study presents the developed algorithm of its solution and the results of numerical simulation.
An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation
Asiri, Sharefa M.; Zayane, Chadia; Laleg-Kirati, Taous-Meriem
2015-01-01
Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the algorithm is emphasized in noise-free and noisy cases and an insight on the impact of measurements’ size and location is provided.
An Adaptive Observer-Based Algorithm for Solving Inverse Source Problem for the Wave Equation
Asiri, Sharefa M.
2015-08-31
Observers are well known in control theory. Originally designed to estimate the hidden states of dynamical systems given some measurements, the observers scope has been recently extended to the estimation of some unknowns, for systems governed by partial differential equations. In this paper, observers are used to solve inverse source problem for a one-dimensional wave equation. An adaptive observer is designed to estimate the state and source components for a fully discretized system. The effectiveness of the algorithm is emphasized in noise-free and noisy cases and an insight on the impact of measurements’ size and location is provided.
Entekhabi, Mozhgan Nora; Isakov, Victor
2018-05-01
In this paper, we will study the increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain Ω with a sufficiently smooth boundary. Using the Fourier transform in the frequency domain, bounds for the Hankel functions and for scattering solutions in the complex plane, improving bounds for the analytic continuation, and the exact observability for the wave equation led us to our goals which are a sharp uniqueness and increasing stability estimate when the wave number interval is growing.
On an inverse source problem for enhanced oil recovery by wave motion maximization in reservoirs
Karve, Pranav M.
2014-12-28
© 2014, Springer International Publishing Switzerland. We discuss an optimization methodology for focusing wave energy to subterranean formations using strong motion actuators placed on the ground surface. The motivation stems from the desire to increase the mobility of otherwise entrapped oil. The goal is to arrive at the spatial and temporal description of surface sources that are capable of maximizing mobility in the target reservoir. The focusing problem is posed as an inverse source problem. The underlying wave propagation problems are abstracted in two spatial dimensions, and the semi-infinite extent of the physical domain is negotiated by a buffer of perfectly-matched-layers (PMLs) placed at the domain’s truncation boundary. We discuss two possible numerical implementations: Their utility for deciding the tempo-spatial characteristics of optimal wave sources is shown via numerical experiments. Overall, the simulations demonstrate the inverse source method’s ability to simultaneously optimize load locations and time signals leading to the maximization of energy delivery to a target formation.
Gross, Lutz; Altinay, Cihan; Fenwick, Joel; Smith, Troy
2014-05-01
The program package escript has been designed for solving mathematical modeling problems using python, see Gross et al. (2013). Its development and maintenance has been funded by the Australian Commonwealth to provide open source software infrastructure for the Australian Earth Science community (recent funding by the Australian Geophysical Observing System EIF (AGOS) and the AuScope Collaborative Research Infrastructure Scheme (CRIS)). The key concepts of escript are based on the terminology of spatial functions and partial differential equations (PDEs) - an approach providing abstraction from the underlying spatial discretization method (i.e. the finite element method (FEM)). This feature presents a programming environment to the user which is easy to use even for complex models. Due to the fact that implementations are independent from data structures simulations are easily portable across desktop computers and scalable compute clusters without modifications to the program code. escript has been successfully applied in a variety of applications including modeling mantel convection, melting processes, volcanic flow, earthquakes, faulting, multi-phase flow, block caving and mineralization (see Poulet et al. 2013). The recent escript release (see Gross et al. (2013)) provides an open framework for solving joint inversion problems for geophysical data sets (potential field, seismic and electro-magnetic). The strategy bases on the idea to formulate the inversion problem as an optimization problem with PDE constraints where the cost function is defined by the data defect and the regularization term for the rock properties, see Gross & Kemp (2013). This approach of first-optimize-then-discretize avoids the assemblage of the - in general- dense sensitivity matrix as used in conventional approaches where discrete programming techniques are applied to the discretized problem (first-discretize-then-optimize). In this paper we will discuss the mathematical framework for
Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten
2018-06-01
This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.
An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach
Asiri, Sharefa M.
2013-05-25
Observers are well known in the theory of dynamical systems. They are used to estimate the states of a system from some measurements. However, recently observers have also been developed to estimate some unknowns for systems governed by Partial differential equations. Our aim is to design an observer to solve inverse source problem for a one dimensional wave equation. Firstly, the problem is discretized in both space and time and then an adaptive observer based on partial field measurements (i.e measurements taken form the solution of the wave equation) is applied to estimate both the states and the source. We see the effectiveness of this observer in both noise-free and noisy cases. In each case, numerical simulations are provided to illustrate the effectiveness of this approach. Finally, we compare the performance of the observer approach with Tikhonov regularization approach.
Uncertainty principles for inverse source problems for electromagnetic and elastic waves
Griesmaier, Roland; Sylvester, John
2018-06-01
In isotropic homogeneous media, far fields of time-harmonic electromagnetic waves radiated by compactly supported volume currents, and elastic waves radiated by compactly supported body force densities can be modelled in very similar fashions. Both are projected restricted Fourier transforms of vector-valued source terms. In this work we generalize two types of uncertainty principles recently developed for far fields of scalar-valued time-harmonic waves in Griesmaier and Sylvester (2017 SIAM J. Appl. Math. 77 154–80) to this vector-valued setting. These uncertainty principles yield stability criteria and algorithms for splitting far fields radiated by collections of well-separated sources into the far fields radiated by individual source components, and for the restoration of missing data segments. We discuss proper regularization strategies for these inverse problems, provide stability estimates based on the new uncertainty principles, and comment on reconstruction schemes. A numerical example illustrates our theoretical findings.
International Nuclear Information System (INIS)
Wang, Wenyan; Han, Bo; Yamamoto, Masahiro
2013-01-01
We propose a new numerical method for reproducing kernel Hilbert space to solve an inverse source problem for a two-dimensional fractional diffusion equation, where we are required to determine an x-dependent function in a source term by data at the final time. The exact solution is represented in the form of a series and the approximation solution is obtained by truncating the series. Furthermore, a technique is proposed to improve some of the existing methods. We prove that the numerical method is convergent under an a priori assumption of the regularity of solutions. The method is simple to implement. Our numerical result shows that our method is effective and that it is robust against noise in L 2 -space in reconstructing a source function. (paper)
An inverse-source problem for maximization of pore-fluid oscillation within poroelastic formations
Jeong, C.; Kallivokas, L. F.
2016-01-01
This paper discusses a mathematical and numerical modeling approach for identification of an unknown optimal loading time signal of a wave source, atop the ground surface, that can maximize the relative wave motion of a single-phase pore fluid within fluid-saturated porous permeable (poroelastic) rock formations, surrounded by non-permeable semi-infinite elastic solid rock formations, in a one-dimensional setting. The motivation stems from a set of field observations, following seismic events and vibrational tests, suggesting that shaking an oil reservoir is likely to improve oil production rates. This maximization problem is cast into an inverse-source problem, seeking an optimal loading signal that minimizes an objective functional – the reciprocal of kinetic energy in terms of relative pore-fluid wave motion within target poroelastic layers. We use the finite element method to obtain the solution of the governing wave physics of a multi-layered system, where the wave equations for the target poroelastic layers and the elastic wave equation for the surrounding non-permeable layers are coupled with each other. We use a partial-differential-equation-constrained-optimization framework (a state-adjoint-control problem approach) to tackle the minimization problem. The numerical results show that the numerical optimizer recovers optimal loading signals, whose dominant frequencies correspond to amplification frequencies, which can also be obtained by a frequency sweep, leading to larger amplitudes of relative pore-fluid wave motion within the target hydrocarbon formation than other signals.
An inverse-source problem for maximization of pore-fluid oscillation within poroelastic formations
Jeong, C.
2016-07-04
This paper discusses a mathematical and numerical modeling approach for identification of an unknown optimal loading time signal of a wave source, atop the ground surface, that can maximize the relative wave motion of a single-phase pore fluid within fluid-saturated porous permeable (poroelastic) rock formations, surrounded by non-permeable semi-infinite elastic solid rock formations, in a one-dimensional setting. The motivation stems from a set of field observations, following seismic events and vibrational tests, suggesting that shaking an oil reservoir is likely to improve oil production rates. This maximization problem is cast into an inverse-source problem, seeking an optimal loading signal that minimizes an objective functional – the reciprocal of kinetic energy in terms of relative pore-fluid wave motion within target poroelastic layers. We use the finite element method to obtain the solution of the governing wave physics of a multi-layered system, where the wave equations for the target poroelastic layers and the elastic wave equation for the surrounding non-permeable layers are coupled with each other. We use a partial-differential-equation-constrained-optimization framework (a state-adjoint-control problem approach) to tackle the minimization problem. The numerical results show that the numerical optimizer recovers optimal loading signals, whose dominant frequencies correspond to amplification frequencies, which can also be obtained by a frequency sweep, leading to larger amplitudes of relative pore-fluid wave motion within the target hydrocarbon formation than other signals.
Inverse logarithmic potential problem
Cherednichenko, V G
1996-01-01
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
International Nuclear Information System (INIS)
Beauchard, K; Cannarsa, P; Yamamoto, M
2014-01-01
The approach to Lipschitz stability for uniformly parabolic equations introduced by Imanuvilov and Yamamoto in 1998 based on Carleman estimates, seems hard to apply to the case of Grushin-type operators of interest to this paper. Indeed, such estimates are still missing for parabolic operators degenerating in the interior of the space domain. Nevertheless, we are able to prove Lipschitz stability results for inverse source problems for such operators, with locally distributed measurements in an arbitrary space dimension. For this purpose, we follow a mixed strategy which combines the approach due to Lebeau and Robbiano, relying on Fourier decomposition and Carleman inequalities for heat equations with non-smooth coefficients (solved by the Fourier modes). As a corollary, we obtain a direct proof of the observability of multidimensional Grushin-type parabolic equations, with locally distributed observations—which is equivalent to null controllability with locally distributed controls. (paper)
Jiang, Daijun; Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro
2017-05-01
In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.
Directory of Open Access Journals (Sweden)
Shoubin Wang
2017-01-01
Full Text Available The compound variable inverse problem which comprises boundary temperature distribution and surface convective heat conduction coefficient of two-dimensional steady heat transfer system with inner heat source is studied in this paper applying the conjugate gradient method. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion results. This paper applies boundary element method to solve the temperature calculation of discrete points in forward problems. The factors of measuring error and the number of measuring points zero error which impact the measurement result are discussed and compared with L-MM method in inverse problems. Instance calculation and analysis prove that the method applied in this paper still has good effectiveness and accuracy even if measurement error exists and the boundary measurement points’ number is reduced. The comparison indicates that the influence of error on the inversion solution can be minimized effectively using this method.
Testing earthquake source inversion methodologies
Page, Morgan T.; Mai, Paul Martin; Schorlemmer, Danijel
2011-01-01
Source Inversion Validation Workshop; Palm Springs, California, 11-12 September 2010; Nowadays earthquake source inversions are routinely performed after large earthquakes and represent a key connection between recorded seismic and geodetic data
Inverse feasibility problems of the inverse maximum flow problems
Indian Academy of Sciences (India)
199–209. c Indian Academy of Sciences. Inverse feasibility problems of the inverse maximum flow problems. ADRIAN DEACONU. ∗ and ELEONOR CIUREA. Department of Mathematics and Computer Science, Faculty of Mathematics and Informatics, Transilvania University of Brasov, Brasov, Iuliu Maniu st. 50,. Romania.
Inverse problem in hydrogeology
Carrera, Jesús; Alcolea, Andrés; Medina, Agustín; Hidalgo, Juan; Slooten, Luit J.
2005-03-01
The state of the groundwater inverse problem is synthesized. Emphasis is placed on aquifer characterization, where modelers have to deal with conceptual model uncertainty (notably spatial and temporal variability), scale dependence, many types of unknown parameters (transmissivity, recharge, boundary conditions, etc.), nonlinearity, and often low sensitivity of state variables (typically heads and concentrations) to aquifer properties. Because of these difficulties, calibration cannot be separated from the modeling process, as it is sometimes done in other fields. Instead, it should be viewed as one step in the process of understanding aquifer behavior. In fact, it is shown that actual parameter estimation methods do not differ from each other in the essence, though they may differ in the computational details. It is argued that there is ample room for improvement in groundwater inversion: development of user-friendly codes, accommodation of variability through geostatistics, incorporation of geological information and different types of data (temperature, occurrence and concentration of isotopes, age, etc.), proper accounting of uncertainty, etc. Despite this, even with existing codes, automatic calibration facilitates enormously the task of modeling. Therefore, it is contended that its use should become standard practice. L'état du problème inverse des eaux souterraines est synthétisé. L'accent est placé sur la caractérisation de l'aquifère, où les modélisateurs doivent jouer avec l'incertitude des modèles conceptuels (notamment la variabilité spatiale et temporelle), les facteurs d'échelle, plusieurs inconnues sur différents paramètres (transmissivité, recharge, conditions aux limites, etc.), la non linéarité, et souvent la sensibilité de plusieurs variables d'état (charges hydrauliques, concentrations) des propriétés de l'aquifère. A cause de ces difficultés, le calibrage ne peut êtreséparé du processus de modélisation, comme c'est le
Inverse problems for Maxwell's equations
Romanov, V G
1994-01-01
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Point-source inversion techniques
Langston, Charles A.; Barker, Jeffrey S.; Pavlin, Gregory B.
1982-11-01
A variety of approaches for obtaining source parameters from waveform data using moment-tensor or dislocation point source models have been investigated and applied to long-period body and surface waves from several earthquakes. Generalized inversion techniques have been applied to data for long-period teleseismic body waves to obtain the orientation, time function and depth of the 1978 Thessaloniki, Greece, event, of the 1971 San Fernando event, and of several events associated with the 1963 induced seismicity sequence at Kariba, Africa. The generalized inversion technique and a systematic grid testing technique have also been used to place meaningful constraints on mechanisms determined from very sparse data sets; a single station with high-quality three-component waveform data is often sufficient to discriminate faulting type (e.g., strike-slip, etc.). Sparse data sets for several recent California earthquakes, for a small regional event associated with the Koyna, India, reservoir, and for several events at the Kariba reservoir have been investigated in this way. Although linearized inversion techniques using the moment-tensor model are often robust, even for sparse data sets, there are instances where the simplifying assumption of a single point source is inadequate to model the data successfully. Numerical experiments utilizing synthetic data and actual data for the 1971 San Fernando earthquake graphically demonstrate that severe problems may be encountered if source finiteness effects are ignored. These techniques are generally applicable to on-line processing of high-quality digital data, but source complexity and inadequacy of the assumed Green's functions are major problems which are yet to be fully addressed.
Statistical perspectives on inverse problems
DEFF Research Database (Denmark)
Andersen, Kim Emil
of the interior of an object from electrical boundary measurements. One part of this thesis concerns statistical approaches for solving, possibly non-linear, inverse problems. Thus inverse problems are recasted in a form suitable for statistical inference. In particular, a Bayesian approach for regularisation...... problem is given in terms of probability distributions. Posterior inference is obtained by Markov chain Monte Carlo methods and new, powerful simulation techniques based on e.g. coupled Markov chains and simulated tempering is developed to improve the computational efficiency of the overall simulation......Inverse problems arise in many scientific disciplines and pertain to situations where inference is to be made about a particular phenomenon from indirect measurements. A typical example, arising in diffusion tomography, is the inverse boundary value problem for non-invasive reconstruction...
The seismic reflection inverse problem
International Nuclear Information System (INIS)
Symes, W W
2009-01-01
The seismic reflection method seeks to extract maps of the Earth's sedimentary crust from transient near-surface recording of echoes, stimulated by explosions or other controlled sound sources positioned near the surface. Reasonably accurate models of seismic energy propagation take the form of hyperbolic systems of partial differential equations, in which the coefficients represent the spatial distribution of various mechanical characteristics of rock (density, stiffness, etc). Thus the fundamental problem of reflection seismology is an inverse problem in partial differential equations: to find the coefficients (or at least some of their properties) of a linear hyperbolic system, given the values of a family of solutions in some part of their domains. The exploration geophysics community has developed various methods for estimating the Earth's structure from seismic data and is also well aware of the inverse point of view. This article reviews mathematical developments in this subject over the last 25 years, to show how the mathematics has both illuminated innovations of practitioners and led to new directions in practice. Two themes naturally emerge: the importance of single scattering dominance and compensation for spectral incompleteness by spatial redundancy. (topical review)
Inverse problems for the Boussinesq system
International Nuclear Information System (INIS)
Fan, Jishan; Jiang, Yu; Nakamura, Gen
2009-01-01
We obtain two results on inverse problems for a 2D Boussinesq system. One is that we prove the Lipschitz stability for the inverse source problem of identifying a time-independent external force in the system with observation data in an arbitrary sub-domain over a time interval of the velocity and the data of velocity and temperature at a fixed positive time t 0 > 0 over the whole spatial domain. The other one is that we prove a conditional stability estimate for an inverse problem of identifying the two initial conditions with a single observation on a sub-domain
Size Estimates in Inverse Problems
Di Cristo, Michele
2014-01-01
Detection of inclusions or obstacles inside a body by boundary measurements is an inverse problems very useful in practical applications. When only finite numbers of measurements are available, we try to detect some information on the embedded
Parameter estimation and inverse problems
Aster, Richard C; Thurber, Clifford H
2005-01-01
Parameter Estimation and Inverse Problems primarily serves as a textbook for advanced undergraduate and introductory graduate courses. Class notes have been developed and reside on the World Wide Web for faciliting use and feedback by teaching colleagues. The authors'' treatment promotes an understanding of fundamental and practical issus associated with parameter fitting and inverse problems including basic theory of inverse problems, statistical issues, computational issues, and an understanding of how to analyze the success and limitations of solutions to these probles. The text is also a practical resource for general students and professional researchers, where techniques and concepts can be readily picked up on a chapter-by-chapter basis.Parameter Estimation and Inverse Problems is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who may not have an extensive mathematical background. It is accompanied by a Web site that...
DEFF Research Database (Denmark)
Karamehmedovic, Mirza; Kirkeby, Adrian; Knudsen, Kim
2018-01-01
setting: From measurements made at a finite set of frequencies we uniquely determine and reconstruct sources in a subspace spanned by finitely many Fourier-Bessel functions. Further, we obtain a constructive criterion for identifying a minimal set of measurement frequencies sufficient for reconstruction......, and under an additional, mild assumption, the reconstruction method is shown to be stable." Our analysis is based on a singular value decomposition of the source-to-measurement forward operators and the distribution of positive zeros of the Bessel functions of the first kind. The reconstruction method...
EDITORIAL: Inverse Problems in Engineering
West, Robert M.; Lesnic, Daniel
2007-01-01
Presented here are 11 noteworthy papers selected from the Fifth International Conference on Inverse Problems in Engineering: Theory and Practice held in Cambridge, UK during 11-15 July 2005. The papers have been peer-reviewed to the usual high standards of this journal and the contributions of reviewers are much appreciated. The conference featured a good balance of the fundamental mathematical concepts of inverse problems with a diverse range of important and interesting applications, which are represented here by the selected papers. Aspects of finite-element modelling and the performance of inverse algorithms are investigated by Autrique et al and Leduc et al. Statistical aspects are considered by Emery et al and Watzenig et al with regard to Bayesian parameter estimation and inversion using particle filters. Electrostatic applications are demonstrated by van Berkel and Lionheart and also Nakatani et al. Contributions to the applications of electrical techniques and specifically electrical tomographies are provided by Wakatsuki and Kagawa, Kim et al and Kortschak et al. Aspects of inversion in optical tomography are investigated by Wright et al and Douiri et al. The authors are representative of the worldwide interest in inverse problems relating to engineering applications and their efforts in producing these excellent papers will be appreciated by many readers of this journal.
Testing earthquake source inversion methodologies
Page, Morgan T.
2011-01-01
Source Inversion Validation Workshop; Palm Springs, California, 11-12 September 2010; Nowadays earthquake source inversions are routinely performed after large earthquakes and represent a key connection between recorded seismic and geodetic data and the complex rupture process at depth. The resulting earthquake source models quantify the spatiotemporal evolution of ruptures. They are also used to provide a rapid assessment of the severity of an earthquake and to estimate losses. However, because of uncertainties in the data, assumed fault geometry and velocity structure, and chosen rupture parameterization, it is not clear which features of these source models are robust. Improved understanding of the uncertainty and reliability of earthquake source inversions will allow the scientific community to use the robust features of kinematic inversions to more thoroughly investigate the complexity of the rupture process and to better constrain other earthquakerelated computations, such as ground motion simulations and static stress change calculations.
Size Estimates in Inverse Problems
Di Cristo, Michele
2014-01-06
Detection of inclusions or obstacles inside a body by boundary measurements is an inverse problems very useful in practical applications. When only finite numbers of measurements are available, we try to detect some information on the embedded object such as its size. In this talk we review some recent results on several inverse problems. The idea is to provide constructive upper and lower estimates of the area/volume of the unknown defect in terms of a quantity related to the work that can be expressed with the available boundary data.
Liu, Yikan
2015-01-01
In this paper, we establish a strong maximum principle for fractional diffusion equations with multiple Caputo derivatives in time, and investigate a related inverse problem of practical importance. Exploiting the solution properties and the involved multinomial Mittag-Leffler functions, we improve the weak maximum principle for the multi-term time-fractional diffusion equation to a stronger one, which is parallel to that for its single-term counterpart as expected. As a direct application, w...
Inverse problem of solar oscillations
International Nuclear Information System (INIS)
Sekii, T.; Shibahashi, H.
1987-01-01
The authors present some preliminary results of numerical simulation to infer the sound velocity distribution in the solar interior from the oscillation data of the Sun as the inverse problem. They analyze the acoustic potential itself by taking account of some factors other than the sound velocity, and infer the sound velocity distribution in the deep interior of the Sun
Inverse scattering problems with multi-frequencies
International Nuclear Information System (INIS)
Bao, Gang; Li, Peijun; Lin, Junshan; Triki, Faouzi
2015-01-01
This paper is concerned with computational approaches and mathematical analysis for solving inverse scattering problems in the frequency domain. The problems arise in a diverse set of scientific areas with significant industrial, medical, and military applications. In addition to nonlinearity, there are two common difficulties associated with the inverse problems: ill-posedness and limited resolution (diffraction limit). Due to the diffraction limit, for a given frequency, only a low spatial frequency part of the desired parameter can be observed from measurements in the far field. The main idea developed here is that if the reconstruction is restricted to only the observable part, then the inversion will become stable. The challenging task is how to design stable numerical methods for solving these inverse scattering problems inspired by the diffraction limit. Recently, novel recursive linearization based algorithms have been presented in an attempt to answer the above question. These methods require multi-frequency scattering data and proceed via a continuation procedure with respect to the frequency from low to high. The objective of this paper is to give a brief review of these methods, their error estimates, and the related mathematical analysis. More attention is paid to the inverse medium and inverse source problems. Numerical experiments are included to illustrate the effectiveness of these methods. (topical review)
Direct and inverse problems of infrared tomography
DEFF Research Database (Denmark)
Sizikov, Valery S.; Evseev, Vadim; Fateev, Alexander
2016-01-01
The problems of infrared tomography-direct (the modeling of measured functions) and inverse (the reconstruction of gaseous medium parameters)-are considered with a laboratory burner flame as an example of an application. The two measurement modes are used: active (ON) with an external IR source...
Inverse problem in nuclear physics
International Nuclear Information System (INIS)
Zakhariev, B.N.
1976-01-01
The method of reconstruction of interaction from the scattering data is formulated in the frame of the R-matrix theory in which the potential is determined by position of resonance Esub(lambda) and their reduced widths γ 2 lambda. In finite difference approximation for the Schroedinger equation this new approach allows to make the logics of the inverse problem IP more clear. A possibility of applications of IP formalism to various nuclear systems is discussed. (author)
Czech Academy of Sciences Publication Activity Database
Tichý, Ondřej; Šmídl, Václav; Hofman, Radek; Stohl, A.
2016-01-01
Roč. 9, č. 11 (2016), s. 4297-4311 ISSN 1991-959X R&D Projects: GA MŠk(CZ) 7F14287 Institutional support: RVO:67985556 Keywords : Linear inverse problem * Bayesian regularization * Source-term determination * Variational Bayes method Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 3.458, year: 2016 http://library.utia.cas.cz/separaty/2016/AS/tichy-0466029.pdf
Introduction to inverse problems for differential equations
Hasanov Hasanoğlu, Alemdar
2017-01-01
This book presents a systematic exposition of the main ideas and methods in treating inverse problems for PDEs arising in basic mathematical models, though it makes no claim to being exhaustive. Mathematical models of most physical phenomena are governed by initial and boundary value problems for PDEs, and inverse problems governed by these equations arise naturally in nearly all branches of science and engineering. The book’s content, especially in the Introduction and Part I, is self-contained and is intended to also be accessible for beginning graduate students, whose mathematical background includes only basic courses in advanced calculus, PDEs and functional analysis. Further, the book can be used as the backbone for a lecture course on inverse and ill-posed problems for partial differential equations. In turn, the second part of the book consists of six nearly-independent chapters. The choice of these chapters was motivated by the fact that the inverse coefficient and source problems considered here a...
Inverse problems in systems biology
International Nuclear Information System (INIS)
Engl, Heinz W; Lu, James; Müller, Stefan; Flamm, Christoph; Schuster, Peter; Kügler, Philipp
2009-01-01
Systems biology is a new discipline built upon the premise that an understanding of how cells and organisms carry out their functions cannot be gained by looking at cellular components in isolation. Instead, consideration of the interplay between the parts of systems is indispensable for analyzing, modeling, and predicting systems' behavior. Studying biological processes under this premise, systems biology combines experimental techniques and computational methods in order to construct predictive models. Both in building and utilizing models of biological systems, inverse problems arise at several occasions, for example, (i) when experimental time series and steady state data are used to construct biochemical reaction networks, (ii) when model parameters are identified that capture underlying mechanisms or (iii) when desired qualitative behavior such as bistability or limit cycle oscillations is engineered by proper choices of parameter combinations. In this paper we review principles of the modeling process in systems biology and illustrate the ill-posedness and regularization of parameter identification problems in that context. Furthermore, we discuss the methodology of qualitative inverse problems and demonstrate how sparsity enforcing regularization allows the determination of key reaction mechanisms underlying the qualitative behavior. (topical review)
Inverse problem in radionuclide transport
International Nuclear Information System (INIS)
Yu, C.
1988-01-01
The disposal of radioactive waste must comply with the performance objectives set forth in 10 CFR 61 for low-level waste (LLW) and 10 CFR 60 for high-level waste (HLW). To determine probable compliance, the proposed disposal system can be modeled to predict its performance. One of the difficulties encountered in such a study is modeling the migration of radionuclides through a complex geologic medium for the long term. Although many radionuclide transport models exist in the literature, the accuracy of the model prediction is highly dependent on the model parameters used. The problem of using known parameters in a radionuclide transport model to predict radionuclide concentrations is a direct problem (DP); whereas the reverse of DP, i.e., the parameter identification problem of determining model parameters from known radionuclide concentrations, is called the inverse problem (IP). In this study, a procedure to solve IP is tested, using the regression technique. Several nonlinear regression programs are examined, and the best one is recommended. 13 refs., 1 tab
Mai, P. M.; Schorlemmer, D.; Page, M.
2012-04-01
Earthquake source inversions image the spatio-temporal rupture evolution on one or more fault planes using seismic and/or geodetic data. Such studies are critically important for earthquake seismology in general, and for advancing seismic hazard analysis in particular, as they reveal earthquake source complexity and help (i) to investigate earthquake mechanics; (ii) to develop spontaneous dynamic rupture models; (iii) to build models for generating rupture realizations for ground-motion simulations. In applications (i - iii), the underlying finite-fault source models are regarded as "data" (input information), but their uncertainties are essentially unknown. After all, source models are obtained from solving an inherently ill-posed inverse problem to which many a priori assumptions and uncertain observations are applied. The Source Inversion Validation (SIV) project is a collaborative effort to better understand the variability between rupture models for a single earthquake (as manifested in the finite-source rupture model database) and to develop robust uncertainty quantification for earthquake source inversions. The SIV project highlights the need to develop a long-standing and rigorous testing platform to examine the current state-of-the-art in earthquake source inversion, and to develop and test novel source inversion approaches. We will review the current status of the SIV project, and report the findings and conclusions of the recent workshops. We will briefly discuss several source-inversion methods, how they treat uncertainties in data, and assess the posterior model uncertainty. Case studies include initial forward-modeling tests on Green's function calculations, and inversion results for synthetic data from spontaneous dynamic crack-like strike-slip earthquake on steeply dipping fault, embedded in a layered crustal velocity-density structure.
Inverse Problems and Uncertainty Quantification
Litvinenko, Alexander
2014-01-06
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) modelare strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. This is especially the case as together with a functional or spectral approach for the forward UQ there is no need for time- consuming and slowly convergent Monte Carlo sampling. The developed sampling- free non-linear Bayesian update is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisa- tion to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of different observation or measurement operators on the update.
Inverse Problems and Uncertainty Quantification
Litvinenko, Alexander; Matthies, Hermann G.
2014-01-01
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) modelare strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. This is especially the case as together with a functional or spectral approach for the forward UQ there is no need for time- consuming and slowly convergent Monte Carlo sampling. The developed sampling- free non-linear Bayesian update is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisa- tion to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of different observation or measurement operators on the update.
Inverse problems and uncertainty quantification
Litvinenko, Alexander
2013-12-18
In a Bayesian setting, inverse problems and uncertainty quantification (UQ)— the propagation of uncertainty through a computational (forward) model—are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. This is especially the case as together with a functional or spectral approach for the forward UQ there is no need for time- consuming and slowly convergent Monte Carlo sampling. The developed sampling- free non-linear Bayesian update is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisa- tion to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of different observation or measurement operators on the update.
Automatic differentiation in geophysical inverse problems
Sambridge, M.; Rickwood, P.; Rawlinson, N.; Sommacal, S.
2007-07-01
Automatic differentiation (AD) is the technique whereby output variables of a computer code evaluating any complicated function (e.g. the solution to a differential equation) can be differentiated with respect to the input variables. Often AD tools take the form of source to source translators and produce computer code without the need for deriving and hand coding of explicit mathematical formulae by the user. The power of AD lies in the fact that it combines the generality of finite difference techniques and the accuracy and efficiency of analytical derivatives, while at the same time eliminating `human' coding errors. It also provides the possibility of accurate, efficient derivative calculation from complex `forward' codes where no analytical derivatives are possible and finite difference techniques are too cumbersome. AD is already having a major impact in areas such as optimization, meteorology and oceanography. Similarly it has considerable potential for use in non-linear inverse problems in geophysics where linearization is desirable, or for sensitivity analysis of large numerical simulation codes, for example, wave propagation and geodynamic modelling. At present, however, AD tools appear to be little used in the geosciences. Here we report on experiments using a state of the art AD tool to perform source to source code translation in a range of geoscience problems. These include calculating derivatives for Gibbs free energy minimization, seismic receiver function inversion, and seismic ray tracing. Issues of accuracy and efficiency are discussed.
Directory of Open Access Journals (Sweden)
O. Tichý
2016-11-01
Full Text Available Estimation of pollutant releases into the atmosphere is an important problem in the environmental sciences. It is typically formalized as an inverse problem using a linear model that can explain observable quantities (e.g., concentrations or deposition values as a product of the source-receptor sensitivity (SRS matrix obtained from an atmospheric transport model multiplied by the unknown source-term vector. Since this problem is typically ill-posed, current state-of-the-art methods are based on regularization of the problem and solution of a formulated optimization problem. This procedure depends on manual settings of uncertainties that are often very poorly quantified, effectively making them tuning parameters. We formulate a probabilistic model, that has the same maximum likelihood solution as the conventional method using pre-specified uncertainties. Replacement of the maximum likelihood solution by full Bayesian estimation also allows estimation of all tuning parameters from the measurements. The estimation procedure is based on the variational Bayes approximation which is evaluated by an iterative algorithm. The resulting method is thus very similar to the conventional approach, but with the possibility to also estimate all tuning parameters from the observations. The proposed algorithm is tested and compared with the standard methods on data from the European Tracer Experiment (ETEX where advantages of the new method are demonstrated. A MATLAB implementation of the proposed algorithm is available for download.
Tichý, Ondřej; Šmídl, Václav; Hofman, Radek; Stohl, Andreas
2016-11-01
Estimation of pollutant releases into the atmosphere is an important problem in the environmental sciences. It is typically formalized as an inverse problem using a linear model that can explain observable quantities (e.g., concentrations or deposition values) as a product of the source-receptor sensitivity (SRS) matrix obtained from an atmospheric transport model multiplied by the unknown source-term vector. Since this problem is typically ill-posed, current state-of-the-art methods are based on regularization of the problem and solution of a formulated optimization problem. This procedure depends on manual settings of uncertainties that are often very poorly quantified, effectively making them tuning parameters. We formulate a probabilistic model, that has the same maximum likelihood solution as the conventional method using pre-specified uncertainties. Replacement of the maximum likelihood solution by full Bayesian estimation also allows estimation of all tuning parameters from the measurements. The estimation procedure is based on the variational Bayes approximation which is evaluated by an iterative algorithm. The resulting method is thus very similar to the conventional approach, but with the possibility to also estimate all tuning parameters from the observations. The proposed algorithm is tested and compared with the standard methods on data from the European Tracer Experiment (ETEX) where advantages of the new method are demonstrated. A MATLAB implementation of the proposed algorithm is available for download.
Source Estimation by Full Wave Form Inversion
Energy Technology Data Exchange (ETDEWEB)
Sjögreen, Björn [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Petersson, N. Anders [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
2013-08-07
Given time-dependent ground motion recordings at a number of receiver stations, we solve the inverse problem for estimating the parameters of the seismic source. The source is modeled as a point moment tensor source, characterized by its location, moment tensor components, the start time, and frequency parameter (rise time) of its source time function. In total, there are 11 unknown parameters. We use a non-linear conjugate gradient algorithm to minimize the full waveform misfit between observed and computed ground motions at the receiver stations. An important underlying assumption of the minimization problem is that the wave propagation is accurately described by the elastic wave equation in a heterogeneous isotropic material. We use a fourth order accurate finite difference method, developed in [12], to evolve the waves forwards in time. The adjoint wave equation corresponding to the discretized elastic wave equation is used to compute the gradient of the misfit, which is needed by the non-linear conjugated minimization algorithm. A new source point moment source discretization is derived that guarantees that the Hessian of the misfit is a continuous function of the source location. An efficient approach for calculating the Hessian is also presented. We show how the Hessian can be used to scale the problem to improve the convergence of the non-linear conjugated gradient algorithm. Numerical experiments are presented for estimating the source parameters from synthetic data in a layer over half-space problem (LOH.1), illustrating rapid convergence of the proposed approach.
An inverse optimal control problem in the electrical discharge ...
Indian Academy of Sciences (India)
Marin Gostimirovic
2018-05-10
May 10, 2018 ... Keywords. EDM process; discharge energy; heat source parameters; inverse problem; optimization. 1. Introduction .... ation, thermal modeling of the EDM process would become ..... simulation of die-sinking EDM. CIRP Ann.
On two-spectra inverse problems
Guliyev, Namig J.
2018-01-01
We consider a two-spectra inverse problem for the one-dimensional Schr\\"{o}dinger equation with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter and provide a complete solution of this problem.
Optimization for nonlinear inverse problem
International Nuclear Information System (INIS)
Boyadzhiev, G.; Brandmayr, E.; Pinat, T.; Panza, G.F.
2007-06-01
The nonlinear inversion of geophysical data in general does not yield a unique solution, but a single model, representing the investigated field, is preferred for an easy geological interpretation of the observations. The analyzed region is constituted by a number of sub-regions where the multi-valued nonlinear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the solution in each sub-region, many acceptable models are obtained for the entire region and this complicates the geological interpretation of geophysical investigations. In this paper are presented new methodologies, capable to select one model, among all acceptable ones, that satisfies different criteria of smoothness in the explored space of solutions. In this work we focus on the non-linear inversion of surface waves dispersion curves, which gives structural models of shear-wave velocity versus depth, but the basic concepts have a general validity. (author)
Approximation of Bayesian Inverse Problems for PDEs
Cotter, S. L.; Dashti, M.; Stuart, A. M.
2010-01-01
Inverse problems are often ill posed, with solutions that depend sensitively on data.n any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability. This paper is based on an approach to regularization, employing a Bayesian formulation of the problem, which leads to a notion of well posedness for inverse problems, at the level of probability measures. The stability which results from this well posedness may be used as t...
Optimization and inverse problems in electromagnetism
Wiak, Sławomir
2003-01-01
From 12 to 14 September 2002, the Academy of Humanities and Economics (AHE) hosted the workshop "Optimization and Inverse Problems in Electromagnetism". After this bi-annual event, a large number of papers were assembled and combined in this book. During the workshop recent developments and applications in optimization and inverse methodologies for electromagnetic fields were discussed. The contributions selected for the present volume cover a wide spectrum of inverse and optimal electromagnetic methodologies, ranging from theoretical to practical applications. A number of new optimal and inverse methodologies were proposed. There are contributions related to dedicated software. Optimization and Inverse Problems in Electromagnetism consists of three thematic chapters, covering: -General papers (survey of specific aspects of optimization and inverse problems in electromagnetism), -Methodologies, -Industrial Applications. The book can be useful to students of electrical and electronics engineering, computer sci...
Inverse radiative transfer problems in two-dimensional heterogeneous media
International Nuclear Information System (INIS)
Tito, Mariella Janette Berrocal
2001-01-01
The analysis of inverse problems in participating media where emission, absorption and scattering take place has several relevant applications in engineering and medicine. Some of the techniques developed for the solution of inverse problems have as a first step the solution of the direct problem. In this work the discrete ordinates method has been used for the solution of the linearized Boltzmann equation in two dimensional cartesian geometry. The Levenberg - Marquardt method has been used for the solution of the inverse problem of internal source and absorption and scattering coefficient estimation. (author)
BOOK REVIEW: Inverse Problems. Activities for Undergraduates
Yamamoto, Masahiro
2003-06-01
This book is a valuable introduction to inverse problems. In particular, from the educational point of view, the author addresses the questions of what constitutes an inverse problem and how and why we should study them. Such an approach has been eagerly awaited for a long time. Professor Groetsch, of the University of Cincinnati, is a world-renowned specialist in inverse problems, in particular the theory of regularization. Moreover, he has made a remarkable contribution to educational activities in the field of inverse problems, which was the subject of his previous book (Groetsch C W 1993 Inverse Problems in the Mathematical Sciences (Braunschweig: Vieweg)). For this reason, he is one of the most qualified to write an introductory book on inverse problems. Without question, inverse problems are important, necessary and appear in various aspects. So it is crucial to introduce students to exercises in inverse problems. However, there are not many introductory books which are directly accessible by students in the first two undergraduate years. As a consequence, students often encounter diverse concrete inverse problems before becoming aware of their general principles. The main purpose of this book is to present activities to allow first-year undergraduates to learn inverse theory. To my knowledge, this book is a rare attempt to do this and, in my opinion, a great success. The author emphasizes that it is very important to teach inverse theory in the early years. He writes; `If students consider only the direct problem, they are not looking at the problem from all sides .... The habit of always looking at problems from the direct point of view is intellectually limiting ...' (page 21). The book is very carefully organized so that teachers will be able to use it as a textbook. After an introduction in chapter 1, sucessive chapters deal with inverse problems in precalculus, calculus, differential equations and linear algebra. In order to let one gain some insight
3rd Annual Workshop on Inverse Problem
2015-01-01
This proceeding volume is based on papers presented on the Third Annual Workshop on Inverse Problems which was organized by the Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, and took place in May 2013 in Stockholm. The purpose of this workshop was to present new analytical developments and numerical techniques for solution of inverse problems for a wide range of applications in acoustics, electromagnetics, optical fibers, medical imaging, geophysics, etc. The contributions in this volume reflect these themes and will be beneficial to researchers who are working in the area of applied inverse problems.
Inverse problems in the Bayesian framework
International Nuclear Information System (INIS)
Calvetti, Daniela; Somersalo, Erkki; Kaipio, Jari P
2014-01-01
The history of Bayesian methods dates back to the original works of Reverend Thomas Bayes and Pierre-Simon Laplace: the former laid down some of the basic principles on inverse probability in his classic article ‘An essay towards solving a problem in the doctrine of chances’ that was read posthumously in the Royal Society in 1763. Laplace, on the other hand, in his ‘Memoirs on inverse probability’ of 1774 developed the idea of updating beliefs and wrote down the celebrated Bayes’ formula in the form we know today. Although not identified yet as a framework for investigating inverse problems, Laplace used the formalism very much in the spirit it is used today in the context of inverse problems, e.g., in his study of the distribution of comets. With the evolution of computational tools, Bayesian methods have become increasingly popular in all fields of human knowledge in which conclusions need to be drawn based on incomplete and noisy data. Needless to say, inverse problems, almost by definition, fall into this category. Systematic work for developing a Bayesian inverse problem framework can arguably be traced back to the 1980s, (the original first edition being published by Elsevier in 1987), although articles on Bayesian methodology applied to inverse problems, in particular in geophysics, had appeared much earlier. Today, as testified by the articles in this special issue, the Bayesian methodology as a framework for considering inverse problems has gained a lot of popularity, and it has integrated very successfully with many traditional inverse problems ideas and techniques, providing novel ways to interpret and implement traditional procedures in numerical analysis, computational statistics, signal analysis and data assimilation. The range of applications where the Bayesian framework has been fundamental goes from geophysics, engineering and imaging to astronomy, life sciences and economy, and continues to grow. There is no question that Bayesian
The ocean circulation inverse problem
National Research Council Canada - National Science Library
Wunsch, C
1996-01-01
.... This book addresses the problem of inferring the state of the ocean circulation, understanding it dynamically, and even forecasting it through a quantitative combination of theory and observation...
Direct Problems and Inverse Problems in Biometric Systems
Mihailescu Marius Iulian
2013-01-01
The article purpose is to describe the two sides of biometrics technologies, direct problems and inverse problems. The advance that we face today in field of Information Technology makes Information Security an inseparable part. The authentication has a huge role when we deal about security. The problems that can appear in implementing and developing biometrics systems is raising many problems, and one of the goal of this article is to focus on direct and inverse problems which is a new and c...
Inverse problems in linear transport theory
International Nuclear Information System (INIS)
Dressler, K.
1988-01-01
Inverse problems for a class of linear kinetic equations are investigated. The aim is to identify the scattering kernel of a transport equation (corresponding to the structure of a background medium) by observing the 'albedo' part of the solution operator for the corresponding direct initial boundary value problem. This means to get information on some integral operator in an integrodifferential equation through on overdetermined boundary value problem. We first derive a constructive method for solving direct halfspace problems and prove a new factorization theorem for the solutions. Using this result we investigate stationary inverse problems with respect to well posedness (e.g. reduce them to classical ill-posed problems, such as integral equations of first kind). In the time-dependent case we show that a quite general inverse problem is well posed and solve it constructively. (orig.)
An inverse problem for evolution inclusions
Ton, Bui An
2002-01-01
An inverse problem, the determination of the shape and a convective coefficient on a part of the boundary from partial measurements of the solution, is studied using 2-person optimal control techniques.
Multiparameter Optimization for Electromagnetic Inversion Problem
Directory of Open Access Journals (Sweden)
M. Elkattan
2017-10-01
Full Text Available Electromagnetic (EM methods have been extensively used in geophysical investigations such as mineral and hydrocarbon exploration as well as in geological mapping and structural studies. In this paper, we developed an inversion methodology for Electromagnetic data to determine physical parameters of a set of horizontal layers. We conducted Forward model using transmission line method. In the inversion part, we solved multi parameter optimization problem where, the parameters are conductivity, dielectric constant, and permeability of each layer. The optimization problem was solved by simulated annealing approach. The inversion methodology was tested using a set of models representing common geological formations.
Radiation Source Mapping with Bayesian Inverse Methods
Hykes, Joshua Michael
We present a method to map the spectral and spatial distributions of radioactive sources using a small number of detectors. Locating and identifying radioactive materials is important for border monitoring, accounting for special nuclear material in processing facilities, and in clean-up operations. Most methods to analyze these problems make restrictive assumptions about the distribution of the source. In contrast, the source-mapping method presented here allows an arbitrary three-dimensional distribution in space and a flexible group and gamma peak distribution in energy. To apply the method, the system's geometry and materials must be known. A probabilistic Bayesian approach is used to solve the resulting inverse problem (IP) since the system of equations is ill-posed. The probabilistic approach also provides estimates of the confidence in the final source map prediction. A set of adjoint flux, discrete ordinates solutions, obtained in this work by the Denovo code, are required to efficiently compute detector responses from a candidate source distribution. These adjoint fluxes are then used to form the linear model to map the state space to the response space. The test for the method is simultaneously locating a set of 137Cs and 60Co gamma sources in an empty room. This test problem is solved using synthetic measurements generated by a Monte Carlo (MCNP) model and using experimental measurements that we collected for this purpose. With the synthetic data, the predicted source distributions identified the locations of the sources to within tens of centimeters, in a room with an approximately four-by-four meter floor plan. Most of the predicted source intensities were within a factor of ten of their true value. The chi-square value of the predicted source was within a factor of five from the expected value based on the number of measurements employed. With a favorable uniform initial guess, the predicted source map was nearly identical to the true distribution
Full traveltime inversion in source domain
Liu, Lu
2017-06-01
This paper presents a new method of source-domain full traveltime inversion (FTI). The objective of this study is automatically building near-surface velocity using the early arrivals of seismic data. This method can generate the inverted velocity that can kinetically best match the reconstructed plane-wave source of early arrivals with true source in source domain. It does not require picking first arrivals for tomography, which is one of the most challenging aspects of ray-based tomographic inversion. Besides, this method does not need estimate the source wavelet, which is a necessity for receiver-domain wave-equation velocity inversion. Furthermore, we applied our method on one synthetic dataset; the results show our method could generate a reasonable background velocity even when shingling first arrivals exist and could provide a good initial velocity for the conventional full waveform inversion (FWI).
Full traveltime inversion in source domain
Liu, Lu; Guo, Bowen; Luo, Yi
2017-01-01
This paper presents a new method of source-domain full traveltime inversion (FTI). The objective of this study is automatically building near-surface velocity using the early arrivals of seismic data. This method can generate the inverted velocity
Solving inversion problems with neural networks
Kamgar-Parsi, Behzad; Gualtieri, J. A.
1990-01-01
A class of inverse problems in remote sensing can be characterized by Q = F(x), where F is a nonlinear and noninvertible (or hard to invert) operator, and the objective is to infer the unknowns, x, from the observed quantities, Q. Since the number of observations is usually greater than the number of unknowns, these problems are formulated as optimization problems, which can be solved by a variety of techniques. The feasibility of neural networks for solving such problems is presently investigated. As an example, the problem of finding the atmospheric ozone profile from measured ultraviolet radiances is studied.
Ensemble Kalman methods for inverse problems
International Nuclear Information System (INIS)
Iglesias, Marco A; Law, Kody J H; Stuart, Andrew M
2013-01-01
The ensemble Kalman filter (EnKF) was introduced by Evensen in 1994 (Evensen 1994 J. Geophys. Res. 99 10143–62) as a novel method for data assimilation: state estimation for noisily observed time-dependent problems. Since that time it has had enormous impact in many application domains because of its robustness and ease of implementation, and numerical evidence of its accuracy. In this paper we propose the application of an iterative ensemble Kalman method for the solution of a wide class of inverse problems. In this context we show that the estimate of the unknown function that we obtain with the ensemble Kalman method lies in a subspace A spanned by the initial ensemble. Hence the resulting error may be bounded above by the error found from the best approximation in this subspace. We provide numerical experiments which compare the error incurred by the ensemble Kalman method for inverse problems with the error of the best approximation in A, and with variants on traditional least-squares approaches, restricted to the subspace A. In so doing we demonstrate that the ensemble Kalman method for inverse problems provides a derivative-free optimization method with comparable accuracy to that achieved by traditional least-squares approaches. Furthermore, we also demonstrate that the accuracy is of the same order of magnitude as that achieved by the best approximation. Three examples are used to demonstrate these assertions: inversion of a compact linear operator; inversion of piezometric head to determine hydraulic conductivity in a Darcy model of groundwater flow; and inversion of Eulerian velocity measurements at positive times to determine the initial condition in an incompressible fluid. (paper)
General inverse problems for regular variation
DEFF Research Database (Denmark)
Damek, Ewa; Mikosch, Thomas Valentin; Rosinski, Jan
2014-01-01
Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed random object is caused by regular variation of components ...
Inverse acoustic problem of N homogeneous scatterers
DEFF Research Database (Denmark)
Berntsen, Svend
2002-01-01
The three-dimensional inverse acoustic medium problem of N homogeneous objects with known geometry and location is considered. It is proven that one scattering experiment is sufficient for the unique determination of the complex wavenumbers of the objects. The mapping from the scattered fields...
Modeling of uncertainties in statistical inverse problems
International Nuclear Information System (INIS)
Kaipio, Jari
2008-01-01
In all real world problems, the models that tie the measurements to the unknowns of interest, are at best only approximations for reality. While moderate modeling and approximation errors can be tolerated with stable problems, inverse problems are a notorious exception. Typical modeling errors include inaccurate geometry, unknown boundary and initial data, properties of noise and other disturbances, and simply the numerical approximations of the physical models. In principle, the Bayesian approach to inverse problems, in which all uncertainties are modeled as random variables, is capable of handling these uncertainties. Depending on the type of uncertainties, however, different strategies may be adopted. In this paper we give an overview of typical modeling errors and related strategies within the Bayesian framework.
Bayesian probability theory and inverse problems
International Nuclear Information System (INIS)
Kopec, S.
1994-01-01
Bayesian probability theory is applied to approximate solving of the inverse problems. In order to solve the moment problem with the noisy data, the entropic prior is used. The expressions for the solution and its error bounds are presented. When the noise level tends to zero, the Bayesian solution tends to the classic maximum entropy solution in the L 2 norm. The way of using spline prior is also shown. (author)
Direct and Inverse Problems in Statistical Wavefields
International Nuclear Information System (INIS)
Wolf, Emil
2002-01-01
In this report account is presented of research carried out during the period September 1, 1999-August 31, 2002 under the sponsorship of the Department of Energy, grant DE-FG02-90ER14119. The research covered several areas of modern optical physics, particularly propagation of partially coherent light and its interaction with deterministic and with random media, spectroscopy with partially coherent light, polarization properties of statistical wave fields, effects of moving diffusers on coherence and on the spectra of light transmitted and scattered by them, reciprocity inequalities involving spatial and angular correlations of partially coherent beams, spreading of partially coherent beams in-random media, inverse source problems, computed and diffraction tomography and partially coherent solitons. We have discovered a new phenomenon in an emerging field of physical optics, known as singular optics; specifically we found that the spectrum of light changes drastically in the neighborhood of points where the intensity has zero value and where, consequently, the phase becomes singular, We noted some potential applications of this phenomenon. The results of our investigations were reported in 39 publications. They are listed on pages 3 to 5. Summaries of these publications are given on pages 6-13. Scientists who have participated in this research are listed on page 14
Inverse and Ill-posed Problems Theory and Applications
Kabanikhin, S I
2011-01-01
The text demonstrates the methods for proving the existence (if et all) and finding of inverse and ill-posed problems solutions in linear algebra, integral and operator equations, integral geometry, spectral inverse problems, and inverse scattering problems. It is given comprehensive background material for linear ill-posed problems and for coefficient inverse problems for hyperbolic, parabolic, and elliptic equations. A lot of examples for inverse problems from physics, geophysics, biology, medicine, and other areas of application of mathematics are included.
The Earthquake‐Source Inversion Validation (SIV) Project
Mai, Paul Martin; Schorlemmer, Danijel; Page, Morgan; Ampuero, Jean‐Paul; Asano, Kimiyuki; Causse, Mathieu; Custodio, Susana; Fan, Wenyuan; Festa, Gaetano; Galis, Martin; Gallovic, Frantisek; Imperatori, Walter; Kä ser, Martin; Malytskyy, Dmytro; Okuwaki, Ryo; Pollitz, Fred; Passone, Luca; Razafindrakoto, Hoby; Sekiguchi, Haruko; Song, Seok Goo; Somala, Surendra N.; Thingbaijam, Kiran Kumar; Twardzik, Cedric; van Driel, Martin; Vyas, Jagdish Chandra; Wang, Rongjiang; Yagi, Yuji; Zielke, Olaf
2016-01-01
Finite-fault earthquake source inversions infer the (time-dependent) displacement on the rupture surface from geophysical data. The resulting earthquake source models document the complexity of the rupture process. However, multiple source models for the same earthquake, obtained by different research teams, often exhibit remarkable dissimilarities. To address the uncertainties in earthquake-source inversion methods and to understand strengths and weaknesses of the various approaches used, the Source Inversion Validation (SIV) project conducts a set of forward-modeling exercises and inversion benchmarks. In this article, we describe the SIV strategy, the initial benchmarks, and current SIV results. Furthermore, we apply statistical tools for quantitative waveform comparison and for investigating source-model (dis)similarities that enable us to rank the solutions, and to identify particularly promising source inversion approaches. All SIV exercises (with related data and descriptions) and statistical comparison tools are available via an online collaboration platform, and we encourage source modelers to use the SIV benchmarks for developing and testing new methods. We envision that the SIV efforts will lead to new developments for tackling the earthquake-source imaging problem.
The Earthquake‐Source Inversion Validation (SIV) Project
Mai, Paul Martin
2016-04-27
Finite-fault earthquake source inversions infer the (time-dependent) displacement on the rupture surface from geophysical data. The resulting earthquake source models document the complexity of the rupture process. However, multiple source models for the same earthquake, obtained by different research teams, often exhibit remarkable dissimilarities. To address the uncertainties in earthquake-source inversion methods and to understand strengths and weaknesses of the various approaches used, the Source Inversion Validation (SIV) project conducts a set of forward-modeling exercises and inversion benchmarks. In this article, we describe the SIV strategy, the initial benchmarks, and current SIV results. Furthermore, we apply statistical tools for quantitative waveform comparison and for investigating source-model (dis)similarities that enable us to rank the solutions, and to identify particularly promising source inversion approaches. All SIV exercises (with related data and descriptions) and statistical comparison tools are available via an online collaboration platform, and we encourage source modelers to use the SIV benchmarks for developing and testing new methods. We envision that the SIV efforts will lead to new developments for tackling the earthquake-source imaging problem.
The Neuroelectromagnetic Inverse Problem and the Zero Dipole Localization Error
Directory of Open Access Journals (Sweden)
Rolando Grave de Peralta
2009-01-01
Full Text Available A tomography of neural sources could be constructed from EEG/MEG recordings once the neuroelectromagnetic inverse problem (NIP is solved. Unfortunately the NIP lacks a unique solution and therefore additional constraints are needed to achieve uniqueness. Researchers are then confronted with the dilemma of choosing one solution on the basis of the advantages publicized by their authors. This study aims to help researchers to better guide their choices by clarifying what is hidden behind inverse solutions oversold by their apparently optimal properties to localize single sources. Here, we introduce an inverse solution (ANA attaining perfect localization of single sources to illustrate how spurious sources emerge and destroy the reconstruction of simultaneously active sources. Although ANA is probably the simplest and robust alternative for data generated by a single dominant source plus noise, the main contribution of this manuscript is to show that zero localization error of single sources is a trivial and largely uninformative property unable to predict the performance of an inverse solution in presence of simultaneously active sources. We recommend as the most logical strategy for solving the NIP the incorporation of sound additional a priori information about neural generators that supplements the information contained in the data.
Analog fault diagnosis by inverse problem technique
Ahmed, Rania F.
2011-12-01
A novel algorithm for detecting soft faults in linear analog circuits based on the inverse problem concept is proposed. The proposed approach utilizes optimization techniques with the aid of sensitivity analysis. The main contribution of this work is to apply the inverse problem technique to estimate the actual parameter values of the tested circuit and so, to detect and diagnose single fault in analog circuits. The validation of the algorithm is illustrated through applying it to Sallen-Key second order band pass filter and the results show that the detecting percentage efficiency was 100% and also, the maximum error percentage of estimating the parameter values is 0.7%. This technique can be applied to any other linear circuit and it also can be extended to be applied to non-linear circuits. © 2011 IEEE.
Moebius inverse problem for distorted black holes
International Nuclear Information System (INIS)
Rosu, H.
1993-01-01
Hawking ''thermal'' radiation could be a means to detect black holes of micron sizes, which may be hovering through the universe. We consider these micro-black holes to be distorted by the presence of some distribution of matter representing a convolution factor for their Hawking radiation. One may hope to determine from their Hawking signals the temperature distribution of their material shells by the inverse black body problem. In 1990, Nan-xian Chen has used a so-called modified Moebius transform to solve the inverse black body problem. We discuss and apply this technique to Hawking radiation. Some comments on supersymmetric applications of Moebius function and transform are also added. (author). 22 refs
Regularized inversion of controlled source and earthquake data
International Nuclear Information System (INIS)
Ramachandran, Kumar
2012-01-01
Estimation of the seismic velocity structure of the Earth's crust and upper mantle from travel-time data has advanced greatly in recent years. Forward modelling trial-and-error methods have been superseded by tomographic methods which allow more objective analysis of large two-dimensional and three-dimensional refraction and/or reflection data sets. The fundamental purpose of travel-time tomography is to determine the velocity structure of a medium by analysing the time it takes for a wave generated at a source point within the medium to arrive at a distribution of receiver points. Tomographic inversion of first-arrival travel-time data is a nonlinear problem since both the velocity of the medium and ray paths in the medium are unknown. The solution for such a problem is typically obtained by repeated application of linearized inversion. Regularization of the nonlinear problem reduces the ill posedness inherent in the tomographic inversion due to the under-determined nature of the problem and the inconsistencies in the observed data. This paper discusses the theory of regularized inversion for joint inversion of controlled source and earthquake data, and results from synthetic data testing and application to real data. The results obtained from tomographic inversion of synthetic data and real data from the northern Cascadia subduction zone show that the velocity model and hypocentral parameters can be efficiently estimated using this approach. (paper)
Formal solutions of inverse scattering problems. III
International Nuclear Information System (INIS)
Prosser, R.T.
1980-01-01
The formal solutions of certain three-dimensional inverse scattering problems presented in papers I and II of this series [J. Math. Phys. 10, 1819 (1969); 17 1175 (1976)] are obtained here as fixed points of a certain nonlinear mapping acting on a suitable Banach space of integral kernels. When the scattering data are sufficiently restricted, this mapping is shown to be a contraction, thereby establishing the existence, uniqueness, and continuous dependence on the data of these formal solutions
Inverse problem of radiofrequency sounding of ionosphere
Velichko, E. N.; Yu. Grishentsev, A.; Korobeynikov, A. G.
2016-01-01
An algorithm for the solution of the inverse problem of vertical ionosphere sounding and a mathematical model of noise filtering are presented. An automated system for processing and analysis of spectrograms of vertical ionosphere sounding based on our algorithm is described. It is shown that the algorithm we suggest has a rather high efficiency. This is supported by the data obtained at the ionospheric stations of the so-called “AIS-M” type.
An inverse problem in a parabolic equation
Directory of Open Access Journals (Sweden)
Zhilin Li
1998-11-01
Full Text Available In this paper, an inverse problem in a parabolic equation is studied. An unknown function in the equation is related to two integral equations in terms of heat kernel. One of the integral equations is well-posed while another is ill-posed. A regularization approach for constructing an approximate solution to the ill-posed integral equation is proposed. Theoretical analysis and numerical experiment are provided to support the method.
Differential equations inverse and direct problems
Favini, Angelo
2006-01-01
DEGENERATE FIRST ORDER IDENTIFICATION PROBLEMS IN BANACH SPACES A NONISOTHERMAL DYNAMICAL GINZBURG-LANDAU MODEL OF SUPERCONDUCTIVITY. EXISTENCE AND UNIQUENESS THEOREMSSOME GLOBAL IN TIME RESULTS FOR INTEGRODIFFERENTIAL PARABOLIC INVERSE PROBLEMSFOURTH ORDER ORDINARY DIFFERENTIAL OPERATORS WITH GENERAL WENTZELL BOUNDARY CONDITIONSTUDY OF ELLIPTIC DIFFERENTIAL EQUATIONS IN UMD SPACESDEGENERATE INTEGRODIFFERENTIAL EQUATIONS OF PARABOLIC TYPE EXPONENTIAL ATTRACTORS FOR SEMICONDUCTOR EQUATIONSCONVERGENCE TO STATIONARY STATES OF SOLUTIONS TO THE SEMILINEAR EQUATION OF VISCOELASTICITY ASYMPTOTIC BEHA
Inverse problems in classical and quantum physics
International Nuclear Information System (INIS)
Almasy, A.A.
2007-01-01
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A
Inverse problems in classical and quantum physics
Energy Technology Data Exchange (ETDEWEB)
Almasy, A.A.
2007-06-29
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A
The Earthquake‐Source Inversion Validation (SIV) Project
Mai, P. Martin; Schorlemmer, Danijel; Page, Morgan T.; Ampuero, Jean-Paul; Asano, Kimiyuki; Causse, Mathieu; Custodio, Susana; Fan, Wenyuan; Festa, Gaetano; Galis, Martin; Gallovic, Frantisek; Imperatori, Walter; Käser, Martin; Malytskyy, Dmytro; Okuwaki, Ryo; Pollitz, Fred; Passone, Luca; Razafindrakoto, Hoby N. T.; Sekiguchi, Haruko; Song, Seok Goo; Somala, Surendra N.; Thingbaijam, Kiran K. S.; Twardzik, Cedric; van Driel, Martin; Vyas, Jagdish C.; Wang, Rongjiang; Yagi, Yuji; Zielke, Olaf
2016-01-01
Finite‐fault earthquake source inversions infer the (time‐dependent) displacement on the rupture surface from geophysical data. The resulting earthquake source models document the complexity of the rupture process. However, multiple source models for the same earthquake, obtained by different research teams, often exhibit remarkable dissimilarities. To address the uncertainties in earthquake‐source inversion methods and to understand strengths and weaknesses of the various approaches used, the Source Inversion Validation (SIV) project conducts a set of forward‐modeling exercises and inversion benchmarks. In this article, we describe the SIV strategy, the initial benchmarks, and current SIV results. Furthermore, we apply statistical tools for quantitative waveform comparison and for investigating source‐model (dis)similarities that enable us to rank the solutions, and to identify particularly promising source inversion approaches. All SIV exercises (with related data and descriptions) and statistical comparison tools are available via an online collaboration platform, and we encourage source modelers to use the SIV benchmarks for developing and testing new methods. We envision that the SIV efforts will lead to new developments for tackling the earthquake‐source imaging problem.
An Entropic Estimator for Linear Inverse Problems
Directory of Open Access Journals (Sweden)
Amos Golan
2012-05-01
Full Text Available In this paper we examine an Information-Theoretic method for solving noisy linear inverse estimation problems which encompasses under a single framework a whole class of estimation methods. Under this framework, the prior information about the unknown parameters (when such information exists, and constraints on the parameters can be incorporated in the statement of the problem. The method builds on the basics of the maximum entropy principle and consists of transforming the original problem into an estimation of a probability density on an appropriate space naturally associated with the statement of the problem. This estimation method is generic in the sense that it provides a framework for analyzing non-normal models, it is easy to implement and is suitable for all types of inverse problems such as small and or ill-conditioned, noisy data. First order approximation, large sample properties and convergence in distribution are developed as well. Analytical examples, statistics for model comparisons and evaluations, that are inherent to this method, are discussed and complemented with explicit examples.
Point sources and multipoles in inverse scattering theory
Potthast, Roland
2001-01-01
Over the last twenty years, the growing availability of computing power has had an enormous impact on the classical fields of direct and inverse scattering. The study of inverse scattering, in particular, has developed rapidly with the ability to perform computational simulations of scattering processes and led to remarkable advances in a range of applications, from medical imaging and radar to remote sensing and seismic exploration. Point Sources and Multipoles in Inverse Scattering Theory provides a survey of recent developments in inverse acoustic and electromagnetic scattering theory. Focusing on methods developed over the last six years by Colton, Kirsch, and the author, this treatment uses point sources combined with several far-reaching techniques to obtain qualitative reconstruction methods. The author addresses questions of uniqueness, stability, and reconstructions for both two-and three-dimensional problems.With interest in extracting information about an object through scattered waves at an all-ti...
The Earthquake Source Inversion Validation (SIV) - Project: Summary, Status, Outlook
Mai, P. M.
2017-12-01
Finite-fault earthquake source inversions infer the (time-dependent) displacement on the rupture surface from geophysical data. The resulting earthquake source models document the complexity of the rupture process. However, this kinematic source inversion is ill-posed and returns non-unique solutions, as seen for instance in multiple source models for the same earthquake, obtained by different research teams, that often exhibit remarkable dissimilarities. To address the uncertainties in earthquake-source inversions and to understand strengths and weaknesses of various methods, the Source Inversion Validation (SIV) project developed a set of forward-modeling exercises and inversion benchmarks. Several research teams then use these validation exercises to test their codes and methods, but also to develop and benchmark new approaches. In this presentation I will summarize the SIV strategy, the existing benchmark exercises and corresponding results. Using various waveform-misfit criteria and newly developed statistical comparison tools to quantify source-model (dis)similarities, the SIV platforms is able to rank solutions and identify particularly promising source inversion approaches. Existing SIV exercises (with related data and descriptions) and all computational tools remain available via the open online collaboration platform; additional exercises and benchmark tests will be uploaded once they are fully developed. I encourage source modelers to use the SIV benchmarks for developing and testing new methods. The SIV efforts have already led to several promising new techniques for tackling the earthquake-source imaging problem. I expect that future SIV benchmarks will provide further innovations and insights into earthquake source kinematics that will ultimately help to better understand the dynamics of the rupture process.
Solving of L0 norm constrained EEG inverse problem.
Xu, Peng; Lei, Xu; Hu, Xiao; Yao, Dezhong
2009-01-01
l(0) norm is an effective constraint used to solve EEG inverse problem for a sparse solution. However, due to the discontinuous and un-differentiable properties, it is an open issue to solve the l(0) norm constrained problem, which is usually instead solved by using some alternative functions like l(1) norm to approximate l(0) norm. In this paper, a continuous and differentiable function having the same form as the transfer function of Butterworth low-pass filter is introduced to approximate l(0) norm constraint involved in EEG inverse problem. The new approximation based approach was compared with l(1) norm and LORETA solutions on a realistic head model using simulated sources. The preliminary results show that this alternative approximation to l(0) norm is promising for the estimation of EEG sources with sparse distribution.
Eigenvectors phase correction in inverse modal problem
Qiao, Guandong; Rahmatalla, Salam
2017-12-01
The solution of the inverse modal problem for the spatial parameters of mechanical and structural systems is heavily dependent on the quality of the modal parameters obtained from the experiments. While experimental and environmental noises will always exist during modal testing, the resulting modal parameters are expected to be corrupted with different levels of noise. A novel methodology is presented in this work to mitigate the errors in the eigenvectors when solving the inverse modal problem for the spatial parameters. The phases of the eigenvector component were utilized as design variables within an optimization problem that minimizes the difference between the calculated and experimental transfer functions. The equation of motion in terms of the modal and spatial parameters was used as a constraint in the optimization problem. Constraints that reserve the positive and semi-positive definiteness and the inter-connectivity of the spatial matrices were implemented using semi-definite programming. Numerical examples utilizing noisy eigenvectors with augmented Gaussian white noise of 1%, 5%, and 10% were used to demonstrate the efficacy of the proposed method. The results showed that the proposed method is superior when compared with a known method in the literature.
Inverse scattering problem in turbulent magnetic fluctuations
Directory of Open Access Journals (Sweden)
R. A. Treumann
2016-08-01
Full Text Available We apply a particular form of the inverse scattering theory to turbulent magnetic fluctuations in a plasma. In the present note we develop the theory, formulate the magnetic fluctuation problem in terms of its electrodynamic turbulent response function, and reduce it to the solution of a special form of the famous Gelfand–Levitan–Marchenko equation of quantum mechanical scattering theory. The last of these applies to transmission and reflection in an active medium. The theory of turbulent magnetic fluctuations does not refer to such quantities. It requires a somewhat different formulation. We reduce the theory to the measurement of the low-frequency electromagnetic fluctuation spectrum, which is not the turbulent spectral energy density. The inverse theory in this form enables obtaining information about the turbulent response function of the medium. The dynamic causes of the electromagnetic fluctuations are implicit to it. Thus, it is of vital interest in low-frequency magnetic turbulence. The theory is developed until presentation of the equations in applicable form to observations of turbulent electromagnetic fluctuations as input from measurements. Solution of the final integral equation should be done by standard numerical methods based on iteration. We point to the possibility of treating power law fluctuation spectra as an example. Formulation of the problem to include observations of spectral power densities in turbulence is not attempted. This leads to severe mathematical problems and requires a reformulation of inverse scattering theory. One particular aspect of the present inverse theory of turbulent fluctuations is that its structure naturally leads to spatial information which is obtained from the temporal information that is inherent to the observation of time series. The Taylor assumption is not needed here. This is a consequence of Maxwell's equations, which couple space and time evolution. The inversion procedure takes
ITOUGH2: Solving TOUGH inverse problems
Energy Technology Data Exchange (ETDEWEB)
Finsterle, S.; Pruess, K. [Lawrence Berkeley Laboratory, CA (United States)
1995-03-01
ITOUGH2 is a program that provides inverse modeling capabilities for the TOUGH2 code. While the main purpose of ITOUGH2 is to estimate two-phase hydraulic properties of calibrating a TOUGH2 model to laboratory or field data, the information obtained by evaluating parameter sensitivities can also be used to optimize the design of an experiment, and to analyze the uncertainty of model predictions. ITOUGH2 has been applied to a number of laboratory and field experiments on different scales. Three examples are discussed in this paper, demonstrating the code`s capability to support test design, data analysis, and model predictions for a variety of TOUGH problems.
Bilinear Inverse Problems: Theory, Algorithms, and Applications
Ling, Shuyang
We will discuss how several important real-world signal processing problems, such as self-calibration and blind deconvolution, can be modeled as bilinear inverse problems and solved by convex and nonconvex optimization approaches. In Chapter 2, we bring together three seemingly unrelated concepts, self-calibration, compressive sensing and biconvex optimization. We show how several self-calibration problems can be treated efficiently within the framework of biconvex compressive sensing via a new method called SparseLift. More specifically, we consider a linear system of equations y = DAx, where the diagonal matrix D (which models the calibration error) is unknown and x is an unknown sparse signal. By "lifting" this biconvex inverse problem and exploiting sparsity in this model, we derive explicit theoretical guarantees under which both x and D can be recovered exactly, robustly, and numerically efficiently. In Chapter 3, we study the question of the joint blind deconvolution and blind demixing, i.e., extracting a sequence of functions [special characters omitted] from observing only the sum of their convolutions [special characters omitted]. In particular, for the special case s = 1, it becomes the well-known blind deconvolution problem. We present a non-convex algorithm which guarantees exact recovery under conditions that are competitive with convex optimization methods, with the additional advantage of being computationally much more efficient. We discuss several applications of the proposed framework in image processing and wireless communications in connection with the Internet-of-Things. In Chapter 4, we consider three different self-calibration models of practical relevance. We show how their corresponding bilinear inverse problems can be solved by both the simple linear least squares approach and the SVD-based approach. As a consequence, the proposed algorithms are numerically extremely efficient, thus allowing for real-time deployment. Explicit theoretical
Data quality for the inverse lsing problem
International Nuclear Information System (INIS)
Decelle, Aurélien; Ricci-Tersenghi, Federico; Zhang, Pan
2016-01-01
There are many methods proposed for inferring parameters of the Ising model from given data, that is a set of configurations generated according to the model itself. However little attention has been paid until now to the data, e.g. how the data is generated, whether the inference error using one set of data could be smaller than using another set of data, etc. In this paper we discuss the data quality problem in the inverse Ising problem, using as a benchmark the kinetic Ising model. We quantify the quality of data using effective rank of the correlation matrix, and show that data gathered in a out-of-equilibrium regime has a better quality than data gathered in equilibrium for coupling reconstruction. We also propose a matrix-perturbation based method for tuning the quality of given data and for removing bad-quality (i.e. redundant) configurations from data. (paper)
Inverse problems for partial differential equations
Isakov, Victor
2017-01-01
This third edition expands upon the earlier edition by adding nearly 40 pages of new material reflecting the analytical and numerical progress in inverse problems in last 10 years. As in the second edition, the emphasis is on new ideas and methods rather than technical improvements. These new ideas include use of the stationary phase method in the two-dimensional elliptic problems and of multi frequencies\\temporal data to improve stability and numerical resolution. There are also numerous corrections and improvements of the exposition throughout. This book is intended for mathematicians working with partial differential equations and their applications, physicists, geophysicists, and financial, electrical, and mechanical engineers involved with nondestructive evaluation, seismic exploration, remote sensing, and various kinds of tomography. Review of the second edition: "The first edition of this excellent book appeared in 1998 and became a standard reference for everyone interested in analysis and numerics of...
Microlocal analysis of a seismic linearized inverse problem
Stolk, C.C.
1999-01-01
The seismic inverse problem is to determine the wavespeed c x in the interior of a medium from measurements at the boundary In this paper we analyze the linearized inverse problem in general acoustic media The problem is to nd a left inverse of the linearized forward map F or equivalently to nd the
Mesoscale inversion of carbon sources and sinks
International Nuclear Information System (INIS)
Lauvaux, T.
2008-01-01
Inverse methods at large scales are used to infer the spatial variability of carbon sources and sinks over the continents but their uncertainties remain large. Atmospheric concentrations integrate the surface flux variability but atmospheric transport models at low resolution are not able to simulate properly the local atmospheric dynamics at the measurement sites. However, the inverse estimates are more representative of the large spatial heterogeneity of the ecosystems compared to direct flux measurements. Top-down and bottom-up methods that aim at quantifying the carbon exchanges between the surface and the atmosphere correspond to different scales and are not easily comparable. During this phD, a mesoscale inverse system was developed to correct carbon fluxes at 8 km resolution. The high resolution transport model MesoNH was used to simulate accurately the variability of the atmospheric concentrations, which allowed us to reduce the uncertainty of the retrieved fluxes. All the measurements used here were observed during the intensive regional campaign CERES of May and June 2005, during which several instrumented towers measured CO 2 concentrations and fluxes in the South West of France. Airborne measurements allowed us to observe concentrations at high altitude but also CO 2 surface fluxes over large parts of the domain. First, the capacity of the inverse system to correct the CO 2 fluxes was estimated using pseudo-data experiments. The largest fraction of the concentration variability was attributed to regional surface fluxes over an area of about 300 km around the site locations depending on the meteorological conditions. Second, an ensemble of simulations allowed us to define the spatial and temporal structures of the transport errors. Finally, the inverse fluxes at 8 km resolution were compared to direct flux measurements. The inverse system has been validated in space and time and showed an improvement of the first guess fluxes from a vegetation model
A tutorial on inverse problems for anomalous diffusion processes
International Nuclear Information System (INIS)
Jin, Bangti; Rundell, William
2015-01-01
Over the last two decades, anomalous diffusion processes in which the mean squares variance grows slower or faster than that in a Gaussian process have found many applications. At a macroscopic level, these processes are adequately described by fractional differential equations, which involves fractional derivatives in time or/and space. The fractional derivatives describe either history mechanism or long range interactions of particle motions at a microscopic level. The new physics can change dramatically the behavior of the forward problems. For example, the solution operator of the time fractional diffusion diffusion equation has only limited smoothing property, whereas the solution for the space fractional diffusion equation may contain weak singularity. Naturally one expects that the new physics will impact related inverse problems in terms of uniqueness, stability, and degree of ill-posedness. The last aspect is especially important from a practical point of view, i.e., stably reconstructing the quantities of interest. In this paper, we employ a formal analytic and numerical way, especially the two-parameter Mittag-Leffler function and singular value decomposition, to examine the degree of ill-posedness of several ‘classical’ inverse problems for fractional differential equations involving a Djrbashian–Caputo fractional derivative in either time or space, which represent the fractional analogues of that for classical integral order differential equations. We discuss four inverse problems, i.e., backward fractional diffusion, sideways problem, inverse source problem and inverse potential problem for time fractional diffusion, and inverse Sturm–Liouville problem, Cauchy problem, backward fractional diffusion and sideways problem for space fractional diffusion. It is found that contrary to the wide belief, the influence of anomalous diffusion on the degree of ill-posedness is not definitive: it can either significantly improve or worsen the conditioning
Strategies for source space limitation in tomographic inverse procedures
International Nuclear Information System (INIS)
George, J.S.; Lewis, P.S.; Schlitt, H.A.; Kaplan, L.; Gorodnitsky, I.; Wood, C.C.
1994-01-01
The use of magnetic recordings for localization of neural activity requires the solution of an ill-posed inverse problem: i.e. the determination of the spatial configuration, orientation, and timecourse of the currents that give rise to a particular observed field distribution. In its general form, this inverse problem has no unique solution; due to superposition and the existence of silent source configurations, a particular magnetic field distribution at the head surface could be produced by any number of possible source configurations. However, by making assumptions concerning the number and properties of neural sources, it is possible to use numerical minimization techniques to determine the source model parameters that best account for the experimental observations while satisfying numerical or physical criteria. In this paper the authors describe progress on the development and validation of inverse procedures that produce distributed estimates of neuronal currents. The goal is to produce a temporal sequence of 3-D tomographic reconstructions of the spatial patterns of neural activation. Such approaches have a number of advantages, in principle. Because they do not require estimates of model order and parameter values (beyond specification of the source space), they minimize the influence of investigator decisions and are suitable for automated analyses. These techniques also allow localization of sources that are not point-like; experimental studies of cognitive processes and of spontaneous brain activity are likely to require distributed source models
The inverse conductivity problem with limited data and applications
International Nuclear Information System (INIS)
Isakov, Victor
2007-01-01
This paper describes recent uniqueness results in inverse problems for semiconductor devices and in the inverse conductivity problem. We remind basic inverse probelsm in semiconductor theory and outline use of an adjoint equation and a proof of uniqueness of piecewise constant doping profile. For the inverse conductivity problem we give a first uniqueness proof when the Dirichlet-to-Neumann map is given at an arbitrarily small part of the boundary of a three-dimensional domain
Fully probabilistic seismic source inversion – Part 1: Efficient parameterisation
Directory of Open Access Journals (Sweden)
S. C. Stähler
2014-11-01
Full Text Available Seismic source inversion is a non-linear problem in seismology where not just the earthquake parameters themselves but also estimates of their uncertainties are of great practical importance. Probabilistic source inversion (Bayesian inference is very adapted to this challenge, provided that the parameter space can be chosen small enough to make Bayesian sampling computationally feasible. We propose a framework for PRobabilistic Inference of Seismic source Mechanisms (PRISM that parameterises and samples earthquake depth, moment tensor, and source time function efficiently by using information from previous non-Bayesian inversions. The source time function is expressed as a weighted sum of a small number of empirical orthogonal functions, which were derived from a catalogue of >1000 source time functions (STFs by a principal component analysis. We use a likelihood model based on the cross-correlation misfit between observed and predicted waveforms. The resulting ensemble of solutions provides full uncertainty and covariance information for the source parameters, and permits propagating these source uncertainties into travel time estimates used for seismic tomography. The computational effort is such that routine, global estimation of earthquake mechanisms and source time functions from teleseismic broadband waveforms is feasible.
Numerical Methods for Bayesian Inverse Problems
Ernst, Oliver
2014-01-06
We present recent results on Bayesian inversion for a groundwater flow problem with an uncertain conductivity field. In particular, we show how direct and indirect measurements can be used to obtain a stochastic model for the unknown. The main tool here is Bayes’ theorem which merges the indirect data with the stochastic prior model for the conductivity field obtained by the direct measurements. Further, we demonstrate how the resulting posterior distribution of the quantity of interest, in this case travel times of radionuclide contaminants, can be obtained by Markov Chain Monte Carlo (MCMC) simulations. Moreover, we investigate new, promising MCMC methods which exploit geometrical features of the posterior and which are suited to infinite dimensions.
On the quantum inverse scattering problem
International Nuclear Information System (INIS)
Maillet, J.M.; Terras, V.
2000-01-01
A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an R-matrix) for a large class of lattice quantum integrable models is given. The principal requirement being the initial condition (R(0)=P, the permutation operator) for the quantum R-matrix solving the Yang-Baxter equation, it applies not only to most known integrable fundamental lattice models (such as Heisenberg spin chains) but also to lattice models with arbitrary number of impurities and to the so-called fused lattice models (including integrable higher spin generalizations of Heisenberg chains). Our method is then applied to several important examples like the sl n XXZ model, the XYZ spin-((1)/(2)) chain and also to the spin-s Heisenberg chains
The inverse problem for Schwinger pair production
Directory of Open Access Journals (Sweden)
F. Hebenstreit
2016-02-01
Full Text Available The production of electron–positron pairs in time-dependent electric fields (Schwinger mechanism depends non-linearly on the applied field profile. Accordingly, the resulting momentum spectrum is extremely sensitive to small variations of the field parameters. Owing to this non-linear dependence it is so far unpredictable how to choose a field configuration such that a predetermined momentum distribution is generated. We show that quantum kinetic theory along with optimal control theory can be used to approximately solve this inverse problem for Schwinger pair production. We exemplify this by studying the superposition of a small number of harmonic components resulting in predetermined signatures in the asymptotic momentum spectrum. In the long run, our results could facilitate the observation of this yet unobserved pair production mechanism in quantum electrodynamics by providing suggestions for tailored field configurations.
Numerical Methods for Bayesian Inverse Problems
Ernst, Oliver; Sprungk, Bjorn; Cliffe, K. Andrew; Starkloff, Hans-Jorg
2014-01-01
We present recent results on Bayesian inversion for a groundwater flow problem with an uncertain conductivity field. In particular, we show how direct and indirect measurements can be used to obtain a stochastic model for the unknown. The main tool here is Bayes’ theorem which merges the indirect data with the stochastic prior model for the conductivity field obtained by the direct measurements. Further, we demonstrate how the resulting posterior distribution of the quantity of interest, in this case travel times of radionuclide contaminants, can be obtained by Markov Chain Monte Carlo (MCMC) simulations. Moreover, we investigate new, promising MCMC methods which exploit geometrical features of the posterior and which are suited to infinite dimensions.
Stochastic inverse problems: Models and metrics
International Nuclear Information System (INIS)
Sabbagh, Elias H.; Sabbagh, Harold A.; Murphy, R. Kim; Aldrin, John C.; Annis, Charles; Knopp, Jeremy S.
2015-01-01
In past work, we introduced model-based inverse methods, and applied them to problems in which the anomaly could be reasonably modeled by simple canonical shapes, such as rectangular solids. In these cases the parameters to be inverted would be length, width and height, as well as the occasional probe lift-off or rotation. We are now developing a formulation that allows more flexibility in modeling complex flaws. The idea consists of expanding the flaw in a sequence of basis functions, and then solving for the expansion coefficients of this sequence, which are modeled as independent random variables, uniformly distributed over their range of values. There are a number of applications of such modeling: 1. Connected cracks and multiple half-moons, which we have noted in a POD set. Ideally we would like to distinguish connected cracks from one long shallow crack. 2. Cracks of irregular profile and shape which have appeared in cold work holes during bolt-hole eddy-current inspection. One side of such cracks is much deeper than other. 3. L or C shaped crack profiles at the surface, examples of which have been seen in bolt-hole cracks. By formulating problems in a stochastic sense, we are able to leverage the stochastic global optimization algorithms in NLSE, which is resident in VIC-3D®, to answer questions of global minimization and to compute confidence bounds using the sensitivity coefficient that we get from NLSE. We will also address the issue of surrogate functions which are used during the inversion process, and how they contribute to the quality of the estimation of the bounds
Stochastic inverse problems: Models and metrics
Sabbagh, Elias H.; Sabbagh, Harold A.; Murphy, R. Kim; Aldrin, John C.; Annis, Charles; Knopp, Jeremy S.
2015-03-01
In past work, we introduced model-based inverse methods, and applied them to problems in which the anomaly could be reasonably modeled by simple canonical shapes, such as rectangular solids. In these cases the parameters to be inverted would be length, width and height, as well as the occasional probe lift-off or rotation. We are now developing a formulation that allows more flexibility in modeling complex flaws. The idea consists of expanding the flaw in a sequence of basis functions, and then solving for the expansion coefficients of this sequence, which are modeled as independent random variables, uniformly distributed over their range of values. There are a number of applications of such modeling: 1. Connected cracks and multiple half-moons, which we have noted in a POD set. Ideally we would like to distinguish connected cracks from one long shallow crack. 2. Cracks of irregular profile and shape which have appeared in cold work holes during bolt-hole eddy-current inspection. One side of such cracks is much deeper than other. 3. L or C shaped crack profiles at the surface, examples of which have been seen in bolt-hole cracks. By formulating problems in a stochastic sense, we are able to leverage the stochastic global optimization algorithms in NLSE, which is resident in VIC-3D®, to answer questions of global minimization and to compute confidence bounds using the sensitivity coefficient that we get from NLSE. We will also address the issue of surrogate functions which are used during the inversion process, and how they contribute to the quality of the estimation of the bounds.
Inverse Problem in Self-assembly
Tkachenko, Alexei
2012-02-01
By decorating colloids and nanoparticles with DNA, one can introduce highly selective key-lock interactions between them. This leads to a new class of systems and problems in soft condensed matter physics. In particular, this opens a possibility to solve inverse problem in self-assembly: how to build an arbitrary desired structure with the bottom-up approach? I will present a theoretical and computational analysis of the hierarchical strategy in attacking this problem. It involves self-assembly of particular building blocks (``octopus particles''), that in turn would assemble into the target structure. On a conceptual level, our approach combines elements of three different brands of programmable self assembly: DNA nanotechnology, nanoparticle-DNA assemblies and patchy colloids. I will discuss the general design principles, theoretical and practical limitations of this approach, and illustrate them with our simulation results. Our crucial result is that not only it is possible to design a system that has a given nanostructure as a ground state, but one can also program and optimize the kinetic pathway for its self-assembly.
Can earthquake source inversion benefit from rotational ground motion observations?
Igel, H.; Donner, S.; Reinwald, M.; Bernauer, M.; Wassermann, J. M.; Fichtner, A.
2015-12-01
With the prospects of instruments to observe rotational ground motions in a wide frequency and amplitude range in the near future we engage in the question how this type of ground motion observation can be used to solve seismic inverse problems. Here, we focus on the question, whether point or finite source inversions can benefit from additional observations of rotational motions. In an attempt to be fair we compare observations from a surface seismic network with N 3-component translational sensors (classic seismometers) with those obtained with N/2 6-component sensors (with additional colocated 3-component rotational motions). Thus we keep the overall number of traces constant. Synthetic seismograms are calculated for known point- or finite-source properties. The corresponding inverse problem is posed in a probabilistic way using the Shannon information content as a measure how the observations constrain the seismic source properties. The results show that with the 6-C subnetworks the source properties are not only equally well recovered (even that would be benefitial because of the substantially reduced logistics installing N/2 sensors) but statistically significant some source properties are almost always better resolved. We assume that this can be attributed to the fact the (in particular vertical) gradient information is contained in the additional rotational motion components. We compare these effects for strike-slip and normal-faulting type sources. Thus the answer to the question raised is a definite "yes". The challenge now is to demonstrate these effects on real data.
An inverse problem for a one-dimensional time-fractional diffusion problem
Jin, Bangti; Rundell, William
2012-01-01
We study an inverse problem of recovering a spatially varying potential term in a one-dimensional time-fractional diffusion equation from the flux measurements taken at a single fixed time corresponding to a given set of input sources. The unique
Inverse Problems in a Bayesian Setting
Matthies, Hermann G.
2016-02-13
In a Bayesian setting, inverse problems and uncertainty quantification (UQ)—the propagation of uncertainty through a computational (forward) model—are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.
Inverse Problems in a Bayesian Setting
Matthies, Hermann G.; Zander, Elmar; Rosić, Bojana V.; Litvinenko, Alexander; Pajonk, Oliver
2016-01-01
In a Bayesian setting, inverse problems and uncertainty quantification (UQ)—the propagation of uncertainty through a computational (forward) model—are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.
Obtaining sparse distributions in 2D inverse problems
Reci, A; Sederman, Andrew John; Gladden, Lynn Faith
2017-01-01
The mathematics of inverse problems has relevance across numerous estimation problems in science and engineering. L1 regularization has attracted recent attention in reconstructing the system properties in the case of sparse inverse problems; i.e., when the true property sought is not adequately described by a continuous distribution, in particular in Compressed Sensing image reconstruction. In this work, we focus on the application of L1 regularization to a class of inverse problems; relaxat...
MAP estimators and their consistency in Bayesian nonparametric inverse problems
Dashti, M.; Law, K. J H; Stuart, A. M.; Voss, J.
2013-01-01
with examples from an inverse problem for the Navier-Stokes equation, motivated by problems arising in weather forecasting, and from the theory of conditioned diffusions, motivated by problems arising in molecular dynamics. © 2013 IOP Publishing Ltd.
On a quadratic inverse eigenvalue problem
International Nuclear Information System (INIS)
Cai, Yunfeng; Xu, Shufang
2009-01-01
This paper concerns the quadratic inverse eigenvalue problem (QIEP) of constructing real symmetric matrices M, C and K of size n × n, with M nonsingular, so that the quadratic matrix polynomial Q(λ) ≡ λ 2 M + λC + K has a completely prescribed set of eigenvalues and eigenvectors. It is shown via construction that the QIEP has a solution if and only if r 0, where r and δ are computable from the prescribed spectral data. A necessary and sufficient condition for the existence of a solution to the QIEP with M being positive definite is also established in a constructive way. Furthermore, two algorithms are developed: one is to solve the QIEP; another is to find a particular solution to the QIEP with the leading coefficient matrix being positive definite, which also provides us an approach to a simultaneous reduction of real symmetric matrix triple (M, C, K) by real congruence. Numerical results show that the two algorithms are feasible and numerically reliable
Machine Learning and Inverse Problem in Geodynamics
Shahnas, M. H.; Yuen, D. A.; Pysklywec, R.
2017-12-01
During the past few decades numerical modeling and traditional HPC have been widely deployed in many diverse fields for problem solutions. However, in recent years the rapid emergence of machine learning (ML), a subfield of the artificial intelligence (AI), in many fields of sciences, engineering, and finance seems to mark a turning point in the replacement of traditional modeling procedures with artificial intelligence-based techniques. The study of the circulation in the interior of Earth relies on the study of high pressure mineral physics, geochemistry, and petrology where the number of the mantle parameters is large and the thermoelastic parameters are highly pressure- and temperature-dependent. More complexity arises from the fact that many of these parameters that are incorporated in the numerical models as input parameters are not yet well established. In such complex systems the application of machine learning algorithms can play a valuable role. Our focus in this study is the application of supervised machine learning (SML) algorithms in predicting mantle properties with the emphasis on SML techniques in solving the inverse problem. As a sample problem we focus on the spin transition in ferropericlase and perovskite that may cause slab and plume stagnation at mid-mantle depths. The degree of the stagnation depends on the degree of negative density anomaly at the spin transition zone. The training and testing samples for the machine learning models are produced by the numerical convection models with known magnitudes of density anomaly (as the class labels of the samples). The volume fractions of the stagnated slabs and plumes which can be considered as measures for the degree of stagnation are assigned as sample features. The machine learning models can determine the magnitude of the spin transition-induced density anomalies that can cause flow stagnation at mid-mantle depths. Employing support vector machine (SVM) algorithms we show that SML techniques
PREFACE: International Conference on Inverse Problems 2010
Hon, Yiu-Chung; Ling, Leevan
2011-03-01
Following the first International Conference on Inverse Problems - Recent Theoretical Development and Numerical Approaches held at the City University of Hong Kong in 2002, the fifth International Conference was held again at the City University during December 13-17, 2010. This fifth conference was jointly organized by Professor Yiu-Chung Hon (Co-Chair, City University of Hong Kong, HKSAR), Dr Leevan Ling (Co-Chair, Hong Kong Baptist University, HKSAR), Professor Jin Cheng (Fudan University, China), Professor June-Yub Lee (Ewha Womans University, South Korea), Professor Gui-Rong Liu (University of Cincinnati, USA), Professor Jenn-Nan Wang (National Taiwan University, Taiwan), and Professor Masahiro Yamamoto (The University of Tokyo, Japan). It was agreed to alternate holding the conference among the above places (China, Japan, Korea, Taiwan, and Hong Kong) once every two years. The next conference has been scheduled to be held at the Southeast University (Nanjing, China) in 2012. The purpose of this series of conferences is to establish a strong collaborative link among the universities of the Asian-Pacific regions and worldwide leading researchers in inverse problems. The conference addressed both theoretical (mathematics), applied (engineering) and developmental aspects of inverse problems. The conference was intended to nurture Asian-American-European collaborations in the evolving interdisciplinary areas and it was envisioned that the conference would lead to long-term commitments and collaborations among the participating countries and researchers. There was a total of more than 100 participants. A call for the submission of papers was sent out after the conference, and a total of 19 papers were finally accepted for publication in this proceedings. The papers included in the proceedings cover a wide scope, which reflects the current flourishing theoretical and numerical research into inverse problems. Finally, as the co-chairs of the Inverse Problems
Inverse problems and inverse scattering of plane waves
Ghosh Roy, Dilip N
2001-01-01
The purpose of this text is to present the theory and mathematics of inverse scattering, in a simple way, to the many researchers and professionals who use it in their everyday research. While applications range across a broad spectrum of disciplines, examples in this text will focus primarly, but not exclusively, on acoustics. The text will be especially valuable for those applied workers who would like to delve more deeply into the fundamentally mathematical character of the subject matter.Practitioners in this field comprise applied physicists, engineers, and technologists, whereas the theory is almost entirely in the domain of abstract mathematics. This gulf between the two, if bridged, can only lead to improvement in the level of scholarship in this highly important discipline. This is the book''s primary focus.
Inverse Problems in Systems Biology: A Critical Review.
Guzzi, Rodolfo; Colombo, Teresa; Paci, Paola
2018-01-01
Systems Biology may be assimilated to a symbiotic cyclic interplaying between the forward and inverse problems. Computational models need to be continuously refined through experiments and in turn they help us to make limited experimental resources more efficient. Every time one does an experiment we know that there will be some noise that can disrupt our measurements. Despite the noise certainly is a problem, the inverse problems already involve the inference of missing information, even if the data is entirely reliable. So the addition of a certain limited noise does not fundamentally change the situation but can be used to solve the so-called ill-posed problem, as defined by Hadamard. It can be seen as an extra source of information. Recent studies have shown that complex systems, among others the systems biology, are poorly constrained and ill-conditioned because it is difficult to use experimental data to fully estimate their parameters. For these reasons was born the concept of sloppy models, a sequence of models of increasing complexity that become sloppy in the limit of microscopic accuracy. Furthermore the concept of sloppy models contains also the concept of un-identifiability, because the models are characterized by many parameters that are poorly constrained by experimental data. Then a strategy needs to be designed to infer, analyze, and understand biological systems. The aim of this work is to provide a critical review to the inverse problems in systems biology defining a strategy to determine the minimal set of information needed to overcome the problems arising from dynamic biological models that generally may have many unknown, non-measurable parameters.
Subspace-based analysis of the ERT inverse problem
Ben Hadj Miled, Mohamed Khames; Miller, Eric L.
2004-05-01
In a previous work, we proposed a source-type formulation to the electrical resistance tomography (ERT) problem. Specifically, we showed that inhomogeneities in the medium can be viewed as secondary sources embedded in the homogeneous background medium and located at positions associated with variation in electrical conductivity. Assuming a piecewise constant conductivity distribution, the support of equivalent sources is equal to the boundary of the inhomogeneity. The estimation of the anomaly shape takes the form of an inverse source-type problem. In this paper, we explore the use of subspace methods to localize the secondary equivalent sources associated with discontinuities in the conductivity distribution. Our first alternative is the multiple signal classification (MUSIC) algorithm which is commonly used in the localization of multiple sources. The idea is to project a finite collection of plausible pole (or dipole) sources onto an estimated signal subspace and select those with largest correlations. In ERT, secondary sources are excited simultaneously but in different ways, i.e. with distinct amplitude patterns, depending on the locations and amplitudes of primary sources. If the number of receivers is "large enough", different source configurations can lead to a set of observation vectors that span the data subspace. However, since sources that are spatially close to each other have highly correlated signatures, seperation of such signals becomes very difficult in the presence of noise. To overcome this problem we consider iterative MUSIC algorithms like R-MUSIC and RAP-MUSIC. These recursive algorithms pose a computational burden as they require multiple large combinatorial searches. Results obtained with these algorithms using simulated data of different conductivity patterns are presented.
Time-reversed absorbing condition: application to inverse problems
International Nuclear Information System (INIS)
Assous, F; Kray, M; Nataf, F; Turkel, E
2011-01-01
The aim of this paper is to introduce time-reversed absorbing conditions in time-reversal methods. They enable one to 'recreate the past' without knowing the source which has emitted the signals that are back-propagated. We present two applications in inverse problems: the reduction of the size of the computational domain and the determination, from boundary measurements, of the location and volume of an unknown inclusion. The method does not rely on any a priori knowledge of the physical properties of the inclusion. Numerical tests with the wave and Helmholtz equations illustrate the efficiency of the method. This technique is fairly insensitive to noise in the data
Source-independent elastic waveform inversion using a logarithmic wavefield
Choi, Yun Seok; Min, Dong Joon
2012-01-01
The logarithmic waveform inversion has been widely developed and applied to some synthetic and real data. In most logarithmic waveform inversion algorithms, the subsurface velocities are updated along with the source estimation. To avoid estimating
Numerical approach to the inverse convection-diffusion problem
International Nuclear Information System (INIS)
Yang, X-H; She, D-X; Li, J-Q
2008-01-01
In this paper, the inverse problem on source term identification in convection-diffusion equation is transformed into an optimization problem. To reduce the computational cost and improve computational accuracy for the optimization problem, a new algorithm, chaos real-coded hybrid-accelerating evolution algorithm (CRHAEA), is proposed, in which an initial population is generated by chaos mapping, and new chaos mutation and simplex evolution operation are used. With the shrinking of searching range, CRHAEA gradually directs to an optimal result with the excellent individuals obtained by real-coded evolution algorithm. Its convergence is analyzed. Its efficiency is demonstrated by 15 test functions. Numerical simulation shows that CRHAEA has some advantages over the real-coded accelerated evolution algorithm, the chaos algorithm and the pure random search algorithm
The isotope density inverse problem in multigroup neutron transport
International Nuclear Information System (INIS)
Zazula, J.M.
1981-01-01
The inverse problem for stationary multigroup anisotropic neutron transport is discussed in order to search for isotope densities in multielement medium. The spatial- and angular-integrated form of neutron transport equation, in terms of the flux in a group - density of an element spatial correlation, leads to a set of integral functionals for the densities weighted by the group fluxes. Some methods of approximation to make the problem uniquently solvable are proposed. Particularly P 0 angular flux information and the spherically-symetrical geometry of an infinite medium are considered. The numerical calculation using this method related to sooner evaluated direct problem data gives promising agreement with primary densities. This approach would be the basis for further application in an elemental analysis of a medium, using an isotopic neutron source and a moving, energy-dependent neutron detector. (author)
Classical limit of the quantum inverse scattering problem
International Nuclear Information System (INIS)
Bogdanov, I.V.
1986-01-01
This paper studies the passage to the limit of classical mechanics which is realized in the formalism of Marchenko's method for a spherically symmetric inverse problem of quantum scattering for fixed angular momentum. The limit is considered for the general case of partial waves with arbitrary values of the orbital number 1>0 in the lowest order of perturbation theory. It is shown how in the limit h→0 in the quantum inverse problem the integral Able transformation characteristic of classical inverse problems arises. The classical inversion formula with delay time is derived from the Marchenko equation
Fast Bayesian Optimal Experimental Design for Seismic Source Inversion
Long, Quan; Motamed, Mohammad; Tempone, Raul
2016-01-01
We develop a fast method for optimally designing experiments [1] in the context of statistical seismic source inversion [2]. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by the elastic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the true parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem.
Fast Bayesian optimal experimental design for seismic source inversion
Long, Quan
2015-07-01
We develop a fast method for optimally designing experiments in the context of statistical seismic source inversion. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by elastodynamic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the "true" parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem. © 2015 Elsevier B.V.
Fast Bayesian Optimal Experimental Design for Seismic Source Inversion
Long, Quan
2016-01-06
We develop a fast method for optimally designing experiments [1] in the context of statistical seismic source inversion [2]. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by the elastic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the true parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem.
Source inversion in the full-wave tomography; Full wave tomography ni okeru source inversion
Energy Technology Data Exchange (ETDEWEB)
Tsuchiya, T [DIA Consultants Co. Ltd., Tokyo (Japan)
1997-10-22
In order to consider effects of characteristics of a vibration source in the full-wave tomography (FWT), a study has been performed on a method to invert vibration source parameters together with V(p)/V(s) distribution. The study has expanded an analysis method which uses as the basic the gradient method invented by Tarantola and the partial space method invented by Sambridge, and conducted numerical experiments. The experiment No. 1 has performed inversion of only the vibration source parameters, and the experiment No. 2 has executed simultaneous inversion of the V(p)/V(s) distribution and the vibration source parameters. The result of the discussions revealed that and effective analytical procedure would be as follows: in order to predict maximum stress, the average vibration source parameters and the property parameters are first inverted simultaneously; in order to estimate each vibration source parameter at a high accuracy, the property parameters are fixed, and each vibration source parameter is inverted individually; and the derived vibration source parameters are fixed, and the property parameters are again inverted from the initial values. 5 figs., 2 tabs.
Turbulence Nature and the Inverse Problem
Pyatnitsky, L. N
2009-01-01
Hydrodynamic equations well describe averaged parameters of turbulent steady flows, at least in pipes where boundary conditions can be estimated. The equations might outline the parameters fluctuations as well, if entry conditions at current boundaries were known. This raises, in addition, the more comprehensive problem of the primary perturbation nature, noted by H.A. Lorentz, which still remains unsolved. Generally, any flow steadiness should be supported by pressure waves emitted by some external source, e.g. a piston or a receiver. The wave plane front in channels quickly takes convex configuration owing to Rayleigh's law of diffraction divergence. The Schlieren technique and pressure wave registration were employed to investigate the wave interaction with boundary layer, while reflecting from the channel wall. The reflection induces boundary-layer local separation and following pressure rapid increase within the perturbation zone. It propagates as an acoustic wave packet of spherical shape, bearing oscil...
Inverse Modelling Problems in Linear Algebra Undergraduate Courses
Martinez-Luaces, Victor E.
2013-01-01
This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…
The inverse spectral problem for pencils of differential operators
International Nuclear Information System (INIS)
Guseinov, I M; Nabiev, I M
2007-01-01
The inverse problem of spectral analysis for a quadratic pencil of Sturm-Liouville operators on a finite interval is considered. A uniqueness theorem is proved, a solution algorithm is presented, and sufficient conditions for the solubility of the inverse problem are obtained. Bibliography: 31 titles.
Formulas in inverse and ill-posed problems
Anikonov, Yu E
1997-01-01
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
A finite-difference contrast source inversion method
International Nuclear Information System (INIS)
Abubakar, A; Hu, W; Habashy, T M; Van den Berg, P M
2008-01-01
We present a contrast source inversion (CSI) algorithm using a finite-difference (FD) approach as its backbone for reconstructing the unknown material properties of inhomogeneous objects embedded in a known inhomogeneous background medium. Unlike the CSI method using the integral equation (IE) approach, the FD-CSI method can readily employ an arbitrary inhomogeneous medium as its background. The ability to use an inhomogeneous background medium has made this algorithm very suitable to be used in through-wall imaging and time-lapse inversion applications. Similar to the IE-CSI algorithm the unknown contrast sources and contrast function are updated alternately to reconstruct the unknown objects without requiring the solution of the full forward problem at each iteration step in the optimization process. The FD solver is formulated in the frequency domain and it is equipped with a perfectly matched layer (PML) absorbing boundary condition. The FD operator used in the FD-CSI method is only dependent on the background medium and the frequency of operation, thus it does not change throughout the inversion process. Therefore, at least for the two-dimensional (2D) configurations, where the size of the stiffness matrix is manageable, the FD stiffness matrix can be inverted using a non-iterative inversion matrix approach such as a Gauss elimination method for the sparse matrix. In this case, an LU decomposition needs to be done only once and can then be reused for multiple source positions and in successive iterations of the inversion. Numerical experiments show that this FD-CSI algorithm has an excellent performance for inverting inhomogeneous objects embedded in an inhomogeneous background medium
An inverse Sturm–Liouville problem with a fractional derivative
Jin, Bangti; Rundell, William
2012-01-01
In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and numerical
On inverse problem of calculus of variations
Energy Technology Data Exchange (ETDEWEB)
Tao, Z-L [College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044 (China)], E-mail: zaolingt@nuist.edu.cn
2008-02-15
Using the semi-inverse method proposed by Ji-Huan He, variational principles are established for some nonlinear equations arising in physics, including the (p, 2p)-mZK equation, Klein-Gordon equation, sine-Gordon equation, Liouville equation, Dodd- Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation.
Source-independent elastic waveform inversion using a logarithmic wavefield
Choi, Yun Seok
2012-01-01
The logarithmic waveform inversion has been widely developed and applied to some synthetic and real data. In most logarithmic waveform inversion algorithms, the subsurface velocities are updated along with the source estimation. To avoid estimating the source wavelet in the logarithmic waveform inversion, we developed a source-independent logarithmic waveform inversion algorithm. In this inversion algorithm, we first normalize the wavefields with the reference wavefield to remove the source wavelet, and then take the logarithm of the normalized wavefields. Based on the properties of the logarithm, we define three types of misfit functions using the following methods: combination of amplitude and phase, amplitude-only, and phase-only. In the inversion, the gradient is computed using the back-propagation formula without directly calculating the Jacobian matrix. We apply our algorithm to noise-free and noise-added synthetic data generated for the modified version of elastic Marmousi2 model, and compare the results with those of the source-estimation logarithmic waveform inversion. For the noise-free data, the source-independent algorithms yield velocity models close to true velocity models. For random-noise data, the source-estimation logarithmic waveform inversion yields better results than the source-independent method, whereas for coherent-noise data, the results are reversed. Numerical results show that the source-independent and source-estimation logarithmic waveform inversion methods have their own merits for random- and coherent-noise data. © 2011.
REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM
DEFF Research Database (Denmark)
Knudsen, Kim; Lassas, Matti; Mueller, Jennifer
2009-01-01
A strategy for regularizing the inversion procedure for the two-dimensional D-bar reconstruction algorithm based on the global uniqueness proof of Nachman [Ann. Math. 143 (1996)] for the ill-posed inverse conductivity problem is presented. The strategy utilizes truncation of the boundary integral...... the convergence of the reconstructed conductivity to the true conductivity as the noise level tends to zero. The results provide a link between two traditions of inverse problems research: theory of regularization and inversion methods based on complex geometrical optics. Also, the procedure is a novel...
Optimization method for identifying the source term in an inverse wave equation
Directory of Open Access Journals (Sweden)
Arumugam Deiveegan
2017-08-01
Full Text Available In this work, we investigate the inverse problem of identifying a space-wise dependent source term of wave equation from the measurement on the boundary. On the basis of the optimal control framework, the inverse problem is transformed into an optimization problem. The existence and necessary condition of the minimizer for the cost functional are obtained. The projected gradient method and two-parameter model function method are applied to the minimization problem and numerical results are illustrated.
Splines employment for inverse problem of nonstationary thermal conduction
International Nuclear Information System (INIS)
Nikonov, S.P.; Spolitak, S.I.
1985-01-01
An analytical solution has been obtained for an inverse problem of nonstationary thermal conduction which is faced in nonstationary heat transfer data processing when the rewetting in channels with uniform annular fuel element imitators is investigated. In solving the problem both boundary conditions and power density within the imitator are regularized via cubic splines constructed with the use of Reinsch algorithm. The solution can be applied for calculation of temperature distribution in the imitator and the heat flux in two-dimensional approximation (r-z geometry) under the condition that the rewetting front velocity is known, and in one-dimensional r-approximation in cases with negligible axial transport or when there is a lack of data about the temperature disturbance source velocity along the channel
An inverse heat transfer problem for optimization of the thermal ...
Indian Academy of Sciences (India)
This paper takes a different approach towards identiﬁcation of the thermal process in machining, using inverse heat transfer problem. Inverse heat transfer method allows the closest possible experimental and analytical approximation of thermal state for a machining process. Based on a temperature measured at any point ...
Basis set expansion for inverse problems in plasma diagnostic analysis
Jones, B.; Ruiz, C. L.
2013-07-01
A basis set expansion method [V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, Rev. Sci. Instrum. 73, 2634 (2002)], 10.1063/1.1482156 is applied to recover physical information about plasma radiation sources from instrument data, which has been forward transformed due to the nature of the measurement technique. This method provides a general approach for inverse problems, and we discuss two specific examples relevant to diagnosing fast z pinches on the 20-25 MA Z machine [M. E. Savage, L. F. Bennett, D. E. Bliss, W. T. Clark, R. S. Coats, J. M. Elizondo, K. R. LeChien, H. C. Harjes, J. M. Lehr, J. E. Maenchen, D. H. McDaniel, M. F. Pasik, T. D. Pointon, A. C. Owen, D. B. Seidel, D. L. Smith, B. S. Stoltzfus, K. W. Struve, W. A. Stygar, L. K. Warne, J. R. Woodworth, C. W. Mendel, K. R. Prestwich, R. W. Shoup, D. L. Johnson, J. P. Corley, K. C. Hodge, T. C. Wagoner, and P. E. Wakeland, in Proceedings of the Pulsed Power Plasma Sciences Conference (IEEE, 2007), p. 979]. First, Abel inversion of time-gated, self-emission x-ray images from a wire array implosion is studied. Second, we present an approach for unfolding neutron time-of-flight measurements from a deuterium gas puff z pinch to recover information about emission time history and energy distribution. Through these examples, we discuss how noise in the measured data limits the practical resolution of the inversion, and how the method handles discontinuities in the source function and artifacts in the projected image. We add to the method a propagation of errors calculation for estimating uncertainties in the inverted solution.
Basis set expansion for inverse problems in plasma diagnostic analysis
Energy Technology Data Exchange (ETDEWEB)
Jones, B.; Ruiz, C. L. [Sandia National Laboratories, PO Box 5800, Albuquerque, New Mexico 87185 (United States)
2013-07-15
A basis set expansion method [V. Dribinski, A. Ossadtchi, V. A. Mandelshtam, and H. Reisler, Rev. Sci. Instrum. 73, 2634 (2002)] is applied to recover physical information about plasma radiation sources from instrument data, which has been forward transformed due to the nature of the measurement technique. This method provides a general approach for inverse problems, and we discuss two specific examples relevant to diagnosing fast z pinches on the 20–25 MA Z machine [M. E. Savage, L. F. Bennett, D. E. Bliss, W. T. Clark, R. S. Coats, J. M. Elizondo, K. R. LeChien, H. C. Harjes, J. M. Lehr, J. E. Maenchen, D. H. McDaniel, M. F. Pasik, T. D. Pointon, A. C. Owen, D. B. Seidel, D. L. Smith, B. S. Stoltzfus, K. W. Struve, W. A. Stygar, L. K. Warne, J. R. Woodworth, C. W. Mendel, K. R. Prestwich, R. W. Shoup, D. L. Johnson, J. P. Corley, K. C. Hodge, T. C. Wagoner, and P. E. Wakeland, in Proceedings of the Pulsed Power Plasma Sciences Conference (IEEE, 2007), p. 979]. First, Abel inversion of time-gated, self-emission x-ray images from a wire array implosion is studied. Second, we present an approach for unfolding neutron time-of-flight measurements from a deuterium gas puff z pinch to recover information about emission time history and energy distribution. Through these examples, we discuss how noise in the measured data limits the practical resolution of the inversion, and how the method handles discontinuities in the source function and artifacts in the projected image. We add to the method a propagation of errors calculation for estimating uncertainties in the inverted solution.
Spectral solution of the inverse Mie problem
Romanov, Andrey V.; Konokhova, Anastasiya I.; Yastrebova, Ekaterina S.; Gilev, Konstantin V.; Strokotov, Dmitry I.; Chernyshev, Andrei V.; Maltsev, Valeri P.; Yurkin, Maxim A.
2017-10-01
We developed a fast method to determine size and refractive index of homogeneous spheres from the power Fourier spectrum of their light-scattering patterns (LSPs), measured with the scanning flow cytometer. Specifically, we used two spectral parameters: the location of the non-zero peak and zero-frequency amplitude, and numerically inverted the map from the space of particle characteristics (size and refractive index) to the space of spectral parameters. The latter parameters can be reliably resolved only for particle size parameter greater than 11, and the inversion is unique only in the limited range of refractive index with upper limit between 1.1 and 1.25 (relative to the medium) depending on the size parameter and particular definition of uniqueness. The developed method was tested on two experimental samples, milk fat globules and spherized red blood cells, and resulted in accuracy not worse than the reference method based on the least-square fit of the LSP with the Mie theory. Moreover, for particles with significant deviation from the spherical shape the spectral method was much closer to the Mie-fit result than the estimated uncertainty of the latter. The spectral method also showed adequate results for synthetic LSPs of spheroids with aspect ratios up to 1.4. Overall, we present a general framework, which can be used to construct an inverse algorithm for any other experimental signals.
Applications of elliptic Carleman inequalities to Cauchy and inverse problems
Choulli, Mourad
2016-01-01
This book presents a unified approach to studying the stability of both elliptic Cauchy problems and selected inverse problems. Based on elementary Carleman inequalities, it establishes three-ball inequalities, which are the key to deriving logarithmic stability estimates for elliptic Cauchy problems and are also useful in proving stability estimates for certain elliptic inverse problems. The book presents three inverse problems, the first of which consists in determining the surface impedance of an obstacle from the far field pattern. The second problem investigates the detection of corrosion by electric measurement, while the third concerns the determination of an attenuation coefficient from internal data, which is motivated by a problem encountered in biomedical imaging.
The philosophical aspect of learning inverse problems of mathematical physics
Directory of Open Access Journals (Sweden)
Виктор Семенович Корнилов
2018-12-01
Full Text Available The article describes specific questions student learning inverse problems of mathematical physics. When teaching inverse problems of mathematical physics to the understanding of the students brought the information that the inverse problems of mathematical physics with a philosophical point of view are the problems of determining the unknown causes of known consequences, and the search for their solutions have great scientific and educational potential. The reasons are specified in the form of unknown coefficients, right side, initial conditions of the mathematical model of inverse problems, and as a consequence are functionals of the solution of this mathematical model. In the process of learning the inverse problems of mathematical physics focuses on the philosophical aspects of the phenomenon of information and identify cause-effect relations. It is emphasized that in the process of logical analysis applied and humanitarian character, students realize that information is always related to the fundamental philosophical questions that the analysis applied and the humanitarian aspects of the obtained results the inverse problem of mathematical physics allows students to make appropriate inferences about the studied process and to, ultimately, new information, to study its properties and understand its value. Philosophical understanding of the notion of information opens up to students a new methodological opportunities to comprehend the world and helps us to reinterpret existing science and philosophy of the theory related to the disclosure of the interrelationship of all phenomena of reality.
Gradient-type methods in inverse parabolic problems
International Nuclear Information System (INIS)
Kabanikhin, Sergey; Penenko, Aleksey
2008-01-01
This article is devoted to gradient-based methods for inverse parabolic problems. In the first part, we present a priori convergence theorems based on the conditional stability estimates for linear inverse problems. These theorems are applied to backwards parabolic problem and sideways parabolic problem. The convergence conditions obtained coincide with sourcewise representability in the self-adjoint backwards parabolic case but they differ in the sideways case. In the second part, a variational approach is formulated for a coefficient identification problem. Using adjoint equations, a formal gradient of an objective functional is constructed. A numerical test illustrates the performance of conjugate gradient algorithm with the formal gradient.
LinvPy : a Python package for linear inverse problems
Beaud, Guillaume François Paul
2016-01-01
The goal of this project is to make a Python package including the tau-estimator algorithm to solve linear inverse problems. The package must be distributed, well documented, easy to use and easy to extend for future developers.
Carleman estimates and applications to inverse problems for hyperbolic systems
Bellassoued, Mourad
2017-01-01
This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions. The formulation is different from that of Dirichlet-to-Neumann maps and can often prove the global uniqueness and Lipschitz stability even with a single measurement. These types of inverse problems include coefficient inverse problems of determining physical parameters in inhomogeneous media that appear in many applications related to electromagnetism, elasticity, and related phenomena. Although the methodology was created in 1981 by Bukhgeim and Klibanov, its comprehensive development has been accomplished only recently. In spite of the wide applicability of the method, there are few monographs focusing on combined accounts of Carleman estimates and applications to inverse problems. The aim in this book is to fill that gap. The basic tool is Carleman estimates, the theory of wh...
A direct sampling method to an inverse medium scattering problem
Ito, Kazufumi; Jin, Bangti; Zou, Jun
2012-01-01
In this work we present a novel sampling method for time harmonic inverse medium scattering problems. It provides a simple tool to directly estimate the shape of the unknown scatterers (inhomogeneous media), and it is applicable even when
Data-Driven Model Order Reduction for Bayesian Inverse Problems
Cui, Tiangang; Youssef, Marzouk; Willcox, Karen
2014-01-01
One of the major challenges in using MCMC for the solution of inverse problems is the repeated evaluation of computationally expensive numerical models. We develop a data-driven projection- based model order reduction technique to reduce
Inverse kinematics problem in robotics using neural networks
Choi, Benjamin B.; Lawrence, Charles
1992-01-01
In this paper, Multilayer Feedforward Networks are applied to the robot inverse kinematic problem. The networks are trained with endeffector position and joint angles. After training, performance is measured by having the network generate joint angles for arbitrary endeffector trajectories. A 3-degree-of-freedom (DOF) spatial manipulator is used for the study. It is found that neural networks provide a simple and effective way to both model the manipulator inverse kinematics and circumvent the problems associated with algorithmic solution methods.
The inverse problem of the magnetostatic nondestructive testing
International Nuclear Information System (INIS)
Pechenkov, A.N.; Shcherbinin, V.E.
2006-01-01
The inverse problem of magnetostatic nondestructive testing consists in the calculation of the shape and magnetic characteristics of a flaw in a uniform magnetized body with measurement of static magnetic field beyond the body. If the flaw does not contain any magnetic material, the inverse problem is reduced to identification of the shape and magnetic susceptibility of the substance. This case has been considered in the study [ru
Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem
Directory of Open Access Journals (Sweden)
Baiyu Wang
2014-01-01
Full Text Available This paper investigates the numerical solution of a class of one-dimensional inverse parabolic problems using the moving least squares approximation; the inverse problem is the determination of an unknown source term depending on time. The collocation method is used for solving the equation; some numerical experiments are presented and discussed to illustrate the stability and high efficiency of the method.
Particle Swarm Optimization and Uncertainty Assessment in Inverse Problems
Directory of Open Access Journals (Sweden)
José L. G. Pallero
2018-01-01
Full Text Available Most inverse problems in the industry (and particularly in geophysical exploration are highly underdetermined because the number of model parameters too high to achieve accurate data predictions and because the sampling of the data space is scarce and incomplete; it is always affected by different kinds of noise. Additionally, the physics of the forward problem is a simplification of the reality. All these facts result in that the inverse problem solution is not unique; that is, there are different inverse solutions (called equivalent, compatible with the prior information that fits the observed data within similar error bounds. In the case of nonlinear inverse problems, these equivalent models are located in disconnected flat curvilinear valleys of the cost-function topography. The uncertainty analysis consists of obtaining a representation of this complex topography via different sampling methodologies. In this paper, we focus on the use of a particle swarm optimization (PSO algorithm to sample the region of equivalence in nonlinear inverse problems. Although this methodology has a general purpose, we show its application for the uncertainty assessment of the solution of a geophysical problem concerning gravity inversion in sedimentary basins, showing that it is possible to efficiently perform this task in a sampling-while-optimizing mode. Particularly, we explain how to use and analyze the geophysical models sampled by exploratory PSO family members to infer different descriptors of nonlinear uncertainty.
Geostatistical regularization operators for geophysical inverse problems on irregular meshes
Jordi, C.; Doetsch, J.; Günther, T.; Schmelzbach, C.; Robertsson, J. OA
2018-05-01
Irregular meshes allow to include complicated subsurface structures into geophysical modelling and inverse problems. The non-uniqueness of these inverse problems requires appropriate regularization that can incorporate a priori information. However, defining regularization operators for irregular discretizations is not trivial. Different schemes for calculating smoothness operators on irregular meshes have been proposed. In contrast to classical regularization constraints that are only defined using the nearest neighbours of a cell, geostatistical operators include a larger neighbourhood around a particular cell. A correlation model defines the extent of the neighbourhood and allows to incorporate information about geological structures. We propose an approach to calculate geostatistical operators for inverse problems on irregular meshes by eigendecomposition of a covariance matrix that contains the a priori geological information. Using our approach, the calculation of the operator matrix becomes tractable for 3-D inverse problems on irregular meshes. We tested the performance of the geostatistical regularization operators and compared them against the results of anisotropic smoothing in inversions of 2-D surface synthetic electrical resistivity tomography (ERT) data as well as in the inversion of a realistic 3-D cross-well synthetic ERT scenario. The inversions of 2-D ERT and seismic traveltime field data with geostatistical regularization provide results that are in good accordance with the expected geology and thus facilitate their interpretation. In particular, for layered structures the geostatistical regularization provides geologically more plausible results compared to the anisotropic smoothness constraints.
Inverse problems in vision and 3D tomography
Mohamad-Djafari, Ali
2013-01-01
The concept of an inverse problem is a familiar one to most scientists and engineers, particularly in the field of signal and image processing, imaging systems (medical, geophysical, industrial non-destructive testing, etc.) and computer vision. In imaging systems, the aim is not just to estimate unobserved images, but also their geometric characteristics from observed quantities that are linked to these unobserved quantities through the forward problem. This book focuses on imagery and vision problems that can be clearly written in terms of an inverse problem where an estimate for the image a
Reconstruction Methods for Inverse Problems with Partial Data
DEFF Research Database (Denmark)
Hoffmann, Kristoffer
This thesis presents a theoretical and numerical analysis of a general mathematical formulation of hybrid inverse problems in impedance tomography. This includes problems from several existing hybrid imaging modalities such as Current Density Impedance Imaging, Magnetic Resonance Electrical...... Impedance Tomography, and Ultrasound Modulated Electrical Impedance Tomography. After giving an introduction to hybrid inverse problems in impedance tomography and the mathematical tools that facilitate the related analysis, we explain in detail the stability properties associated with the classification...... of a linearised hybrid inverse problem. This is done using pseudo-differential calculus and theory for overdetermined boundary value problem. Using microlocal analysis we then present novel results on the propagation of singularities, which give a precise description of the distinct features of solutions...
Stabilizing inverse problems by internal data
International Nuclear Information System (INIS)
Kuchment, Peter; Steinhauer, Dustin
2012-01-01
Several newly developing hybrid imaging methods (e.g., those combining electrical impedance or optical imaging with acoustics) enable one to obtain some auxiliary interior information (usually some combination of the electrical conductivity and the current) about the parameters of the tissues. This information, in turn, happens to stabilize the exponentially unstable and thus low-resolution optical and electrical impedance tomography. Various known instances of this effect have been studied individually. We show that there is a simple general technique (covering all known cases) that shows what kinds of interior data stabilize the reconstruction, and why. Namely, we show when the linearized problem becomes an elliptic pseudo-differential one, and thus stable. Stability here is meant as the problem being Fredholm, so the local uniqueness is not shown and probably does not hold in such generality. (paper)
Stabilizing inverse problems by internal data
Kuchment, Peter
2012-07-30
Several newly developing hybrid imaging methods (e.g., those combining electrical impedance or optical imaging with acoustics) enable one to obtain some auxiliary interior information (usually some combination of the electrical conductivity and the current) about the parameters of the tissues. This information, in turn, happens to stabilize the exponentially unstable and thus low-resolution optical and electrical impedance tomography. Various known instances of this effect have been studied individually. We show that there is a simple general technique (covering all known cases) that shows what kinds of interior data stabilize the reconstruction, and why. Namely, we show when the linearized problem becomes an elliptic pseudo-differential one, and thus stable. Stability here is meant as the problem being Fredholm, so the local uniqueness is not shown and probably does not hold in such generality. © 2012 IOP Publishing Ltd.
Inverse and Control Problems in Electromagnetics
1994-10-14
subject of multicriteria optimization has been most thoroughly developed in the literature of mathematical economics and is most often associated there...8217, Lecture Notes in Economics and Marhemcrical Systems. Vol. 152. Springer. Berlin. 1978. 6. Kirsch. A. and Wilde. P., "Tie optimization of directivity and...indentation D, The geometry of the problem is shown in Fig. 1. The domain the upper half wace , and a such that (E. H) and (E’, HI) of interest is that
Linearized versus non-linear inverse methods for seismic localization of underground sources
DEFF Research Database (Denmark)
Oh, Geok Lian; Jacobsen, Finn
2013-01-01
The problem of localization of underground sources from seismic measurements detected by several geophones located on the ground surface is addressed. Two main approaches to the solution of the problem are considered: a beamforming approach that is derived from the linearized inversion problem, a...
An inverse problem approach to pattern recognition in industry
Directory of Open Access Journals (Sweden)
Ali Sever
2015-01-01
Full Text Available Many works have shown strong connections between learning and regularization techniques for ill-posed inverse problems. A careful analysis shows that a rigorous connection between learning and regularization for inverse problem is not straightforward. In this study, pattern recognition will be viewed as an ill-posed inverse problem and applications of methods from the theory of inverse problems to pattern recognition are studied. A new learning algorithm derived from a well-known regularization model is generated and applied to the task of reconstruction of an inhomogeneous object as pattern recognition. Particularly, it is demonstrated that pattern recognition can be reformulated in terms of inverse problems defined by a Riesz-type kernel. This reformulation can be employed to design a learning algorithm based on a numerical solution of a system of linear equations. Finally, numerical experiments have been carried out with synthetic experimental data considering a reasonable level of noise. Good recoveries have been achieved with this methodology, and the results of these simulations are compatible with the existing methods. The comparison results show that the Regularization-based learning algorithm (RBA obtains a promising performance on the majority of the test problems. In prospects, this method can be used for the creation of automated systems for diagnostics, testing, and control in various fields of scientific and applied research, as well as in industry.
One-dimensional inverse problems of mathematical physics
Lavrent'ev, M M; Yakhno, V G; Schulenberger, J R
1986-01-01
This monograph deals with the inverse problems of determining a variable coefficient and right side for hyperbolic and parabolic equations on the basis of known solutions at fixed points of space for all times. The problems are one-dimensional in nature since the desired coefficient of the equation is a function of only one coordinate, while the desired right side is a function only of time. The authors use methods based on the spectral theory of ordinary differential operators of second order and also methods which make it possible to reduce the investigation of the inverse problems to the in
Inverse problems basics, theory and applications in geophysics
Richter, Mathias
2016-01-01
The overall goal of the book is to provide access to the regularized solution of inverse problems relevant in geophysics without requiring more mathematical knowledge than is taught in undergraduate math courses for scientists and engineers. From abstract analysis only the concept of functions as vectors is needed. Function spaces are introduced informally in the course of the text, when needed. Additionally, a more detailed, but still condensed introduction is given in Appendix B. A second goal is to elaborate the single steps to be taken when solving an inverse problem: discretization, regularization and practical solution of the regularized optimization problem. These steps are shown in detail for model problems from the fields of inverse gravimetry and seismic tomography. The intended audience is mathematicians, physicists and engineers having a good working knowledge of linear algebra and analysis at the upper undergraduate level.
Inverse problems in ordinary differential equations and applications
Llibre, Jaume
2016-01-01
This book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties. The Nambu bracket is the central tool in developing this approach. The authors start characterizing the ordinary differential equations in R^N which have a given set of partial integrals or first integrals. The results obtained are applied first to planar polynomial differential systems with a given set of such integrals, second to solve the 16th Hilbert problem restricted to generic algebraic limit cycles, third for solving the inverse problem for constrained Lagrangian and Hamiltonian mechanical systems, fourth for studying the integrability of a constrained rigid body. Finally the authors conclude with an analysis on nonholonomic mechanics, a generalization of the Hamiltonian principle, and the statement an solution of the inverse problem in vakonomic mechanics.
Inverse random source scattering for the Helmholtz equation in inhomogeneous media
Li, Ming; Chen, Chuchu; Li, Peijun
2018-01-01
This paper is concerned with an inverse random source scattering problem in an inhomogeneous background medium. The wave propagation is modeled by the stochastic Helmholtz equation with the source driven by additive white noise. The goal is to reconstruct the statistical properties of the random source such as the mean and variance from the boundary measurement of the radiated random wave field at multiple frequencies. Both the direct and inverse problems are considered. We show that the direct problem has a unique mild solution by a constructive proof. For the inverse problem, we derive Fredholm integral equations, which connect the boundary measurement of the radiated wave field with the unknown source function. A regularized block Kaczmarz method is developed to solve the ill-posed integral equations. Numerical experiments are included to demonstrate the effectiveness of the proposed method.
Coefficient Inverse Problem for Poisson's Equation in a Cylinder
Solov'ev, V. V.
2011-01-01
The inverse problem of determining the coefficient on the right-hand side of Poisson's equation in a cylindrical domain is considered. The Dirichlet boundary value problem is studied. Two types of additional information (overdetermination) can be specified: (i) the trace of the solution to the
Unfolding in particle physics: A window on solving inverse problems
International Nuclear Information System (INIS)
Spano, F.
2013-01-01
Unfolding is the ensemble of techniques aimed at resolving inverse, ill-posed problems. A pedagogical introduction to the origin and main problems related to unfolding is presented and used as the the stepping stone towards the illustration of some of the most common techniques that are currently used in particle physics experiments. (authors)
Time reversal imaging, Inverse problems and Adjoint Tomography}
Montagner, J.; Larmat, C. S.; Capdeville, Y.; Kawakatsu, H.; Fink, M.
2010-12-01
With the increasing power of computers and numerical techniques (such as spectral element methods), it is possible to address a new class of seismological problems. The propagation of seismic waves in heterogeneous media is simulated more and more accurately and new applications developed, in particular time reversal methods and adjoint tomography in the three-dimensional Earth. Since the pioneering work of J. Claerbout, theorized by A. Tarantola, many similarities were found between time-reversal methods, cross-correlations techniques, inverse problems and adjoint tomography. By using normal mode theory, we generalize the scalar approach of Draeger and Fink (1999) and Lobkis and Weaver (2001) to the 3D- elastic Earth, for theoretically understanding time-reversal method on global scale. It is shown how to relate time-reversal methods on one hand, with auto-correlations of seismograms for source imaging and on the other hand, with cross-correlations between receivers for structural imaging and retrieving Green function. Time-reversal methods were successfully applied in the past to acoustic waves in many fields such as medical imaging, underwater acoustics, non destructive testing and to seismic waves in seismology for earthquake imaging. In the case of source imaging, time reversal techniques make it possible an automatic location in time and space as well as the retrieval of focal mechanism of earthquakes or unknown environmental sources . We present here some applications at the global scale of these techniques on synthetic tests and on real data, such as Sumatra-Andaman (Dec. 2004), Haiti (Jan. 2010), as well as glacial earthquakes and seismic hum.
Inverse planning for x-ray rotation therapy: a general solution of the inverse problem
International Nuclear Information System (INIS)
Oelfke, U.; Bortfeld, T.
1999-01-01
Rotation therapy with photons is currently under investigation for the delivery of intensity modulated radiotherapy (IMRT). An analytical approach for inverse treatment planning of this radiotherapy technique is described. The inverse problem for the delivery of arbitrary 2D dose profiles is first formulated and then solved analytically. In contrast to previously applied strategies for solving the inverse problem, it is shown that the most general solution for the fluence profiles consists of two independent solutions of different parity. A first analytical expression for both fluence profiles is derived. The mathematical derivation includes two different strategies, an elementary expansion of fluence and dose into polynomials and a more practical approach in terms of Fourier transforms. The obtained results are discussed in the context of previous work on this problem. (author)
Variational structure of inverse problems in wave propagation and vibration
Energy Technology Data Exchange (ETDEWEB)
Berryman, J.G.
1995-03-01
Practical algorithms for solving realistic inverse problems may often be viewed as problems in nonlinear programming with the data serving as constraints. Such problems are most easily analyzed when it is possible to segment the solution space into regions that are feasible (satisfying all the known constraints) and infeasible (violating some of the constraints). Then, if the feasible set is convex or at least compact, the solution to the problem will normally lie on the boundary of the feasible set. A nonlinear program may seek the solution by systematically exploring the boundary while satisfying progressively more constraints. Examples of inverse problems in wave propagation (traveltime tomography) and vibration (modal analysis) will be presented to illustrate how the variational structure of these problems may be used to create nonlinear programs using implicit variational constraints.
Regularization method for solving the inverse scattering problem
International Nuclear Information System (INIS)
Denisov, A.M.; Krylov, A.S.
1985-01-01
The inverse scattering problem for the Schroedinger radial equation consisting in determining the potential according to the scattering phase is considered. The problem of potential restoration according to the phase specified with fixed error in a finite range is solved by the regularization method based on minimization of the Tikhonov's smoothing functional. The regularization method is used for solving the problem of neutron-proton potential restoration according to the scattering phases. The determined potentials are given in the table
Iterative Reconstruction Methods for Hybrid Inverse Problems in Impedance Tomography
DEFF Research Database (Denmark)
Hoffmann, Kristoffer; Knudsen, Kim
2014-01-01
For a general formulation of hybrid inverse problems in impedance tomography the Picard and Newton iterative schemes are adapted and four iterative reconstruction algorithms are developed. The general problem formulation includes several existing hybrid imaging modalities such as current density...... impedance imaging, magnetic resonance electrical impedance tomography, and ultrasound modulated electrical impedance tomography, and the unified approach to the reconstruction problem encompasses several algorithms suggested in the literature. The four proposed algorithms are implemented numerically in two...
PREFACE: Inverse Problems in Applied Sciences—towards breakthrough
Cheng, Jin; Iso, Yuusuke; Nakamura, Gen; Yamamoto, Masahiro
2007-06-01
These are the proceedings of the international conference `Inverse Problems in Applied Sciences—towards breakthrough' which was held at Hokkaido University, Sapporo, Japan on 3-7 July 2006 (http://coe.math.sci.hokudai.ac.jp/sympo/inverse/). There were 88 presentations and more than 100 participants, and we are proud to say that the conference was very successful. Nowadays, many new activities on inverse problems are flourishing at many centers of research around the world, and the conference has successfully gathered a world-wide variety of researchers. We believe that this volume contains not only main papers, but also conveys the general status of current research into inverse problems. This conference was the third biennial international conference on inverse problems, the core of which is the Pan-Pacific Asian area. The purpose of this series of conferences is to establish and develop constant international collaboration, especially among the Pan-Pacific Asian countries, and to lead the organization of activities concerning inverse problems centered in East Asia. The first conference was held at City University of Hong Kong in January 2002 and the second was held at Fudan University in June 2004. Following the preceding two successes, the third conference was organized in order to extend the scope of activities and build useful bridges to the next conference in Seoul in 2008. Therefore this third biennial conference was intended not only to establish collaboration and links between researchers in Asia and leading researchers worldwide in inverse problems but also to nurture interdisciplinary collaboration in theoretical fields such as mathematics, applied fields and evolving aspects of inverse problems. For these purposes, we organized tutorial lectures, serial lectures and a panel discussion as well as conference research presentations. This volume contains three lecture notes from the tutorial and serial lectures, and 22 papers. Especially at this
International Nuclear Information System (INIS)
Azimi, A.; Hannani, S.K.; Farhanieh, B.
2005-01-01
In this article, a comparison between two iterative inverse techniques to solve simultaneously two unknown functions of axisymmetric transient inverse heat conduction problems in semi complex geometries is presented. The multi-block structured grid together with blocked-interface nodes is implemented for geometric decomposition of physical domain. Numerical scheme for solution of transient heat conduction equation is the finite element method with frontal technique to solve algebraic system of discrete equations. The inverse heat conduction problem involves simultaneous unknown time varying heat generation and time-space varying boundary condition estimation. Two parameter-estimation techniques are considered, Levenberg-Marquardt scheme and conjugate gradient method with adjoint problem. Numerically computed exact and noisy data are used for the measured transient temperature data needed in the inverse solution. The results of the present study for a configuration including two joined disks with different heights are compared to those of exact heat source and temperature boundary condition, and show good agreement. (author)
Application of the unwrapped phase inversion to land data without source estimation
Choi, Yun Seok
2015-08-19
Unwrapped phase inversion with a strong damping was developed to solve the phase wrapping problem in frequency-domain waveform inversion. In this study, we apply the unwrapped phase inversion to band-limited real land data, for which the available minimum frequency is quite high. An important issue of the data is a strong ambiguity of source-ignition time (or source shift) shown in a seismogram. A source-estimation approach does not fully address the issue of source shift, since the velocity model and the source wavelet are updated simultaneously and interact with each other. We suggest a source-independent unwrapped phase inversion approach instead of relying on source-estimation from this land data. In the source-independent approach, the phase of the modeled data converges not to the exact phase value of the observed data, but to the relative phase value (or the trend of phases); thus it has the potential to solve the ambiguity of source-ignition time in a seismogram and work better than the source-estimation approach. Numerical examples show the validation of the source-independent unwrapped phase inversion, especially for land field data having an ambiguity in the source-ignition time.
A Survey on Inverse Problems for Applied Sciences
Directory of Open Access Journals (Sweden)
Fatih Yaman
2013-01-01
Full Text Available The aim of this paper is to introduce inversion-based engineering applications and to investigate some of the important ones from mathematical point of view. To do this we employ acoustic, electromagnetic, and elastic waves for presenting different types of inverse problems. More specifically, we first study location, shape, and boundary parameter reconstruction algorithms for the inaccessible targets in acoustics. The inverse problems for the time-dependent differential equations of isotropic and anisotropic elasticity are reviewed in the following section of the paper. These problems were the objects of the study by many authors in the last several decades. The physical interpretations for almost all of these problems are given, and the geophysical applications for some of them are described. In our last section, an introduction with many links into the literature is given for modern algorithms which combine techniques from classical inverse problems with stochastic tools into ensemble methods both for data assimilation as well as for forecasting.
Liu, Lu; Fei, Tong; Luo, Yi; Guo, Bowen
2017-01-01
This paper presents a workflow for near-surface velocity automatic estimation using the early arrivals of seismic data. This workflow comprises two methods, source-domain full traveltime inversion (FTI) and early-arrival waveform inversion. Source
Data-Driven Model Order Reduction for Bayesian Inverse Problems
Cui, Tiangang
2014-01-06
One of the major challenges in using MCMC for the solution of inverse problems is the repeated evaluation of computationally expensive numerical models. We develop a data-driven projection- based model order reduction technique to reduce the computational cost of numerical PDE evaluations in this context.
A variational Bayesian method to inverse problems with impulsive noise
Jin, Bangti
2012-01-01
We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve
Solution of Milne problem by Laplace transformation with numerical inversion
International Nuclear Information System (INIS)
Campos Velho, H.F. de.
1987-12-01
The Milne problem for monoenergetic neutrons, by Laplace Transform of the neutron transport integral equation with numerical inversion of the transformed solution by gaussian quadrature, using the fatorization of the dispersion function. The resulted is solved compared its analitical solution. (author) [pt
An inverse heat transfer problem for optimization of the thermal ...
Indian Academy of Sciences (India)
Department of Production Engineering, Faculty of Technical Science, ... ductivity of manufacturing and high levels of machining quality and accuracy, are the most ... inverse problems are today successfully applied in identification, design, control and optimiza- ...... of Machine Tools and Manufacture, 35(5): 751–760.
Solving probabilistic inverse problems rapidly with prior samples
Käufl, Paul; Valentine, Andrew P.; de Wit, Ralph W.; Trampert, Jeannot
2016-01-01
Owing to the increasing availability of computational resources, in recent years the probabilistic solution of non-linear, geophysical inverse problems by means of sampling methods has become increasingly feasible. Nevertheless, we still face situations in which a Monte Carlo approach is not
A mathematical framework for inverse wave problems in heterogeneous media
Blazek, K.D.; Stolk, C.; Symes, W.W.
2013-01-01
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The coefficients of these time-dependent partial differential equations
A general approach to posterior contraction in nonparametric inverse problems
Knapik, Bartek; Salomond, Jean Bernard
In this paper, we propose a general method to derive an upper bound for the contraction rate of the posterior distribution for nonparametric inverse problems. We present a general theorem that allows us to derive contraction rates for the parameter of interest from contraction rates of the related
Toward precise solution of one-dimensional velocity inverse problems
International Nuclear Information System (INIS)
Gray, S.; Hagin, F.
1980-01-01
A family of one-dimensional inverse problems are considered with the goal of reconstructing velocity profiles to reasonably high accuracy. The travel-time variable change is used together with an iteration scheme to produce an effective algorithm for computation. Under modest assumptions the scheme is shown to be convergent
International Nuclear Information System (INIS)
Kılıç, Emre; Eibert, Thomas F.
2015-01-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained
Energy Technology Data Exchange (ETDEWEB)
Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.
2015-05-01
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.
An inverse Sturm–Liouville problem with a fractional derivative
Jin, Bangti
2012-05-01
In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and numerical reconstructions of the potential with a Newton method from finite spectral data are presented. Surprisingly, it allows very satisfactory reconstructions for both smooth and discontinuous potentials, provided that the order . α∈. (1,. 2) of fractional derivative is sufficiently away from 2. © 2012 Elsevier Inc.
An inverse problem for a one-dimensional time-fractional diffusion problem
Jin, Bangti
2012-06-26
We study an inverse problem of recovering a spatially varying potential term in a one-dimensional time-fractional diffusion equation from the flux measurements taken at a single fixed time corresponding to a given set of input sources. The unique identifiability of the potential is shown for two cases, i.e. the flux at one end and the net flux, provided that the set of input sources forms a complete basis in L 2(0, 1). An algorithm of the quasi-Newton type is proposed for the efficient and accurate reconstruction of the coefficient from finite data, and the injectivity of the Jacobian is discussed. Numerical results for both exact and noisy data are presented. © 2012 IOP Publishing Ltd.
Bayesian inverse problems for functions and applications to fluid mechanics
International Nuclear Information System (INIS)
Cotter, S L; Dashti, M; Robinson, J C; Stuart, A M
2009-01-01
In this paper we establish a mathematical framework for a range of inverse problems for functions, given a finite set of noisy observations. The problems are hence underdetermined and are often ill-posed. We study these problems from the viewpoint of Bayesian statistics, with the resulting posterior probability measure being defined on a space of functions. We develop an abstract framework for such problems which facilitates application of an infinite-dimensional version of Bayes theorem, leads to a well-posedness result for the posterior measure (continuity in a suitable probability metric with respect to changes in data), and also leads to a theory for the existence of maximizing the posterior probability (MAP) estimators for such Bayesian inverse problems on function space. A central idea underlying these results is that continuity properties and bounds on the forward model guide the choice of the prior measure for the inverse problem, leading to the desired results on well-posedness and MAP estimators; the PDE analysis and probability theory required are thus clearly dileneated, allowing a straightforward derivation of results. We show that the abstract theory applies to some concrete applications of interest by studying problems arising from data assimilation in fluid mechanics. The objective is to make inference about the underlying velocity field, on the basis of either Eulerian or Lagrangian observations. We study problems without model error, in which case the inference is on the initial condition, and problems with model error in which case the inference is on the initial condition and on the driving noise process or, equivalently, on the entire time-dependent velocity field. In order to undertake a relatively uncluttered mathematical analysis we consider the two-dimensional Navier–Stokes equation on a torus. The case of Eulerian observations—direct observations of the velocity field itself—is then a model for weather forecasting. The case of
A New Wave Equation Based Source Location Method with Full-waveform Inversion
Wu, Zedong
2017-05-26
Locating the source of a passively recorded seismic event is still a challenging problem, especially when the velocity is unknown. Many imaging approaches to focus the image do not address the velocity issue and result in images plagued with illumination artifacts. We develop a waveform inversion approach with an additional penalty term in the objective function to reward the focusing of the source image. This penalty term is relaxed early to allow for data fitting, and avoid cycle skipping, using an extended source. At the later stages the focusing of the image dominates the inversion allowing for high resolution source and velocity inversion. We also compute the source location explicitly and numerical tests show that we obtain good estimates of the source locations with this approach.
Uhlmann, Gunther
2008-07-01
This volume represents the proceedings of the fourth Applied Inverse Problems (AIP) international conference and the first congress of the Inverse Problems International Association (IPIA) which was held in Vancouver, Canada, June 25 29, 2007. The organizing committee was formed by Uri Ascher, University of British Columbia, Richard Froese, University of British Columbia, Gary Margrave, University of Calgary, and Gunther Uhlmann, University of Washington, chair. The conference was part of the activities of the Pacific Institute of Mathematical Sciences (PIMS) Collaborative Research Group on inverse problems (http://www.pims.math.ca/scientific/collaborative-research-groups/past-crgs). This event was also supported by grants from NSF and MITACS. Inverse Problems (IP) are problems where causes for a desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development. The enormous increase in computing power and the development of powerful algorithms have made it possible to apply the techniques of IP to real-world problems of growing complexity. Applications include a number of medical as well as other imaging techniques, location of oil and mineral deposits in the earth's substructure, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modelling in the life sciences. The series of Applied Inverse Problems (AIP) Conferences aims to provide a primary international forum for academic and industrial researchers working on all aspects of inverse problems, such as mathematical modelling, functional analytic methods, computational approaches, numerical algorithms etc. The steering committee of the AIP conferences consists of Heinz Engl (Johannes Kepler Universität, Austria), Joyce McLaughlin (RPI, USA), William Rundell (Texas A&M, USA), Erkki Somersalo (Helsinki University of Technology
Application of the kernel method to the inverse geosounding problem.
Hidalgo, Hugo; Sosa León, Sonia; Gómez-Treviño, Enrique
2003-01-01
Determining the layered structure of the earth demands the solution of a variety of inverse problems; in the case of electromagnetic soundings at low induction numbers, the problem is linear, for the measurements may be represented as a linear functional of the electrical conductivity distribution. In this paper, an application of the support vector (SV) regression technique to the inversion of electromagnetic data is presented. We take advantage of the regularizing properties of the SV learning algorithm and use it as a modeling technique with synthetic and field data. The SV method presents better recovery of synthetic models than Tikhonov's regularization. As the SV formulation is solved in the space of the data, which has a small dimension in this application, a smaller problem than that considered with Tikhonov's regularization is produced. For field data, the SV formulation develops models similar to those obtained via linear programming techniques, but with the added characteristic of robustness.
Numerical investigation of the inverse blackbody radiation problem
International Nuclear Information System (INIS)
Xin Tan, Guo-zhen Yang, Ben-yuan Gu
1994-01-01
A numerical algorithm for the inverse blackbody radiation problem, which is the determination of the temperature distribution of a thermal radiator (TDTR) from its total radiated power spectrum (TRPS), is presented, based on the general theory of amplitude-phase retrieval. With application of this new algorithm, the ill-posed nature of the Fredholm equation of the first kind can be largely overcome and a convergent solution to high accuracy can be obtained. By incorporation of the hybrid input-output algorithm into our algorithm, the convergent process can be substantially expedited and the stagnation problem of the solution can be averted. From model calculations it is found that the new algorithm can also provide a robust reconstruction of the TDTR from the noise-corrupted data of the TRPS. Therefore the new algorithm may offer a useful approach to solving the ill-posed inverse problem. 18 refs., 9 figs
SIAM conference on inverse problems: Geophysical applications. Final technical report
Energy Technology Data Exchange (ETDEWEB)
NONE
1995-12-31
This conference was the second in a series devoted to a particular area of inverse problems. The theme of this series is to discuss problems of major scientific importance in a specific area from a mathematical perspective. The theme of this symposium was geophysical applications. In putting together the program we tried to include a wide range of mathematical scientists and to interpret geophysics in as broad a sense as possible. Our speaker came from industry, government laboratories, and diverse departments in academia. We managed to attract a geographically diverse audience with participation from five continents. There were talks devoted to seismology, hydrology, determination of the earth`s interior on a global scale as well as oceanographic and atmospheric inverse problems.
Integral geometry and inverse problems for hyperbolic equations
Romanov, V G
1974-01-01
There are currently many practical situations in which one wishes to determine the coefficients in an ordinary or partial differential equation from known functionals of its solution. These are often called "inverse problems of mathematical physics" and may be contrasted with problems in which an equation is given and one looks for its solution under initial and boundary conditions. Although inverse problems are often ill-posed in the classical sense, their practical importance is such that they may be considered among the pressing problems of current mathematical re search. A. N. Tihonov showed [82], [83] that there is a broad class of inverse problems for which a particular non-classical definition of well-posed ness is appropriate. This new definition requires that a solution be unique in a class of solutions belonging to a given subset M of a function space. The existence of a solution in this set is assumed a priori for some set of data. The classical requirement of continuous dependence of the solutio...
A hybrid algorithm for solving inverse problems in elasticity
Directory of Open Access Journals (Sweden)
Barabasz Barbara
2014-12-01
Full Text Available The paper offers a new approach to handling difficult parametric inverse problems in elasticity and thermo-elasticity, formulated as global optimization ones. The proposed strategy is composed of two phases. In the first, global phase, the stochastic hp-HGS algorithm recognizes the basins of attraction of various objective minima. In the second phase, the local objective minimizers are closer approached by steepest descent processes executed singly in each basin of attraction. The proposed complex strategy is especially dedicated to ill-posed problems with multimodal objective functionals. The strategy offers comparatively low computational and memory costs resulting from a double-adaptive technique in both forward and inverse problem domains. We provide a result on the Lipschitz continuity of the objective functional composed of the elastic energy and the boundary displacement misfits with respect to the unknown constitutive parameters. It allows common scaling of the accuracy of solving forward and inverse problems, which is the core of the introduced double-adaptive technique. The capability of the proposed method of finding multiple solutions is illustrated by a computational example which consists in restoring all feasible Young modulus distributions minimizing an objective functional in a 3D domain of a photo polymer template obtained during step and flash imprint lithography.
MAP estimators and their consistency in Bayesian nonparametric inverse problems
Dashti, M.
2013-09-01
We consider the inverse problem of estimating an unknown function u from noisy measurements y of a known, possibly nonlinear, map applied to u. We adopt a Bayesian approach to the problem and work in a setting where the prior measure is specified as a Gaussian random field μ0. We work under a natural set of conditions on the likelihood which implies the existence of a well-posed posterior measure, μy. Under these conditions, we show that the maximum a posteriori (MAP) estimator is well defined as the minimizer of an Onsager-Machlup functional defined on the Cameron-Martin space of the prior; thus, we link a problem in probability with a problem in the calculus of variations. We then consider the case where the observational noise vanishes and establish a form of Bayesian posterior consistency for the MAP estimator. We also prove a similar result for the case where the observation of can be repeated as many times as desired with independent identically distributed noise. The theory is illustrated with examples from an inverse problem for the Navier-Stokes equation, motivated by problems arising in weather forecasting, and from the theory of conditioned diffusions, motivated by problems arising in molecular dynamics. © 2013 IOP Publishing Ltd.
MAP estimators and their consistency in Bayesian nonparametric inverse problems
International Nuclear Information System (INIS)
Dashti, M; Law, K J H; Stuart, A M; Voss, J
2013-01-01
We consider the inverse problem of estimating an unknown function u from noisy measurements y of a known, possibly nonlinear, map G applied to u. We adopt a Bayesian approach to the problem and work in a setting where the prior measure is specified as a Gaussian random field μ 0 . We work under a natural set of conditions on the likelihood which implies the existence of a well-posed posterior measure, μ y . Under these conditions, we show that the maximum a posteriori (MAP) estimator is well defined as the minimizer of an Onsager–Machlup functional defined on the Cameron–Martin space of the prior; thus, we link a problem in probability with a problem in the calculus of variations. We then consider the case where the observational noise vanishes and establish a form of Bayesian posterior consistency for the MAP estimator. We also prove a similar result for the case where the observation of G(u) can be repeated as many times as desired with independent identically distributed noise. The theory is illustrated with examples from an inverse problem for the Navier–Stokes equation, motivated by problems arising in weather forecasting, and from the theory of conditioned diffusions, motivated by problems arising in molecular dynamics. (paper)
Potentials of the inverse scattering problem in the three-nucleon problem
International Nuclear Information System (INIS)
Pushkash, A.M.; Simenog, I.V.; Shapoval, D.V.
1993-01-01
Possibilities of using the method of the inverse scattering problem for describing simultaneously the two-nucleon and the low-energy three-nucleon data in the S-interaction approximation are examined. 20 refs., 3 figs., 1 tab
Zielke, O.; McDougall, D.; Mai, P. M.; Babuska, I.
2014-12-01
One fundamental aspect of seismic hazard mitigation is gaining a better understanding of the rupture process. Because direct observation of the relevant parameters and properties is not possible, other means such as kinematic source inversions are used instead. By constraining the spatial and temporal evolution of fault slip during an earthquake, those inversion approaches may enable valuable insights in the physics of the rupture process. However, due to the underdetermined nature of this inversion problem (i.e., inverting a kinematic source model for an extended fault based on seismic data), the provided solutions are generally non-unique. Here we present a statistical (Bayesian) inversion approach based on an open-source library for uncertainty quantification (UQ) called QUESO that was developed at ICES (UT Austin). The approach has advantages with respect to deterministic inversion approaches as it provides not only a single (non-unique) solution but also provides uncertainty bounds with it. Those uncertainty bounds help to qualitatively and quantitatively judge how well constrained an inversion solution is and how much rupture complexity the data reliably resolve. The presented inversion scheme uses only tele-seismically recorded body waves but future developments may lead us towards joint inversion schemes. After giving an insight in the inversion scheme ifself (based on delayed rejection adaptive metropolis, DRAM) we explore the method's resolution potential. For that, we synthetically generate tele-seismic data, add for example different levels of noise and/or change fault plane parameterization and then apply our inversion scheme in the attempt to extract the (known) kinematic rupture model. We conclude with exemplary inverting real tele-seismic data of a recent large earthquake and compare those results with deterministically derived kinematic source models provided by other research groups.
On multiple level-set regularization methods for inverse problems
International Nuclear Information System (INIS)
DeCezaro, A; Leitão, A; Tai, X-C
2009-01-01
We analyze a multiple level-set method for solving inverse problems with piecewise constant solutions. This method corresponds to an iterated Tikhonov method for a particular Tikhonov functional G α based on TV–H 1 penalization. We define generalized minimizers for our Tikhonov functional and establish an existence result. Moreover, we prove convergence and stability results of the proposed Tikhonov method. A multiple level-set algorithm is derived from the first-order optimality conditions for the Tikhonov functional G α , similarly as the iterated Tikhonov method. The proposed multiple level-set method is tested on an inverse potential problem. Numerical experiments show that the method is able to recover multiple objects as well as multiple contrast levels
A variational Bayesian method to inverse problems with impulsive noise
Jin, Bangti
2012-01-01
We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback-Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm. © 2011 Elsevier Inc.
Relevance vector machine technique for the inverse scattering problem
International Nuclear Information System (INIS)
Wang Fang-Fang; Zhang Ye-Rong
2012-01-01
A novel method based on the relevance vector machine (RVM) for the inverse scattering problem is presented in this paper. The nonlinearity and the ill-posedness inherent in this problem are simultaneously considered. The nonlinearity is embodied in the relation between the scattered field and the target property, which can be obtained through the RVM training process. Besides, rather than utilizing regularization, the ill-posed nature of the inversion is naturally accounted for because the RVM can produce a probabilistic output. Simulation results reveal that the proposed RVM-based approach can provide comparative performances in terms of accuracy, convergence, robustness, generalization, and improved performance in terms of sparse property in comparison with the support vector machine (SVM) based approach. (general)
Multi-frequency direct sampling method in inverse scattering problem
Kang, Sangwoo; Lambert, Marc; Park, Won-Kwang
2017-10-01
We consider the direct sampling method (DSM) for the two-dimensional inverse scattering problem. Although DSM is fast, stable, and effective, some phenomena remain unexplained by the existing results. We show that the imaging function of the direct sampling method can be expressed by a Bessel function of order zero. We also clarify the previously unexplained imaging phenomena and suggest multi-frequency DSM to overcome traditional DSM. Our method is evaluated in simulation studies using both single and multiple frequencies.
Quantum method of the inverse scattering problem. Pt. 1
International Nuclear Information System (INIS)
Sklyamin, E.K.; Takhtadzhyan, L.A.; Faddeev, L.D.
1978-12-01
In this work the authors use a formulation for the method of the inverse scattering problem for quantum-mechanical models of the field theory, that can be found in a quantization of these fully integrable systems. As the most important example serves the system (sinγ) 2 with the movement equation: γtt -γxx + m 2 /β sinβγ = 0 that is known under the specification Sine-Gordon-equation. (orig.) [de
Frequency-domain elastic full waveform inversion using encoded simultaneous sources
Jeong, W.; Son, W.; Pyun, S.; Min, D.
2011-12-01
Currently, numerous studies have endeavored to develop robust full waveform inversion and migration algorithms. These processes require enormous computational costs, because of the number of sources in the survey. To avoid this problem, the phase encoding technique for prestack migration was proposed by Romero (2000) and Krebs et al. (2009) proposed the encoded simultaneous-source inversion technique in the time domain. On the other hand, Ben-Hadj-Ali et al. (2011) demonstrated the robustness of the frequency-domain full waveform inversion with simultaneous sources for noisy data changing the source assembling. Although several studies on simultaneous-source inversion tried to estimate P- wave velocity based on the acoustic wave equation, seismic migration and waveform inversion based on the elastic wave equations are required to obtain more reliable subsurface information. In this study, we propose a 2-D frequency-domain elastic full waveform inversion technique using phase encoding methods. In our algorithm, the random phase encoding method is employed to calculate the gradients of the elastic parameters, source signature estimation and the diagonal entries of approximate Hessian matrix. The crosstalk for the estimated source signature and the diagonal entries of approximate Hessian matrix are suppressed with iteration as for the gradients. Our 2-D frequency-domain elastic waveform inversion algorithm is composed using the back-propagation technique and the conjugate-gradient method. Source signature is estimated using the full Newton method. We compare the simultaneous-source inversion with the conventional waveform inversion for synthetic data sets of the Marmousi-2 model. The inverted results obtained by simultaneous sources are comparable to those obtained by individual sources, and source signature is successfully estimated in simultaneous source technique. Comparing the inverted results using the pseudo Hessian matrix with previous inversion results
Choi, Yun Seok; Alkhalifah, Tariq Ali
2011-01-01
Full waveform inversion requires a good estimation of the source wavelet to improve our chances of a successful inversion. This is especially true for an encoded multisource time-domain implementation, which, conventionally, requires separate
Introduction to the 30th volume of Inverse Problems
Louis, Alfred K.
2014-01-01
The field of inverse problems is a fast-developing domain of research originating from the practical demands of finding the cause when a result is observed. The woodpecker, searching for insects, is probing a tree using sound waves: the information searched for is whether there is an insect or not, hence a 0-1 decision. When the result has to contain more information, ad hoc solutions are not at hand and more sophisticated methods have to be developed. Right from its first appearance, the field of inverse problems has been characterized by an interdisciplinary nature: the interpretation of measured data, reinforced by mathematical models serving the analyzing questions of observability, stability and resolution, developing efficient, stable and accurate algorithms to gain as much information as possible from the input and to feedback to the questions of optimal measurement configuration. As is typical for a new area of research, facets of it are separated and studied independently. Hence, fields such as the theory of inverse scattering, tomography in general and regularization methods have developed. However, all aspects have to be reassembled to arrive at the best possible solution to the problem at hand. This development is reflected by the first and still leading journal in the field, Inverse Problems. Founded by pioneers Roy Pike from London and Pierre Sabatier from Montpellier, who enjoyably describes the journal's nascence in his book Rêves et Combats d'un Enseignant-Chercheur, Retour Inverse [1], the journal has developed successfully over the last few decades. Neither the Editors-in-Chief, formerly called Honorary Editors, nor the board or authors could have set the path to success alone. Their fruitful interplay, complemented by the efficient and highly competent publishing team at IOP Publishing, has been fundamental. As such it is my honor and pleasure to follow my renowned colleagues Pierre Sabatier, Mario Bertero, Frank Natterer, Alberto Grünbaum and
From inverse problems to learning: a Statistical Mechanics approach
Baldassi, Carlo; Gerace, Federica; Saglietti, Luca; Zecchina, Riccardo
2018-01-01
We present a brief introduction to the statistical mechanics approaches for the study of inverse problems in data science. We then provide concrete new results on inferring couplings from sampled configurations in systems characterized by an extensive number of stable attractors in the low temperature regime. We also show how these result are connected to the problem of learning with realistic weak signals in computational neuroscience. Our techniques and algorithms rely on advanced mean-field methods developed in the context of disordered systems.
Energy Technology Data Exchange (ETDEWEB)
Tito, Mariella Janette Berrocal
2001-01-01
The analysis of inverse problems in participating media where emission, absorption and scattering take place has several relevant applications in engineering and medicine. Some of the techniques developed for the solution of inverse problems have as a first step the solution of the direct problem. In this work the discrete ordinates method has been used for the solution of the linearized Boltzmann equation in two dimensional cartesian geometry. The Levenberg - Marquardt method has been used for the solution of the inverse problem of internal source and absorption and scattering coefficient estimation. (author)
International Nuclear Information System (INIS)
Moura, C.A. de.
1976-09-01
We propose an algorithm for computing the potential V(x) associated to the one-dimensional Schroedinger operator E identical to - d 2 /dx 2 + V(x) -infinite < x< infinite from knowledge of the S.matrix, more exactly, of one of the reelection coefficients. The convergence of the algorithm is guaranteed by the stability results obtained for both the direct and inverse problems
Integrating the Toda Lattice with Self-Consistent Source via Inverse Scattering Method
International Nuclear Information System (INIS)
Urazboev, Gayrat
2012-01-01
In this work, there is shown that the solutions of Toda lattice with self-consistent source can be found by the inverse scattering method for the discrete Sturm-Liuville operator. For the considered problem the one-soliton solution is obtained.
Nonlinear problems in fluid dynamics and inverse scattering: Nonlinear waves and inverse scattering
Ablowitz, Mark J.
1994-12-01
Research investigations involving the fundamental understanding and applications of nonlinear wave motion and related studies of inverse scattering and numerical computation have been carried out and a number of significant results have been obtained. A class of nonlinear wave equations which can be solved by the inverse scattering transform (IST) have been studied, including the Kadaomtsev-Petviashvili (KP) equation, the Davey-Stewartson equation, and the 2+1 Toda system. The solutions obtained by IST correspond to the Cauchy initial value problem with decaying initial data. We have also solved two important systems via the IST method: a 'Volterra' system in 2+1 dimensions and a new one dimensional nonlinear equation which we refer to as the Toda differential-delay equation. Research in computational chaos in moderate to long time numerical simulations continues.
Inverse problem for in vivo NMR spatial localization
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Hasenfeld, A.C.
1985-11-01
The basic physical problem of NMR spatial localization is considered. To study diseased sites, one must solve the problem of adequately localizing the NMR signal. We formulate this as an inverse problem. As the NMR Bloch equations determine the motion of nuclear spins in applied magnetic fields, a theoretical study is undertaken to answer the question of how to design magnetic field configurations to achieve these localized excited spin populations. Because of physical constraints in the production of the relevant radiofrequency fields, the problem factors into a temporal one and a spatial one. We formulate the temporal problem as a nonlinear transformation, called the Bloch Transform, from the rf input to the magnetization response. In trying to invert this transformation, both linear (for the Fourier Transform) and nonlinear (for the Bloch Transform) modes of radiofrequency excitation are constructed. The spatial problem is essentially a statics problem for the Maxwell equations of electromagnetism, as the wavelengths of the radiation considered are on the order of ten meters, and so propagation effects are negligible. In the general case, analytic solutions are unavailable, and so the methods of computer simulation are used to map the rf field spatial profiles. Numerical experiments are also performed to verify the theoretical analysis, and experimental confirmation of the theory is carried out on the 0.5 Tesla IBM/Oxford Imaging Spectrometer at the LBL NMR Medical Imaging Facility. While no explicit inverse is constructed to ''solve'' this problem, the combined theoretical/numerical analysis is validated experimentally, justifying the approximations made. 56 refs., 31 figs.
Inverse problem for in vivo NMR spatial localization
International Nuclear Information System (INIS)
Hasenfeld, A.C.
1985-11-01
The basic physical problem of NMR spatial localization is considered. To study diseased sites, one must solve the problem of adequately localizing the NMR signal. We formulate this as an inverse problem. As the NMR Bloch equations determine the motion of nuclear spins in applied magnetic fields, a theoretical study is undertaken to answer the question of how to design magnetic field configurations to achieve these localized excited spin populations. Because of physical constraints in the production of the relevant radiofrequency fields, the problem factors into a temporal one and a spatial one. We formulate the temporal problem as a nonlinear transformation, called the Bloch Transform, from the rf input to the magnetization response. In trying to invert this transformation, both linear (for the Fourier Transform) and nonlinear (for the Bloch Transform) modes of radiofrequency excitation are constructed. The spatial problem is essentially a statics problem for the Maxwell equations of electromagnetism, as the wavelengths of the radiation considered are on the order of ten meters, and so propagation effects are negligible. In the general case, analytic solutions are unavailable, and so the methods of computer simulation are used to map the rf field spatial profiles. Numerical experiments are also performed to verify the theoretical analysis, and experimental confirmation of the theory is carried out on the 0.5 Tesla IBM/Oxford Imaging Spectrometer at the LBL NMR Medical Imaging Facility. While no explicit inverse is constructed to ''solve'' this problem, the combined theoretical/numerical analysis is validated experimentally, justifying the approximations made. 56 refs., 31 figs
Efficient Inversion of Mult-frequency and Multi-Source Electromagnetic Data
Energy Technology Data Exchange (ETDEWEB)
Gary D. Egbert
2007-03-22
The project covered by this report focused on development of efficient but robust non-linear inversion algorithms for electromagnetic induction data, in particular for data collected with multiple receivers, and multiple transmitters, a situation extremely common in eophysical EM subsurface imaging methods. A key observation is that for such multi-transmitter problems each step in commonly used linearized iterative limited memory search schemes such as conjugate gradients (CG) requires solution of forward and adjoint EM problems for each of the N frequencies or sources, essentially generating data sensitivities for an N dimensional data-subspace. These multiple sensitivities allow a good approximation to the full Jacobian of the data mapping to be built up in many fewer search steps than would be required by application of textbook optimization methods, which take no account of the multiplicity of forward problems that must be solved for each search step. We have applied this idea to a develop a hybrid inversion scheme that combines features of the iterative limited memory type methods with a Newton-type approach using a partial calculation of the Jacobian. Initial tests on 2D problems show that the new approach produces results essentially identical to a Newton type Occam minimum structure inversion, while running more rapidly than an iterative (fixed regularization parameter) CG style inversion. Memory requirements, while greater than for something like CG, are modest enough that even in 3D the scheme should allow 3D inverse problems to be solved on a common desktop PC, at least for modest (~ 100 sites, 15-20 frequencies) data sets. A secondary focus of the research has been development of a modular system for EM inversion, using an object oriented approach. This system has proven useful for more rapid prototyping of inversion algorithms, in particular allowing initial development and testing to be conducted with two-dimensional example problems, before
Irving, J.; Koepke, C.; Elsheikh, A. H.
2017-12-01
Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward process model linking subsurface parameters to measured data, which is typically assumed to be known perfectly in the inversion procedure. However, in order to make the stochastic solution of the inverse problem computationally tractable using, for example, Markov-chain-Monte-Carlo (MCMC) methods, fast approximations of the forward model are commonly employed. This introduces model error into the problem, which has the potential to significantly bias posterior statistics and hamper data integration efforts if not properly accounted for. Here, we present a new methodology for addressing the issue of model error in Bayesian solutions to hydrogeophysical inverse problems that is geared towards the common case where these errors cannot be effectively characterized globally through some parametric statistical distribution or locally based on interpolation between a small number of computed realizations. Rather than focusing on the construction of a global or local error model, we instead work towards identification of the model-error component of the residual through a projection-based approach. In this regard, pairs of approximate and detailed model runs are stored in a dictionary that grows at a specified rate during the MCMC inversion procedure. At each iteration, a local model-error basis is constructed for the current test set of model parameters using the K-nearest neighbour entries in the dictionary, which is then used to separate the model error from the other error sources before computing the likelihood of the proposed set of model parameters. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar traveltime data for three different subsurface parameterizations of varying complexity. The synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed in the inversion
Incremental projection approach of regularization for inverse problems
Energy Technology Data Exchange (ETDEWEB)
Souopgui, Innocent, E-mail: innocent.souopgui@usm.edu [The University of Southern Mississippi, Department of Marine Science (United States); Ngodock, Hans E., E-mail: hans.ngodock@nrlssc.navy.mil [Naval Research Laboratory (United States); Vidard, Arthur, E-mail: arthur.vidard@imag.fr; Le Dimet, François-Xavier, E-mail: ledimet@imag.fr [Laboratoire Jean Kuntzmann (France)
2016-10-15
This paper presents an alternative approach to the regularized least squares solution of ill-posed inverse problems. Instead of solving a minimization problem with an objective function composed of a data term and a regularization term, the regularization information is used to define a projection onto a convex subspace of regularized candidate solutions. The objective function is modified to include the projection of each iterate in the place of the regularization. Numerical experiments based on the problem of motion estimation for geophysical fluid images, show the improvement of the proposed method compared with regularization methods. For the presented test case, the incremental projection method uses 7 times less computation time than the regularization method, to reach the same error target. Moreover, at convergence, the incremental projection is two order of magnitude more accurate than the regularization method.
Sequential Inverse Problems Bayesian Principles and the Logistic Map Example
Duan, Lian; Farmer, Chris L.; Moroz, Irene M.
2010-09-01
Bayesian statistics provides a general framework for solving inverse problems, but is not without interpretation and implementation problems. This paper discusses difficulties arising from the fact that forward models are always in error to some extent. Using a simple example based on the one-dimensional logistic map, we argue that, when implementation problems are minimal, the Bayesian framework is quite adequate. In this paper the Bayesian Filter is shown to be able to recover excellent state estimates in the perfect model scenario (PMS) and to distinguish the PMS from the imperfect model scenario (IMS). Through a quantitative comparison of the way in which the observations are assimilated in both the PMS and the IMS scenarios, we suggest that one can, sometimes, measure the degree of imperfection.
A direct sampling method to an inverse medium scattering problem
Ito, Kazufumi
2012-01-10
In this work we present a novel sampling method for time harmonic inverse medium scattering problems. It provides a simple tool to directly estimate the shape of the unknown scatterers (inhomogeneous media), and it is applicable even when the measured data are only available for one or two incident directions. A mathematical derivation is provided for its validation. Two- and three-dimensional numerical simulations are presented, which show that the method is accurate even with a few sets of scattered field data, computationally efficient, and very robust with respect to noises in the data. © 2012 IOP Publishing Ltd.
Solution of inverse localization problem associated to multistatic radar system
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Boutkhil M.
2016-01-01
Full Text Available This work deals with the problem of inverse localization by a target with the aim to retrieve the position of the target, given the intensity and phase of the electromagnetic waves scattered by this object. Assuming the surface cross section to be known as well as the intensity and phase of the scattered waves, the target position was reconstructed through the echo signals scattered of each bistatic. We develop in the same time a multistatic ambiguity function trough bistatic ambiguity function to investigate several fundamental aspects that determine multistatic radar performance. We used a multistatic radar constructed of two bistatic radars, two transmitters and one receiver.
On Lambda and Time Operators: the Inverse Intertwining Problem Revisited
Gómez-Cubillo, F.; Suchanecki, Z.; Villullas, S.
2011-07-01
An exact theory of irreversibility was proposed by Misra, Prigogine and Courbage, based on non-unitary similarity transformations Λ that intertwine reversible dynamics and irreversible ones. This would advocate the idea that irreversible behavior would originate at the microscopic level. Reversible evolution with an internal time operator have the intertwining property. Recently the inverse intertwining problem has been answered in the negative, that is, not every unitary evolution allowing such Λ-transformation has an internal time. This work contributes new results in this direction.
Trinification, the hierarchy problem, and inverse seesaw neutrino masses
International Nuclear Information System (INIS)
Cauet, Christophe; Paes, Heinrich; Wiesenfeldt, Soeren
2011-01-01
In minimal trinification models light neutrino masses can be generated via a radiative seesaw mechanism, where the masses of the right-handed neutrinos originate from loops involving Higgs and fermion fields at the unification scale. This mechanism is absent in models aiming at solving or ameliorating the hierarchy problem, such as low-energy supersymmetry, since the large seesaw scale disappears. In this case, neutrino masses need to be generated via a TeV-scale mechanism. In this paper, we investigate an inverse seesaw mechanism and discuss some phenomenological consequences.
A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems
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Fatemeh Mohammad
2014-05-01
Full Text Available In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem $Ax = \\lambda Bx$[Q.~Ye and P.~Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011 1697-1715]. In particular, the linear convergence property of the inverse subspace iteration is preserved.
The Adjoint Method for the Inverse Problem of Option Pricing
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Shou-Lei Wang
2014-01-01
Full Text Available The estimation of implied volatility is a typical PDE inverse problem. In this paper, we propose the TV-L1 model for identifying the implied volatility. The optimal volatility function is found by minimizing the cost functional measuring the discrepancy. The gradient is computed via the adjoint method which provides us with an exact value of the gradient needed for the minimization procedure. We use the limited memory quasi-Newton algorithm (L-BFGS to find the optimal and numerical examples shows the effectiveness of the presented method.
One-dimensional scattering problem for inverse square potential
International Nuclear Information System (INIS)
Mineev, V.S.
1990-01-01
Analytical continuation of the solution for the Schroedinger equation of inverse square potential, together with the modified method for variation of constants makes it possible to construct admittable self-adjoint extensions and to completely analyze the respective scattering problem along the entire line. In this case, the current density conservation and the wave function continuity when passing through the singular point x=0 require, that a 8-shaped induced potential should be introduced in the Schroedinger equation. The relevant calculations have shown that the potential x -2 can be either absolutely penetrable or absolutely impenetrable. 16 refs
Topological inversion for solution of geodesy-constrained geophysical problems
Saltogianni, Vasso; Stiros, Stathis
2015-04-01
Geodetic data, mostly GPS observations, permit to measure displacements of selected points around activated faults and volcanoes, and on the basis of geophysical models, to model the underlying physical processes. This requires inversion of redundant systems of highly non-linear equations with >3 unknowns; a situation analogous to the adjustment of geodetic networks. However, in geophysical problems inversion cannot be based on conventional least-squares techniques, and is based on numerical inversion techniques (a priori fixing of some variables, optimization in steps with values of two variables each time to be regarded fixed, random search in the vicinity of approximate solutions). Still these techniques lead to solutions trapped in local minima, to correlated estimates and to solutions with poor error control (usually sampling-based approaches). To overcome these problems, a numerical-topological, grid-search based technique in the RN space is proposed (N the number of unknown variables). This technique is in fact a generalization and refinement of techniques used in lighthouse positioning and in some cases of low-accuracy 2-D positioning using Wi-Fi etc. The basic concept is to assume discrete possible ranges of each variable, and from these ranges to define a grid G in the RN space, with some of the gridpoints to approximate the true solutions of the system. Each point of hyper-grid G is then tested whether it satisfies the observations, given their uncertainty level, and successful grid points define a sub-space of G containing the true solutions. The optimal (minimal) space containing one or more solutions is obtained using a trial-and-error approach, and a single optimization factor. From this essentially deterministic identification of the set of gridpoints satisfying the system of equations, at a following step, a stochastic optimal solution is computed corresponding to the center of gravity of this set of gridpoints. This solution corresponds to a
Inverse free electron laser accelerator for advanced light sources
Directory of Open Access Journals (Sweden)
J. P. Duris
2012-06-01
Full Text Available We discuss the inverse free electron laser (IFEL scheme as a compact high gradient accelerator solution for driving advanced light sources such as a soft x-ray free electron laser amplifier or an inverse Compton scattering based gamma-ray source. In particular, we present a series of new developments aimed at improving the design of future IFEL accelerators. These include a new procedure to optimize the choice of the undulator tapering, a new concept for prebunching which greatly improves the fraction of trapped particles and the final energy spread, and a self-consistent study of beam loading effects which leads to an energy-efficient high laser-to-beam power conversion.
Retrieving global aerosol sources from satellites using inverse modeling
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O. Dubovik
2008-01-01
Full Text Available Understanding aerosol effects on global climate requires knowing the global distribution of tropospheric aerosols. By accounting for aerosol sources, transports, and removal processes, chemical transport models simulate the global aerosol distribution using archived meteorological fields. We develop an algorithm for retrieving global aerosol sources from satellite observations of aerosol distribution by inverting the GOCART aerosol transport model.
The inversion is based on a generalized, multi-term least-squares-type fitting, allowing flexible selection and refinement of a priori algorithm constraints. For example, limitations can be placed on retrieved quantity partial derivatives, to constrain global aerosol emission space and time variability in the results. Similarities and differences between commonly used inverse modeling and remote sensing techniques are analyzed. To retain the high space and time resolution of long-period, global observational records, the algorithm is expressed using adjoint operators.
Successful global aerosol emission retrievals at 2°×2.5 resolution were obtained by inverting GOCART aerosol transport model output, assuming constant emissions over the diurnal cycle, and neglecting aerosol compositional differences. In addition, fine and coarse mode aerosol emission sources were inverted separately from MODIS fine and coarse mode aerosol optical thickness data, respectively. These assumptions are justified, based on observational coverage and accuracy limitations, producing valuable aerosol source locations and emission strengths. From two weeks of daily MODIS observations during August 2000, the global placement of fine mode aerosol sources agreed with available independent knowledge, even though the inverse method did not use any a priori information about aerosol sources, and was initialized with a "zero aerosol emission" assumption. Retrieving coarse mode aerosol emissions was less successful
Using Inverse Problem Methods with Surveillance Data in Pneumococcal Vaccination
Sutton, Karyn L.; Banks, H. T.; Castillo-Chavez, Carlos
2010-01-01
The design and evaluation of epidemiological control strategies is central to public health policy. While inverse problem methods are routinely used in many applications, this remains an area in which their use is relatively rare, although their potential impact is great. We describe methods particularly relevant to epidemiological modeling at the population level. These methods are then applied to the study of pneumococcal vaccination strategies as a relevant example which poses many challenges common to other infectious diseases. We demonstrate that relevant yet typically unknown parameters may be estimated, and show that a calibrated model may used to assess implemented vaccine policies through the estimation of parameters if vaccine history is recorded along with infection and colonization information. Finally, we show how one might determine an appropriate level of refinement or aggregation in the age-structured model given age-stratified observations. These results illustrate ways in which the collection and analysis of surveillance data can be improved using inverse problem methods. PMID:20209093
Digital holography of particles: benefits of the 'inverse problem' approach
International Nuclear Information System (INIS)
Gire, J; Denis, L; Fournier, C; Soulez, F; Ducottet, C; Thiébaut, E
2008-01-01
The potential of in-line digital holography to locate and measure the size of particles distributed throughout a volume (in one shot) has been established. These measurements are fundamental for the study of particle trajectories in fluid flow. The most important issues in digital holography today are poor depth positioning accuracy, transverse field-of-view limitations, border artifacts and computational burdens. We recently suggested an 'inverse problem' approach to address some of these issues for the processing of particle digital holograms. The described algorithm improves axial positioning accuracy, gives particle diameters with sub-micrometer accuracy, eliminates border effects and increases the size of the studied volume. This approach for processing particle holograms pushes back some classical constraints. For example, the Nyquist criterion is no longer a restriction for the recording step and the studied volume is no longer confined to the field of view delimited by the sensor borders. In this paper we present a review of the limitations commonly found in digital holography. We then discuss the benefits of the 'inverse problem' approach and the influence of some experimental parameters in this framework
Reconstructing the Hopfield network as an inverse Ising problem
International Nuclear Information System (INIS)
Huang Haiping
2010-01-01
We test four fast mean-field-type algorithms on Hopfield networks as an inverse Ising problem. The equilibrium behavior of Hopfield networks is simulated through Glauber dynamics. In the low-temperature regime, the simulated annealing technique is adopted. Although performances of these network reconstruction algorithms on the simulated network of spiking neurons are extensively studied recently, the analysis of Hopfield networks is lacking so far. For the Hopfield network, we found that, in the retrieval phase favored when the network wants to memory one of stored patterns, all the reconstruction algorithms fail to extract interactions within a desired accuracy, and the same failure occurs in the spin-glass phase where spurious minima show up, while in the paramagnetic phase, albeit unfavored during the retrieval dynamics, the algorithms work well to reconstruct the network itself. This implies that, as an inverse problem, the paramagnetic phase is conversely useful for reconstructing the network while the retrieval phase loses all the information about interactions in the network except for the case where only one pattern is stored. The performances of algorithms are studied with respect to the system size, memory load, and temperature; sample-to-sample fluctuations are also considered.
NON-INVASIVE INVERSE PROBLEM IN CIVIL ENGINEERING
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Jan Havelka
2017-11-01
Full Text Available In this contribution we focus on recovery of spatial distribution of material parameters utilizing only non-invasive boundary measurements. Such methods has gained its importance as imaging techniques in medicine, geophysics or archaeology. We apply similar principles for non-stationary heat transfer in civil engineering. In oppose to standard technique which rely on external loading devices, we assume the natural fluctuation of temperature throughout day and night can provide sufficient information to recover the underlying material parameters. The inverse problem was solved by a modified regularised Gauss-Newton iterative scheme and the underlying forward problem is solved with a finite element space-time discretisation. We show a successful reconstruction of material parameters on a synthetic example with real measurements. The virtual experiment also reveals the insensitivity to practical precision of sensor measurements.
The Inverse Problem of Identification of Hydrogen Permeability Model
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Yury V. Zaika
2018-01-01
Full Text Available One of the technological challenges for hydrogen materials science is the currently active search for structural materials with important applications (including the ITER project and gas-separation plants. One had to estimate the parameters of diffusion and sorption to numerically model the different scenarios and experimental conditions of the material usage (including extreme ones. The article presents boundary value problems of hydrogen permeability and thermal desorption with dynamical boundary conditions. A numerical method is developed for TDS spectrum simulation, where only integration of a nonlinear system of low order ordinary differential equations is required. The main final output of the article is a noise-resistant algorithm for solving the inverse problem of parametric identification for the aggregated experiment where desorption and diffusion are dynamically interrelated (without the artificial division of studies into the diffusion limited regime (DLR and the surface limited regime (SLR.
Optimization method for an evolutional type inverse heat conduction problem
International Nuclear Information System (INIS)
Deng Zuicha; Yu Jianning; Yang Liu
2008-01-01
This paper deals with the determination of a pair (q, u) in the heat conduction equation u t -u xx +q(x,t)u=0, with initial and boundary conditions u(x,0)=u 0 (x), u x vertical bar x=0 =u x vertical bar x=1 =0, from the overspecified data u(x, t) = g(x, t). By the time semi-discrete scheme, the problem is transformed into a sequence of inverse problems in which the unknown coefficients are purely space dependent. Based on the optimal control framework, the existence, uniqueness and stability of the solution (q, u) are proved. A necessary condition which is a couple system of a parabolic equation and parabolic variational inequality is deduced
Optimization method for an evolutional type inverse heat conduction problem
Deng, Zui-Cha; Yu, Jian-Ning; Yang, Liu
2008-01-01
This paper deals with the determination of a pair (q, u) in the heat conduction equation u_t-u_{xx}+q(x,t)u=0, with initial and boundary conditions u(x,0)=u_0(x),\\qquad u_x|_{x=0}=u_x|_{x=1}=0, from the overspecified data u(x, t) = g(x, t). By the time semi-discrete scheme, the problem is transformed into a sequence of inverse problems in which the unknown coefficients are purely space dependent. Based on the optimal control framework, the existence, uniqueness and stability of the solution (q, u) are proved. A necessary condition which is a couple system of a parabolic equation and parabolic variational inequality is deduced.
Inverse problem for extragalactic transport of ultra-high energy cosmic rays
International Nuclear Information System (INIS)
Ptuskin, V.S.; Rogovaya, S.I.; Zirakashvili, V.N.
2015-01-01
The energy spectra and composition of ultra-high energy cosmic rays are changing in a course of propagation in the expanding Universe filled with background radiation. We developed a numerical code for solution of inverse problem for cosmic-ray transport equations that allows the determination of average source spectra of different nuclei from the cosmic ray spectra observed at the Earth. Employing this approach, the injection spectra of protons and Iron nuclei in extragalactic sources are found assuming that only these species are accelerated at the source. The data from the Auger experiment and the combined data from the Telescope Array + HiRes experiments are used to illustrate the method
Inverse problem for extragalactic transport of ultra-high energy cosmic rays
Energy Technology Data Exchange (ETDEWEB)
Ptuskin, V.S.; Rogovaya, S.I.; Zirakashvili, V.N., E-mail: vptuskin@izmiran.ru, E-mail: rogovaya@izmiran.ru, E-mail: zirak@izmiran.ru [Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation of the Russian Academy of Sciences (IZMIRAN), Troitsk, Moscow, 142190 (Russian Federation)
2015-03-01
The energy spectra and composition of ultra-high energy cosmic rays are changing in a course of propagation in the expanding Universe filled with background radiation. We developed a numerical code for solution of inverse problem for cosmic-ray transport equations that allows the determination of average source spectra of different nuclei from the cosmic ray spectra observed at the Earth. Employing this approach, the injection spectra of protons and Iron nuclei in extragalactic sources are found assuming that only these species are accelerated at the source. The data from the Auger experiment and the combined data from the Telescope Array + HiRes experiments are used to illustrate the method.
Inverse problem and uncertainty quantification: application to compressible gas dynamics
International Nuclear Information System (INIS)
Birolleau, Alexandre
2014-01-01
This thesis deals with uncertainty propagation and the resolution of inverse problems together with their respective acceleration via Polynomial Chaos. The object of this work is to present a state of the art and a numerical analysis of this stochastic spectral method, in order to understand its pros and cons when tackling the probabilistic study of hydrodynamical instabilities in Richtmyer-Meshkov shock tube experiments. The first chapter is introductory and allows understanding the stakes of being able to accurately take into account uncertainties in compressible gas dynamics simulations. The second chapter is both an illustrative state of the art on generalized Polynomial Chaos and a full numerical analysis of the method keeping in mind the final application on hydrodynamical problems developing shocks and discontinuous solutions. In this chapter, we introduce a new method, naming iterative generalized Polynomial Chaos, which ensures a gain with respect to generalized Polynomial Chaos, especially with non smooth solutions. Chapter three is closely related to an accepted publication in Communication in Computational Physics. It deals with stochastic inverse problems and introduces bayesian inference. It also emphasizes the possibility of accelerating the bayesian inference thanks to iterative generalized Polynomial Chaos described in the previous chapter. Theoretical convergence is established and illustrated on several test-cases. The last chapter consists in the application of the above materials to a complex and ambitious compressible gas dynamics problem (Richtmyer-Meshkov shock tube configuration) together with a deepened study of the physico-numerical phenomenon at stake. Finally, in the appendix, we also present some interesting research paths we quickly tackled during this thesis. (author) [fr
Comparison of optimal design methods in inverse problems
International Nuclear Information System (INIS)
Banks, H T; Holm, K; Kappel, F
2011-01-01
Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst–Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667–77; De Gaetano A and Arino O 2000 J. Math. Biol. 40 136–68; Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979–90)
Comparison of optimal design methods in inverse problems
Banks, H. T.; Holm, K.; Kappel, F.
2011-07-01
Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).
Tangborn, Andrew; Cooper, Robert; Pawson, Steven; Sun, Zhibin
2009-01-01
We present a source inversion technique for chemical constituents that uses assimilated constituent observations rather than directly using the observations. The method is tested with a simple model problem, which is a two-dimensional Fourier-Galerkin transport model combined with a Kalman filter for data assimilation. Inversion is carried out using a Green's function method and observations are simulated from a true state with added Gaussian noise. The forecast state uses the same spectral spectral model, but differs by an unbiased Gaussian model error, and emissions models with constant errors. The numerical experiments employ both simulated in situ and satellite observation networks. Source inversion was carried out by either direct use of synthetically generated observations with added noise, or by first assimilating the observations and using the analyses to extract observations. We have conducted 20 identical twin experiments for each set of source and observation configurations, and find that in the limiting cases of a very few localized observations, or an extremely large observation network there is little advantage to carrying out assimilation first. However, in intermediate observation densities, there decreases in source inversion error standard deviation using the Kalman filter algorithm followed by Green's function inversion by 50% to 95%.
Sound source reconstruction using inverse boundary element calculations
DEFF Research Database (Denmark)
Schuhmacher, Andreas; Hald, Jørgen; Rasmussen, Karsten Bo
2003-01-01
Whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure, the aim in this work is to reverse the process, i.e., to determine vibration from acoustic field data. This inverse problem is brought on a form suited ...... it is demonstrated that the L-curve criterion is robust with respect to the errors in a real measurement situation. In particular, it is shown that the L-curve criterion is superior to the more conventional generalized cross-validation (GCV) approach for the present tire noise studies....
Invisibility problem in acoustics, electromagnetism and heat transfer. Inverse design method
Alekseev, G.; Tokhtina, A.; Soboleva, O.
2017-10-01
Two approaches (direct design and inverse design methods) for solving problems of designing devices providing invisibility of material bodies of detection using different physical fields - electromagnetic, acoustic and static are discussed. The second method is applied for solving problems of designing cloaking devices for the 3D stationary thermal scattering model. Based on this method the design problems under study are reduced to respective control problems. The material parameters (radial and tangential heat conductivities) of the inhomogeneous anisotropic medium filling the thermal cloak and the density of auxiliary heat sources play the role of controls. A unique solvability of direct thermal scattering problem in the Sobolev space is proved and the new estimates of solutions are established. Using these results, the solvability of control problem is proved and the optimality system is derived. Based on analysis of optimality system, the stability estimates of optimal solutions are established and numerical algorithms for solving particular thermal cloaking problem are proposed.
Information criteria to estimate hyperparameters in groundwater inverse problems
Zanini, A.; Tanda, M. G.; Woodbury, A. D.
2017-12-01
One of the main issues in groundwater modeling is the knowledge of the hydraulic parameters such as transmissivity and storativity. In literature there are several efficacious inverse methods that are able to estimate these unknown properties. Most methods assume, as a priori knowledge, the form of the variogram (or covariance function) of the unknown parameters. The hyperparameters of the variogram (or covariance function) can be inferred from observations, assumed known or estimated. Information criteria are widely used in inverse problems in several disciplines (such as geophysics, hydrology, ...) to estimate the hyperparameters. In this work, in order to estimate the hyperparameters, we consider the Akaike Information Criterion (AIC) and the Akaike Bayesian Information Criterion (ABIC). AIC is computed as -2 ln[fitted model]+2 number of unknown parameters. The iterative procedure allows to identify the hyperparameters that minimize the AIC. The ABIC is similar to the AIC in form and is computed in terms of the Bayesian likelihood; it is appropriate when prior information is considered in the form of prior probability. ABIC = -2 ln[predictive distribution]+2 (number of hyperparameters). The predictive distribution is the normalizing constant that is at the denominator of the Bayes theorem and represents the pdf of observing the data with the uncertainty in the model parameters marginalized out of consideration. The correct hyperparameters are evaluated at the minimum value of the ABIC. In this work we compare the results obtained from AIC to ABIC, using a literature example and we describe pros and cons of the two approaches.
Solution accelerators for large scale 3D electromagnetic inverse problems
International Nuclear Information System (INIS)
Newman, Gregory A.; Boggs, Paul T.
2004-01-01
We provide a framework for preconditioning nonlinear 3D electromagnetic inverse scattering problems using nonlinear conjugate gradient (NLCG) and limited memory (LM) quasi-Newton methods. Key to our approach is the use of an approximate adjoint method that allows for an economical approximation of the Hessian that is updated at each inversion iteration. Using this approximate Hessian as a preconditoner, we show that the preconditioned NLCG iteration converges significantly faster than the non-preconditioned iteration, as well as converging to a data misfit level below that observed for the non-preconditioned method. Similar conclusions are also observed for the LM iteration; preconditioned with the approximate Hessian, the LM iteration converges faster than the non-preconditioned version. At this time, however, we see little difference between the convergence performance of the preconditioned LM scheme and the preconditioned NLCG scheme. A possible reason for this outcome is the behavior of the line search within the LM iteration. It was anticipated that, near convergence, a step size of one would be approached, but what was observed, instead, were step lengths that were nowhere near one. We provide some insights into the reasons for this behavior and suggest further research that may improve the performance of the LM methods
Sparse contrast-source inversion using linear-shrinkage-enhanced inexact Newton method
Desmal, Abdulla
2014-07-01
A contrast-source inversion scheme is proposed for microwave imaging of domains with sparse content. The scheme uses inexact Newton and linear shrinkage methods to account for the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem, respectively. Thresholded shrinkage iterations are accelerated using a preconditioning technique. Additionally, during Newton iterations, the weight of the penalty term is reduced consistently with the quadratic convergence of the Newton method to increase accuracy and efficiency. Numerical results demonstrate the applicability of the proposed method.
Sparse contrast-source inversion using linear-shrinkage-enhanced inexact Newton method
Desmal, Abdulla; Bagci, Hakan
2014-01-01
A contrast-source inversion scheme is proposed for microwave imaging of domains with sparse content. The scheme uses inexact Newton and linear shrinkage methods to account for the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem, respectively. Thresholded shrinkage iterations are accelerated using a preconditioning technique. Additionally, during Newton iterations, the weight of the penalty term is reduced consistently with the quadratic convergence of the Newton method to increase accuracy and efficiency. Numerical results demonstrate the applicability of the proposed method.
Davari, Sadegh; Sha, Lui
1992-01-01
In the design of real-time systems, tasks are often assigned priorities. Preemptive priority driven schedulers are used to schedule tasks to meet the timing requirements. Priority inversion is the term used to describe the situation when a higher priority task's execution is delayed by lower priority tasks. Priority inversion can occur when there is contention for resources among tasks of different priorities. The duration of priority inversion could be long enough to cause tasks to miss their dead lines. Priority inversion cannot be completely eliminated. However, it is important to identify sources of priority inversion and minimize the duration of priority inversion. In this paper, a comprehensive review of the problem of and solutions to unbounded priority inversion is presented.
An inverse problem for a mathematical model of aquaponic agriculture
Bobak, Carly; Kunze, Herb
2017-01-01
Aquaponic agriculture is a sustainable ecosystem that relies on a symbiotic relationship between fish and macrophytes. While the practice has been growing in popularity, relatively little mathematical models exist which aim to study the system processes. In this paper, we present a system of ODEs which aims to mathematically model the population and concetrations dynamics present in an aquaponic environment. Values of the parameters in the system are estimated from the literature so that simulated results can be presented to illustrate the nature of the solutions to the system. As well, a brief sensitivity analysis is performed in order to identify redundant parameters and highlight those which may need more reliable estimates. Specifically, an inverse problem with manufactured data for fish and plants is presented to demonstrate the ability of the collage theorem to recover parameter estimates.
Alloy design as an inverse problem of cluster expansion models
DEFF Research Database (Denmark)
Larsen, Peter Mahler; Kalidindi, Arvind R.; Schmidt, Søren
2017-01-01
Central to a lattice model of an alloy system is the description of the energy of a given atomic configuration, which can be conveniently developed through a cluster expansion. Given a specific cluster expansion, the ground state of the lattice model at 0 K can be solved by finding the configurat......Central to a lattice model of an alloy system is the description of the energy of a given atomic configuration, which can be conveniently developed through a cluster expansion. Given a specific cluster expansion, the ground state of the lattice model at 0 K can be solved by finding...... the inverse problem in terms of energetically distinct configurations, using a constraint satisfaction model to identify constructible configurations, and show that a convex hull can be used to identify ground states. To demonstrate the approach, we solve for all ground states for a binary alloy in a 2D...
Using mixed data in the inverse scattering problem
International Nuclear Information System (INIS)
Lassaut, M.; Larsen, S.Y.; Sofianos, S.A.; Wallet, J.C.
2008-01-01
Consider the fixed-l inverse scattering problem. We show that the zeros of the regular solution of the Schroedinger equation, τ n (E), which are monotonic functions of the energy, determine a unique potential when the domain of the energy is such that the τ n (E) range from zero to infinity. This suggest that the use of the mixed data of phase-shifts (δ(l 0 , k),k ≥ k 0 ) set-theoretic union (δ(l,k 0 ),l ≥ l 0 ), for which the zeros of the regular solution are monotonic in both domains, and range from zero to infinity, offers the possibility of determining the potential in a unique way. (author)
Resolving the existence of Higgsinos in the LHC inverse problem
International Nuclear Information System (INIS)
Jung, Sunghoon
2014-01-01
The LHC inverse problem is infamously challenging when neutralinos and charginos are heavy and pure and other superparticles are decoupled. This limit is becoming more relevant to particle physics nowadays. Fortunately, in this limit, Higgsinos produce a distinctive signature if they are the LSPs or NLSPs. The identifying signature is the presence of equal numbers of Z bosons and Higgs bosons in NLSP productions and subsequent decays at hadron colliders. The signature is derived from the Goldstone equivalence theorem by which partial widths into Z and Higgs bosons are inherently related and from the fact that Higgsinos consist of two indistinguishable neutralinos. Thus it is valid in general for many supersymmetry models; exceptions may happen when Higgsino NLSPs decay to weakly coupled LSPs such as axinos or gravitinos.
On the inverse problem of dissipative scattering theory. 3
International Nuclear Information System (INIS)
Neidhardt, H.
1988-01-01
Considering a scattering theory in the class of contractions on Hilbert spaces one solves the inverse problem in an operaor-theoretical manner. The solution is obtained underthe very general assumptions that the free evolutions are different for different time directions that not only the perturbed or full evolutions but also the free evolutions are given by contractions. It is shown that the class of contractive Hankel operators can be viewed as a set of scattering operators. This implies the possibility that the scattering operator can be compact. Moreover, the result is applied to the so-called Lax-Phillips scattering theory with losses restoring a result of B.S. Pavlov on the completion of this theory in a quite different manner. 15 refs
MARE2DEM: a 2-D inversion code for controlled-source electromagnetic and magnetotelluric data
Key, Kerry
2016-10-01
This work presents MARE2DEM, a freely available code for 2-D anisotropic inversion of magnetotelluric (MT) data and frequency-domain controlled-source electromagnetic (CSEM) data from onshore and offshore surveys. MARE2DEM parametrizes the inverse model using a grid of arbitrarily shaped polygons, where unstructured triangular or quadrilateral grids are typically used due to their ease of construction. Unstructured grids provide significantly more geometric flexibility and parameter efficiency than the structured rectangular grids commonly used by most other inversion codes. Transmitter and receiver components located on topographic slopes can be tilted parallel to the boundary so that the simulated electromagnetic fields accurately reproduce the real survey geometry. The forward solution is implemented with a goal-oriented adaptive finite-element method that automatically generates and refines unstructured triangular element grids that conform to the inversion parameter grid, ensuring accurate responses as the model conductivity changes. This dual-grid approach is significantly more efficient than the conventional use of a single grid for both the forward and inverse meshes since the more detailed finite-element meshes required for accurate responses do not increase the memory requirements of the inverse problem. Forward solutions are computed in parallel with a highly efficient scaling by partitioning the data into smaller independent modeling tasks consisting of subsets of the input frequencies, transmitters and receivers. Non-linear inversion is carried out with a new Occam inversion approach that requires fewer forward calls. Dense matrix operations are optimized for memory and parallel scalability using the ScaLAPACK parallel library. Free parameters can be bounded using a new non-linear transformation that leaves the transformed parameters nearly the same as the original parameters within the bounds, thereby reducing non-linear smoothing effects. Data
Liu, Lu
2017-08-17
This paper presents a workflow for near-surface velocity automatic estimation using the early arrivals of seismic data. This workflow comprises two methods, source-domain full traveltime inversion (FTI) and early-arrival waveform inversion. Source-domain FTI is capable of automatically generating a background velocity that can kinematically match the reconstructed plane-wave sources of early arrivals with true plane-wave sources. This method does not require picking first arrivals for inversion, which is one of the most challenging aspects of ray-based first-arrival tomographic inversion. Moreover, compared with conventional Born-based methods, source-domain FTI can distinguish between slower or faster initial model errors via providing the correct sign of the model gradient. In addition, this method does not need estimation of the source wavelet, which is a requirement for receiver-domain wave-equation velocity inversion. The model derived from source-domain FTI is then used as input to early-arrival waveform inversion to obtain the short-wavelength velocity components. We have tested the workflow on synthetic and field seismic data sets. The results show source-domain FTI can generate reasonable background velocities for early-arrival waveform inversion even when subsurface velocity reversals are present and the workflow can produce a high-resolution near-surface velocity model.
Inverse problem of Ocean Acoustic Tomography (OAT) - A numerical experiment
Digital Repository Service at National Institute of Oceanography (India)
Murty, T.V.R.; Somayajulu, Y.K.; Mahadevan, R.; Murty, C.S.
Acoustic model simulation experiments related to the forward and inverse aspects of ocean tomography have been taken up with a view to estimate the vertical sound speed field by inverting the travel time data. Two methods of inversion have been...
Methods and Algorithms for Solving Inverse Problems for Fractional Advection-Dispersion Equations
Aldoghaither, Abeer
2015-11-12
Fractional calculus has been introduced as an e cient tool for modeling physical phenomena, thanks to its memory and hereditary properties. For example, fractional models have been successfully used to describe anomalous di↵usion processes such as contaminant transport in soil, oil flow in porous media, and groundwater flow. These models capture important features of particle transport such as particles with velocity variations and long-rest periods. Mathematical modeling of physical phenomena requires the identification of pa- rameters and variables from available measurements. This is referred to as an inverse problem. In this work, we are interested in studying theoretically and numerically inverse problems for space Fractional Advection-Dispersion Equation (FADE), which is used to model solute transport in porous media. Identifying parameters for such an equa- tion is important to understand how chemical or biological contaminants are trans- ported throughout surface aquifer systems. For instance, an estimate of the di↵eren- tiation order in groundwater contaminant transport model can provide information about soil properties, such as the heterogeneity of the medium. Our main contribution is to propose a novel e cient algorithm based on modulat-ing functions to estimate the coe cients and the di↵erentiation order for space FADE, which can be extended to general fractional Partial Di↵erential Equation (PDE). We also show how the method can be applied to the source inverse problem. This work is divided into two parts: In part I, the proposed method is described and studied through an extensive numerical analysis. The local convergence of the proposed two-stage algorithm is proven for 1D space FADE. The properties of this method are studied along with its limitations. Then, the algorithm is generalized to the 2D FADE. In part II, we analyze direct and inverse source problems for a space FADE. The problem consists of recovering the source term using final
Inverse kinetics for subcritical systems with external neutron source
International Nuclear Information System (INIS)
Carvalho Gonçalves, Wemerson de; Martinez, Aquilino Senra; Carvalho da Silva, Fernando
2017-01-01
Highlights: • It was developed formalism for reactivity calculation. • The importance function is related to the system subcriticality. • The importance function is also related with the value of the external source. • The equations were analyzed for seven different levels of sub criticality. • The results are physically consistent with others formalism discussed in the paper. - Abstract: Nuclear reactor reactivity is one of the most important properties since it is directly related to the reactor control during the power operation. This reactivity is influenced by the neutron behavior in the reactor core. The time-dependent neutrons behavior in response to any change in material composition is important for the reactor operation safety. Transient changes may occur during the reactor startup or shutdown and due to accidental disturbances of the reactor operation. Therefore, it is very important to predict the time-dependent neutron behavior population induced by changes in neutron multiplication. Reactivity determination in subcritical systems driven by an external neutron source can be obtained through the solution of the inverse kinetics equation for subcritical nuclear reactors. The main purpose of this paper is to find the solution of the inverse kinetics equation the main purpose of this paper is to device the inverse kinetics equations for subcritical systems based in a previous paper published by the authors (Gonçalves et al., 2015) and by (Gandini and Salvatores, 2002; Dulla et al., 2006). The solutions of those equations were also obtained. Formulations presented in this paper were tested for seven different values of k eff with external neutrons source constant in time and for a powers ratio varying exponentially over time.
Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods.
Gramfort, Alexandre; Kowalski, Matthieu; Hämäläinen, Matti
2012-04-07
Magneto- and electroencephalography (M/EEG) measure the electromagnetic fields produced by the neural electrical currents. Given a conductor model for the head, and the distribution of source currents in the brain, Maxwell's equations allow one to compute the ensuing M/EEG signals. Given the actual M/EEG measurements and the solution of this forward problem, one can localize, in space and in time, the brain regions that have produced the recorded data. However, due to the physics of the problem, the limited number of sensors compared to the number of possible source locations, and measurement noise, this inverse problem is ill-posed. Consequently, additional constraints are needed. Classical inverse solvers, often called minimum norm estimates (MNE), promote source estimates with a small ℓ₂ norm. Here, we consider a more general class of priors based on mixed norms. Such norms have the ability to structure the prior in order to incorporate some additional assumptions about the sources. We refer to such solvers as mixed-norm estimates (MxNE). In the context of M/EEG, MxNE can promote spatially focal sources with smooth temporal estimates with a two-level ℓ₁/ℓ₂ mixed-norm, while a three-level mixed-norm can be used to promote spatially non-overlapping sources between different experimental conditions. In order to efficiently solve the optimization problems of MxNE, we introduce fast first-order iterative schemes that for the ℓ₁/ℓ₂ norm give solutions in a few seconds making such a prior as convenient as the simple MNE. Furthermore, thanks to the convexity of the optimization problem, we can provide optimality conditions that guarantee global convergence. The utility of the methods is demonstrated both with simulations and experimental MEG data.
Schuster, Thomas; Hofmann, Bernd; Kaltenbacher, Barbara
2012-10-01
of concrete instances with special properties. The aim of this special section is to provide a forum for highly topical ongoing work in the area of regularization in Banach spaces, its numerics and its applications. Indeed, we have been lucky enough to obtain a number of excellent papers both from colleagues who have previously been contributing to this topic and from researchers entering the field due to its relevance in practical inverse problems. We would like to thank all contributers for enabling us to present a high quality collection of papers on topics ranging from various aspects of regularization via efficient numerical solution to applications in PDE models. We give a brief overview of the contributions included in this issue (here ordered alphabetically by first author). In their paper, Iterative regularization with general penalty term—theory and application to L1 and TV regularization, Radu Bot and Torsten Hein provide an extension of the Landweber iteration for linear operator equations in Banach space to general operators in place of the inverse duality mapping, which corresponds to the use of general regularization functionals in variational regularization. The L∞ topology in data space corresponds to the frequently occuring situation of uniformly distributed data noise. A numerically efficient solution of the resulting Tikhonov regularization problem via a Moreau-Yosida appriximation and a semismooth Newton method, along with a δ-free regularization parameter choice rule, is the topic of the paper L∞ fitting for inverse problems with uniform noise by Christian Clason. Extension of convergence rates results from classical source conditions to their generalization via variational inequalities with a priori and a posteriori stopping rules is the main contribution of the paper Regularization of linear ill-posed problems by the augmented Lagrangian method and variational inequalities by Klaus Frick and Markus Grasmair, again in the context of some
Hermite Polynomials and the Inverse Problem for Collisionless Equilibria
Allanson, O.; Neukirch, T.; Troscheit, S.; Wilson, F.
2017-12-01
It is long established that Hermite polynomial expansions in either velocity or momentum space can elegantly encode the non-Maxwellian velocity-space structure of a collisionless plasma distribution function (DF). In particular, Hermite polynomials in the canonical momenta naturally arise in the consideration of the 'inverse problem in collisionless equilibria' (IPCE): "for a given macroscopic/fluid equilibrium, what are the self-consistent Vlasov-Maxwell equilibrium DFs?". This question is of particular interest for the equilibrium and stability properties of a given macroscopic configuration, e.g. a current sheet. It can be relatively straightforward to construct a formal solution to IPCE by a Hermite expansion method, but several important questions remain regarding the use of this method. We present recent work that considers the necessary conditions of non-negativity, convergence, and the existence of all moments of an equilibrium DF solution found for IPCE. We also establish meaningful analogies between the equations that link the microscopic and macrosopic descriptions of the Vlasov-Maxwell equilibrium, and those that solve the initial value problem for the heat equation. In the language of the heat equation, IPCE poses the pressure tensor as the 'present' heat distribution over an infinite domain, and the non-Maxwellian features of the DF as the 'past' distribution. We find sufficient conditions for the convergence of the Hermite series representation of the DF, and prove that the non-negativity of the DF can be dependent on the magnetisation of the plasma. For DFs that decay at least as quickly as exp(-v^2/4), we show non-negativity is guaranteed for at least a finite range of magnetisation values, as parameterised by the ratio of the Larmor radius to the gradient length scale. 1. O. Allanson, T. Neukirch, S. Troscheit & F. Wilson: From one-dimensional fields to Vlasov equilibria: theory and application of Hermite polynomials, Journal of Plasma Physics, 82
Comparative study of direct and inverse problems of cracked beams
Directory of Open Access Journals (Sweden)
Mahieddine Chettah
2018-01-01
Full Text Available In recent decades, the analysis and evaluation of the cracked structures were hot spots in several engineering fields and has been the subject of great interest with important and comprehensive surveys covering various methodologies and applications, in order to obtain reliable and effective methods to maintain the safety and performance of structures on a proactive basis. The presence of a crack, not only causes a local variation in the structural parameters (e.g., the stiffness of a beam at its location, but it also has a global effect which affects the overall dynamic behavior of the structure (such as the natural frequencies. For this reason, the dynamic characterization of the cracked structures can be used to detect damage from non-destructive testing. The objective of this paper is to compare the accuracy and ability of two methods to correctly predict the results for both direct problem to find natural frequencies and inverse problem to find crack’s locations and depths of a cracked simply supported beam. Several cases of crack depths and crack locations are investigated. The crack is supposed to remain open. The Euler–Bernoulli beam theory is employed to model the cracked beam and the crack is represented as a rotational spring with a sectional flexibility. In the first method, the transfer matrix method is used; the cracked beam is modeled as two uniform sub-segments connected by a rotational spring located at the cracked section. In the second method which is based on the Rayleigh’s method, the mode shape of the cracked beam is constructed by adding a cubic polynomial function to that of the undamaged beam. By applying the compatibility conditions at crack’s location and the corresponding boundary conditions, the general forms of characteristic equations for this cracked system are obtained. The two methods are then utilized to determine the locations and depths by using any two natural frequencies of a cracked simply
Inverse Problems in Geodynamics Using Machine Learning Algorithms
Shahnas, M. H.; Yuen, D. A.; Pysklywec, R. N.
2018-01-01
During the past few decades numerical studies have been widely employed to explore the style of circulation and mixing in the mantle of Earth and other planets. However, in geodynamical studies there are many properties from mineral physics, geochemistry, and petrology in these numerical models. Machine learning, as a computational statistic-related technique and a subfield of artificial intelligence, has rapidly emerged recently in many fields of sciences and engineering. We focus here on the application of supervised machine learning (SML) algorithms in predictions of mantle flow processes. Specifically, we emphasize on estimating mantle properties by employing machine learning techniques in solving an inverse problem. Using snapshots of numerical convection models as training samples, we enable machine learning models to determine the magnitude of the spin transition-induced density anomalies that can cause flow stagnation at midmantle depths. Employing support vector machine algorithms, we show that SML techniques can successfully predict the magnitude of mantle density anomalies and can also be used in characterizing mantle flow patterns. The technique can be extended to more complex geodynamic problems in mantle dynamics by employing deep learning algorithms for putting constraints on properties such as viscosity, elastic parameters, and the nature of thermal and chemical anomalies.
Ragon, Théa; Sladen, Anthony; Simons, Mark
2018-05-01
The ill-posed nature of earthquake source estimation derives from several factors including the quality and quantity of available observations and the fidelity of our forward theory. Observational errors are usually accounted for in the inversion process. Epistemic errors, which stem from our simplified description of the forward problem, are rarely dealt with despite their potential to bias the estimate of a source model. In this study, we explore the impact of uncertainties related to the choice of a fault geometry in source inversion problems. The geometry of a fault structure is generally reduced to a set of parameters, such as position, strike and dip, for one or a few planar fault segments. While some of these parameters can be solved for, more often they are fixed to an uncertain value. We propose a practical framework to address this limitation by following a previously implemented method exploring the impact of uncertainties on the elastic properties of our models. We develop a sensitivity analysis to small perturbations of fault dip and position. The uncertainties in fault geometry are included in the inverse problem under the formulation of the misfit covariance matrix that combines both prediction and observation uncertainties. We validate this approach with the simplified case of a fault that extends infinitely along strike, using both Bayesian and optimization formulations of a static inversion. If epistemic errors are ignored, predictions are overconfident in the data and source parameters are not reliably estimated. In contrast, inclusion of uncertainties in fault geometry allows us to infer a robust posterior source model. Epistemic uncertainties can be many orders of magnitude larger than observational errors for great earthquakes (Mw > 8). Not accounting for uncertainties in fault geometry may partly explain observed shallow slip deficits for continental earthquakes. Similarly, ignoring the impact of epistemic errors can also bias estimates of
A 2D forward and inverse code for streaming potential problems
Soueid Ahmed, A.; Jardani, A.; Revil, A.
2013-12-01
The self-potential method corresponds to the passive measurement of the electrical field in response to the occurrence of natural sources of current in the ground. One of these sources corresponds to the streaming current associated with the flow of the groundwater. We can therefore apply the self- potential method to recover non-intrusively some information regarding the groundwater flow. We first solve the forward problem starting with the solution of the groundwater flow problem, then computing the source current density, and finally solving a Poisson equation for the electrical potential. We use the finite-element method to solve the relevant partial differential equations. In order to reduce the number of (petrophysical) model parameters required to solve the forward problem, we introduced an effective charge density tensor of the pore water, which can be determined directly from the permeability tensor for neutral pore waters. The second aspect of our work concerns the inversion of the self-potential data using Tikhonov regularization with smoothness and weighting depth constraints. This approach accounts for the distribution of the electrical resistivity, which can be independently and approximately determined from electrical resistivity tomography. A numerical code, SP2DINV, has been implemented in Matlab to perform both the forward and inverse modeling. Three synthetic case studies are discussed.
Inversion of Atmospheric Tracer Measurements, Localization of Sources
Issartel, J.-P.; Cabrit, B.; Hourdin, F.; Idelkadi, A.
When abnormal concentrations of a pollutant are observed in the atmosphere, the question of its origin arises immediately. The radioactivity from Tchernobyl was de- tected in Sweden before the accident was announced. This situation emphasizes the psychological, political and medical stakes of a rapid identification of sources. In tech- nical terms, most industrial sources can be modeled as a fixed point at ground level with undetermined duration. The classical method of identification involves the cal- culation of a backtrajectory departing from the detector with an upstream integration of the wind field. We were first involved in such questions as we evaluated the ef- ficiency of the international monitoring network planned in the frame of the Com- prehensive Test Ban Treaty. We propose a new approach of backtracking based upon the use of retroplumes associated to available measurements. Firstly the retroplume is related to inverse transport processes, describing quantitatively how the air in a sam- ple originates from regions that are all the more extended and diffuse as we go back far in the past. Secondly it clarifies the sensibility of the measurement with respect to all potential sources. It is therefore calculated by adjoint equations including of course diffusive processes. Thirdly, the statistical interpretation, valid as far as sin- gle particles are concerned, should not be used to investigate the position and date of a macroscopic source. In that case, the retroplume rather induces a straightforward constraint between the intensity of the source and its position. When more than one measurements are available, including zero valued measurements, the source satisfies the same number of linear relations tightly related to the retroplumes. This system of linear relations can be handled through the simplex algorithm in order to make the above intensity-position correlation more restrictive. This method enables to manage in a quantitative manner the
International Nuclear Information System (INIS)
Ma Xiang; Zabaras, Nicholas
2009-01-01
A new approach to modeling inverse problems using a Bayesian inference method is introduced. The Bayesian approach considers the unknown parameters as random variables and seeks the probabilistic distribution of the unknowns. By introducing the concept of the stochastic prior state space to the Bayesian formulation, we reformulate the deterministic forward problem as a stochastic one. The adaptive hierarchical sparse grid collocation (ASGC) method is used for constructing an interpolant to the solution of the forward model in this prior space which is large enough to capture all the variability/uncertainty in the posterior distribution of the unknown parameters. This solution can be considered as a function of the random unknowns and serves as a stochastic surrogate model for the likelihood calculation. Hierarchical Bayesian formulation is used to derive the posterior probability density function (PPDF). The spatial model is represented as a convolution of a smooth kernel and a Markov random field. The state space of the PPDF is explored using Markov chain Monte Carlo algorithms to obtain statistics of the unknowns. The likelihood calculation is performed by directly sampling the approximate stochastic solution obtained through the ASGC method. The technique is assessed on two nonlinear inverse problems: source inversion and permeability estimation in flow through porous media
Direct sampling methods for inverse elastic scattering problems
Ji, Xia; Liu, Xiaodong; Xi, Yingxia
2018-03-01
We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using the different component of the far field patterns. Only inner products are involved in the computation, thus the novel sampling methods are very simple and fast to be implemented. With the help of the factorization of the far field operator, we give a lower bound of the proposed indicator functionals for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functionals decay like the Bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functionals continuously dependent on the far field patterns, which further implies that the novel sampling methods are extremely stable with respect to data error. For the case when the observation directions are restricted into the limited aperture, we firstly introduce some data retrieval techniques to obtain those data that can not be measured directly and then use the proposed direct sampling methods for location and shape reconstructions. Finally, some numerical simulations in two dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed sampling methods, even for multiple multiscale cases and limited-aperture problems.
Solving Inverse Detection Problems Using Passive Radiation Signatures
International Nuclear Information System (INIS)
Favorite, Jeffrey A.; Armstrong, Jerawan C.; Vaquer, Pablo A.
2012-01-01
The ability to reconstruct an unknown radioactive object based on its passive gamma-ray and neutron signatures is very important in homeland security applications. Often in the analysis of unknown radioactive objects, for simplicity or speed or because there is no other information, they are modeled as spherically symmetric regardless of their actual geometry. In these presentation we discuss the accuracy and implications of this approximation for decay gamma rays and for neutron-induced gamma rays. We discuss an extension of spherical raytracing (for uncollided fluxes) that allows it to be used when the exterior shielding is flat or cylindrical. We revisit some early results in boundary perturbation theory, showing that the Roussopolos estimate is the correct one to use when the quantity of interest is the flux or leakage on the boundary. We apply boundary perturbation theory to problems in which spherically symmetric systems are perturbed in asymmetric nonspherical ways. We apply mesh adaptive direct search (MADS) algorithms to object reconstructions. We present a benchmark test set that may be used to quantitatively evaluate inverse detection methods.
Beamforming Through Regularized Inverse Problems in Ultrasound Medical Imaging.
Szasz, Teodora; Basarab, Adrian; Kouame, Denis
2016-12-01
Beamforming (BF) in ultrasound (US) imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum (DAS) is still extensively used nowadays in clinical applications, due to its real-time capabilities. The most common alternatives are minimum variance (MV) method and its variants, which overcome the drawbacks of DAS, at the cost of higher computational complexity that limits its utilization in real-time applications. In this paper, we propose to perform BF in US imaging through a regularized inverse problem based on a linear model relating the reflected echoes to the signal to be recovered. Our approach presents two major advantages: 1) its flexibility in the choice of statistical assumptions on the signal to be beamformed (Laplacian and Gaussian statistics are tested herein) and 2) its robustness to a reduced number of pulse emissions. The proposed framework is flexible and allows for choosing the right tradeoff between noise suppression and sharpness of the resulted image. We illustrate the performance of our approach on both simulated and experimental data, with in vivo examples of carotid and thyroid. Compared with DAS, MV, and two other recently published BF techniques, our method offers better spatial resolution, respectively contrast, when using Laplacian and Gaussian priors.
Inverse Ising problem in continuous time: A latent variable approach
Donner, Christian; Opper, Manfred
2017-12-01
We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.
Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrodinger equation
Klibanov, Michael V.; Romanov, Vladimir G.
2014-01-01
The inverse scattering problem of the reconstruction of the unknown potential with compact support in the 3-d Schr\\"odinger equation is considered. Only the modulus of the scattering complex valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. Therefore, a long standing problem posed in 1977 by K. Chadan and P.C. Sabatier in their book "Inverse Problems in Quantum Scattering Theory" is solved.
Physics-based Inverse Problem to Deduce Marine Atmospheric Boundary Layer Parameters
2017-03-07
knowledge and capabilities in the use and development of inverse problem techniques to deduce atmospheric parameters. WORK COMPLETED The research completed...please find the Final Technical Report with SF 298 for Dr. Erin E. Hackett’s ONR grant entitled Physics -based Inverse Problem to Deduce Marine...From- To) 07/03/2017 Final Technica l Dec 2012- Dec 2016 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Physics -based Inverse Problem to Deduce Marine
Children's strategies to solving additive inverse problems: a preliminary analysis
Ding, Meixia; Auxter, Abbey E.
2017-03-01
Prior studies show that elementary school children generally "lack" formal understanding of inverse relations. This study goes beyond lack to explore what children might "have" in their existing conception. A total of 281 students, kindergarten to third grade, were recruited to respond to a questionnaire that involved both contextual and non-contextual tasks on inverse relations, requiring both computational and explanatory skills. Results showed that children demonstrated better performance in computation than explanation. However, many students' explanations indicated that they did not necessarily utilize inverse relations for computation. Rather, they appeared to possess partial understanding, as evidenced by their use of part-whole structure, which is a key to understanding inverse relations. A close inspection of children's solution strategies further revealed that the sophistication of children's conception of part-whole structure varied in representation use and unknown quantity recognition, which suggests rich opportunities to develop students' understanding of inverse relations in lower elementary classrooms.
Inverse compton light source: a compact design proposal
Energy Technology Data Exchange (ETDEWEB)
Deitrick, Kirsten Elizabeth [Old Dominion Univ., Norfolk, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2017-05-01
In the last decade, there has been an increasing demand for a compact Inverse Compton Light Source (ICLS) which is capable of producing high-quality X-rays by colliding an electron beam and a high-quality laser. It is only in recent years when both SRF and laser technology have advanced enough that compact sources can approach the quality found at large installations such as the Advanced Photon Source at Argonne National Laboratory. Previously, X-ray sources were either high flux and brilliance at a large facility or many orders of magnitude lesser when produced by a bremsstrahlung source. A recent compact source was constructed by Lyncean Technologies using a storage ring to produce the electron beam used to scatter the incident laser beam. By instead using a linear accelerator system for the electron beam, a significant increase in X-ray beam quality is possible, though even subsequent designs also featuring a storage ring offer improvement. Preceding the linear accelerator with an SRF reentrant gun allows for an extremely small transverse emittance, increasing the brilliance of the resulting X-ray source. In order to achieve sufficiently small emittances, optimization was done regarding both the geometry of the gun and the initial electron bunch distribution produced off the cathode. Using double-spoke SRF cavities to comprise the linear accelerator allows for an electron beam of reasonable size to be focused at the interaction point, while preserving the low emittance that was generated by the gun. An aggressive final focusing section following the electron beam's exit from the accelerator produces the small spot size at the interaction point which results in an X-ray beam of high flux and brilliance. Taking all of these advancements together, a world class compact X-ray source has been designed. It is anticipated that this source would far outperform the conventional bremsstrahlung and many other compact ICLSs, while coming closer to performing at the
pyGIMLi: An open-source library for modelling and inversion in geophysics
Rücker, Carsten; Günther, Thomas; Wagner, Florian M.
2017-12-01
Many tasks in applied geosciences cannot be solved by single measurements, but require the integration of geophysical, geotechnical and hydrological methods. Numerical simulation techniques are essential both for planning and interpretation, as well as for the process understanding of modern geophysical methods. These trends encourage open, simple, and modern software architectures aiming at a uniform interface for interdisciplinary and flexible modelling and inversion approaches. We present pyGIMLi (Python Library for Inversion and Modelling in Geophysics), an open-source framework that provides tools for modelling and inversion of various geophysical but also hydrological methods. The modelling component supplies discretization management and the numerical basis for finite-element and finite-volume solvers in 1D, 2D and 3D on arbitrarily structured meshes. The generalized inversion framework solves the minimization problem with a Gauss-Newton algorithm for any physical forward operator and provides opportunities for uncertainty and resolution analyses. More general requirements, such as flexible regularization strategies, time-lapse processing and different sorts of coupling individual methods are provided independently of the actual methods used. The usage of pyGIMLi is first demonstrated by solving the steady-state heat equation, followed by a demonstration of more complex capabilities for the combination of different geophysical data sets. A fully coupled hydrogeophysical inversion of electrical resistivity tomography (ERT) data of a simulated tracer experiment is presented that allows to directly reconstruct the underlying hydraulic conductivity distribution of the aquifer. Another example demonstrates the improvement of jointly inverting ERT and ultrasonic data with respect to saturation by a new approach that incorporates petrophysical relations in the inversion. Potential applications of the presented framework are manifold and include time
New prospects in direct, inverse and control problems for evolution equations
Fragnelli, Genni; Mininni, Rosa
2014-01-01
This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences. Applied sciences consider situations in which the evolution of a given system over time is observed, and the related models can be formulated in terms of evolution equations (EEs). These equations have been studied intensively in theoretical research and are the source of an enormous number of applications. In this volume, particular attention is given to direct, inverse and control problems for EEs. The book provides an updated overview of the field, revealing its richness and vitality.
Elastic frequency-domain finite-difference contrast source inversion method
International Nuclear Information System (INIS)
He, Qinglong; Chen, Yong; Han, Bo; Li, Yang
2016-01-01
In this work, we extend the finite-difference contrast source inversion (FD-CSI) method to the frequency-domain elastic wave equations, where the parameters describing the subsurface structure are simultaneously reconstructed. The FD-CSI method is an iterative nonlinear inversion method, which exhibits several strengths. First, the finite-difference operator only relies on the background media and the given angular frequency, both of which are unchanged during inversion. Therefore, the matrix decomposition is performed only once at the beginning of the iteration if a direct solver is employed. This makes the inversion process relatively efficient in terms of the computational cost. In addition, the FD-CSI method automatically normalizes different parameters, which could avoid the numerical problems arising from the difference of the parameter magnitude. We exploit a parallel implementation of the FD-CSI method based on the domain decomposition method, ensuring a satisfactory scalability for large-scale problems. A simple numerical example with a homogeneous background medium is used to investigate the convergence of the elastic FD-CSI method. Moreover, the Marmousi II model proposed as a benchmark for testing seismic imaging methods is presented to demonstrate the performance of the elastic FD-CSI method in an inhomogeneous background medium. (paper)
New Insights on the Uncertainties in Finite-Fault Earthquake Source Inversion
Razafindrakoto, Hoby
2015-04-01
New Insights on the Uncertainties in Finite-Fault Earthquake Source Inversion Hoby Njara Tendrisoa Razafindrakoto Earthquake source inversion is a non-linear problem that leads to non-unique solutions. The aim of this dissertation is to understand the uncertainty and reliability in earthquake source inversion, as well as to quantify variability in earthquake rupture models. The source inversion is performed using a Bayesian inference. This technique augments optimization approaches through its ability to image the entire solution space which is consistent with the data and prior information. In this study, the uncertainty related to the choice of source-time function and crustal structure is investigated. Three predefined analytical source-time functions are analyzed; isosceles triangle, Yoffe with acceleration time of 0.1 and 0.3 s. The use of the isosceles triangle as source-time function is found to bias the finite-fault source inversion results. It accelerates the rupture to propagate faster compared to that of the Yoffe function. Moreover, it generates an artificial linear correlation between parameters that does not exist for the Yoffe source-time functions. The effect of inadequate knowledge of Earth’s crustal structure in earthquake rupture models is subsequently investigated. The results show that one-dimensional structure variability leads to parameters resolution changes, with a broadening of the posterior 5 PDFs and shifts in the peak location. These changes in the PDFs of kinematic parameters are associated with the blurring effect of using incorrect Earth structure. As an application to real earthquake, finite-fault source models for the 2009 L’Aquila earthquake are examined using one- and three-dimensional crustal structures. One- dimensional structure is found to degrade the data fitting. However, there is no significant effect on the rupture parameters aside from differences in the spatial slip extension. Stable features are maintained for both
From inverse problems in mathematical physiology to quantitative differential diagnoses.
Directory of Open Access Journals (Sweden)
Sven Zenker
2007-11-01
Full Text Available The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting, using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge. We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of
From Inverse Problems in Mathematical Physiology to Quantitative Differential Diagnoses
Zenker, Sven; Rubin, Jonathan; Clermont, Gilles
2007-01-01
The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting), using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge). We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of differential diagnoses
Inverse Problem Approach for the Alignment of Electron Tomographic Series
International Nuclear Information System (INIS)
Tran, V.D.; Moreaud, M.; Thiebaut, E.; Denis, L.; Becker, J.M.
2014-01-01
In the refining industry, morphological measurements of particles have become an essential part in the characterization catalyst supports. Through these parameters, one can infer the specific physico-chemical properties of the studied materials. One of the main acquisition techniques is electron tomography (or nano-tomography). 3D volumes are reconstructed from sets of projections from different angles made by a Transmission Electron Microscope (TEM). This technique provides a real three-dimensional information at the nano-metric scale. A major issue in this method is the misalignment of the projections that contributes to the reconstruction. The current alignment techniques usually employ fiducial markers such as gold particles for a correct alignment of the images. When the use of markers is not possible, the correlation between adjacent projections is used to align them. However, this method sometimes fails. In this paper, we propose a new method based on the inverse problem approach where a certain criterion is minimized using a variant of the Nelder and Mead simplex algorithm. The proposed approach is composed of two steps. The first step consists of an initial alignment process, which relies on the minimization of a cost function based on robust statistics measuring the similarity of a projection to its previous projections in the series. It reduces strong shifts resulting from the acquisition between successive projections. In the second step, the pre-registered projections are used to initialize an iterative alignment-refinement process which alternates between (i) volume reconstructions and (ii) registrations of measured projections onto simulated projections computed from the volume reconstructed in (i). At the end of this process, we have a correct reconstruction of the volume, the projections being correctly aligned. Our method is tested on simulated data and shown to estimate accurately the translation, rotation and scale of arbitrary transforms. We
A solution to the inverse problem in ocean acoustics
Digital Repository Service at National Institute of Oceanography (India)
Murty, T.V.R.; Somayajulu, Y.K.; Mahadevan, R.; Murty, C.S.; Sastry, J.S.
stratified ocean, considering the range independent nature of the medium, geophysical inverse techniques are employed to reconstruct the sound speed profile. The reconstructed profile for a six layer ocean, with five energetic modes, is in good agreement...
International Nuclear Information System (INIS)
Namjoo, A.; Sarvari, S.M. Hosseini; Behzadmehr, A.; Mansouri, S.H.
2009-01-01
In this paper, an inverse analysis is performed for estimation of source term distribution from the measured exit radiation intensities at the boundary surfaces in a one-dimensional absorbing, emitting and isotropically scattering medium between two parallel plates with variable refractive index. The variation of refractive index is assumed to be linear. The radiative transfer equation is solved by the constant quadrature discrete ordinate method. The inverse problem is formulated as an optimization problem for minimizing an objective function which is expressed as the sum of square deviations between measured and estimated exit radiation intensities at boundary surfaces. The conjugate gradient method is used to solve the inverse problem through an iterative procedure. The effects of various variables on source estimation are investigated such as type of source function, errors in the measured data and system parameters, gradient of refractive index across the medium, optical thickness, single scattering albedo and boundary emissivities. The results show that in the case of noisy input data, variation of system parameters may affect the inverse solution, especially at high error values in the measured data. The error in measured data plays more important role than the error in radiative system parameters except the refractive index distribution; however the accuracy of source estimation is very sensitive toward error in refractive index distribution. Therefore, refractive index distribution and measured exit intensities should be measured accurately with a limited error bound, in order to have an accurate estimation of source term in a graded index medium.
An inverse source location algorithm for radiation portal monitor applications
International Nuclear Information System (INIS)
Miller, Karen A.; Charlton, William S.
2010-01-01
Radiation portal monitors are being deployed at border crossings throughout the world to prevent the smuggling of nuclear and radiological materials; however, a tension exists between security and the free-flow of commerce. Delays at ports-of-entry have major economic implications, so it is imperative to minimize portal monitor screening time. We have developed an algorithm to locate a radioactive source using a distributed array of detectors, specifically for use at border crossings. To locate the source, we formulated an optimization problem where the objective function describes the least-squares difference between the actual and predicted detector measurements. The predicted measurements are calculated by solving the 3-D deterministic neutron transport equation given an estimated source position. The source position is updated using the steepest descent method, where the gradient of the objective function with respect to the source position is calculated using adjoint transport calculations. If the objective function is smaller than the convergence criterion, then the source position has been identified. This paper presents the derivation of the underlying equations in the algorithm as well as several computational test cases used to characterize its accuracy.
Avdyushev, Victor A.
2017-12-01
Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the
Solving inverse problems of mathematical physics by means of the PHOENICS software package
Energy Technology Data Exchange (ETDEWEB)
Matsevity, Y; Lushpenko, S [Institute for Problems in Machinery, National Academy of Sciences of Ukraine Pozharskogo, Kharkov (Ukraine)
1998-12-31
Several approaches on organizing solution of inverse problems by means of PHOENICS on the basis of the technique of automated fitting are proposing. A version of a `nondestructive` method of using PHOENICS in the inverse problem solution regime and the ways of altering the program in the case of introducing optimization facilities in it are under consideration. (author) 12 refs.
An Inverse Eigenvalue Problem for a Vibrating String with Two Dirichlet Spectra
Rundell, William; Sacks, Paul
2013-01-01
A classical inverse problem is "can you hear the density of a string clamped at both ends?" The mathematical model gives rise to an inverse Sturm-Liouville problem for the unknown density ñ, and it is well known that the answer is negative
Solving inverse problems of mathematical physics by means of the PHOENICS software package
Energy Technology Data Exchange (ETDEWEB)
Matsevity, Y.; Lushpenko, S. [Institute for Problems in Machinery, National Academy of Sciences of Ukraine Pozharskogo, Kharkov (Ukraine)
1997-12-31
Several approaches on organizing solution of inverse problems by means of PHOENICS on the basis of the technique of automated fitting are proposing. A version of a `nondestructive` method of using PHOENICS in the inverse problem solution regime and the ways of altering the program in the case of introducing optimization facilities in it are under consideration. (author) 12 refs.
International Nuclear Information System (INIS)
Ziqi Sun
1993-01-01
During the past few years a considerable interest has been focused on the inverse boundary value problem for the Schroedinger operator with a scalar (electric) potential. The popularity gained by this subject seems to be due to its connection with the inverse scattering problem at fixed energy, the inverse conductivity problem and other important inverse problems. This paper deals with an inverse boundary value problem for the Schroedinger operator with vector (electric and magnetic) potentials. As in the case of the scalar potential, results of this study would have immediate consequences in the inverse scattering problem for magnetic field at fixed energy. On the other hand, inverse boundary value problems for elliptic operators are of independent interest. The study is partly devoted to the understanding of the inverse boundary value problem for a class of general elliptic operator of second order. Note that a self-adjoint elliptic operator of second order with Δ as its principal symbol can always be written as a Schroedinger operator with vector potentials
Brown, Malcolm
2009-01-01
Inversions are fascinating phenomena. They are reversals of the normal or expected order. They occur across a wide variety of contexts. What do inversions have to do with learning spaces? The author suggests that they are a useful metaphor for the process that is unfolding in higher education with respect to education. On the basis of…
International Nuclear Information System (INIS)
Huang, C.-H.; Wu, H.-H.
2006-01-01
In the present study an inverse hyperbolic heat conduction problem is solved by the conjugate gradient method (CGM) in estimating the unknown boundary heat flux based on the boundary temperature measurements. Results obtained in this inverse problem will be justified based on the numerical experiments where three different heat flux distributions are to be determined. Results show that the inverse solutions can always be obtained with any arbitrary initial guesses of the boundary heat flux. Moreover, the drawbacks of the previous study for this similar inverse problem, such as (1) the inverse solution has phase error and (2) the inverse solution is sensitive to measurement error, can be avoided in the present algorithm. Finally, it is concluded that accurate boundary heat flux can be estimated in this study
International Nuclear Information System (INIS)
Barnea, N.; Liverts, E.
2010-01-01
In this paper we present an analytic expression for the Lorentz integral transform of an arbitrary response function expressed as a polynomial times a decaying exponent. The resulting expression is applied to the inversion problem of the Lorentz integral transform, simplifying the inversion procedure and improving the accuracy of the procedure. We have presented analytic formulae for a family of basis function often used in the inversion of the LIT function. These formulae allow for an efficient and accurate inversion. The quality and the stability of the resulting inversions were demonstrated through two different examples yielding outstanding results. (author)
The inverse problem: Ocean tides derived from earth tide observations
Kuo, J. T.
1978-01-01
Indirect mapping ocean tides by means of land and island-based tidal gravity measurements is presented. The inverse scheme of linear programming is used for indirect mapping of ocean tides. Open ocean tides were measured by the numerical integration of Laplace's tidal equations.
Skeletonized inversion of surface wave: Active source versus controlled noise comparison
Li, Jing; Hanafy, Sherif
2016-01-01
We have developed a skeletonized inversion method that inverts the S-wave velocity distribution from surface-wave dispersion curves. Instead of attempting to fit every wiggle in the surface waves with predicted data, it only inverts the picked dispersion curve, thereby mitigating the problem of getting stuck in a local minimum. We have applied this method to a synthetic model and seismic field data from Qademah fault, located at the western side of Saudi Arabia. For comparison, we have performed dispersion analysis for an active and controlled noise source seismic data that had some receivers in common with the passive array. The active and passive data show good agreement in the dispersive characteristics. Our results demonstrated that skeletonized inversion can obtain reliable 1D and 2D S-wave velocity models for our geologic setting. A limitation is that we need to build layered initial model to calculate the Jacobian matrix, which is time consuming.
Skeletonized inversion of surface wave: Active source versus controlled noise comparison
Li, Jing
2016-07-14
We have developed a skeletonized inversion method that inverts the S-wave velocity distribution from surface-wave dispersion curves. Instead of attempting to fit every wiggle in the surface waves with predicted data, it only inverts the picked dispersion curve, thereby mitigating the problem of getting stuck in a local minimum. We have applied this method to a synthetic model and seismic field data from Qademah fault, located at the western side of Saudi Arabia. For comparison, we have performed dispersion analysis for an active and controlled noise source seismic data that had some receivers in common with the passive array. The active and passive data show good agreement in the dispersive characteristics. Our results demonstrated that skeletonized inversion can obtain reliable 1D and 2D S-wave velocity models for our geologic setting. A limitation is that we need to build layered initial model to calculate the Jacobian matrix, which is time consuming.
Energy Technology Data Exchange (ETDEWEB)
Aguilo Valentin, Miguel Alejandro [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2016-07-01
This study presents a new nonlinear programming formulation for the solution of inverse problems. First, a general inverse problem formulation based on the compliance error functional is presented. The proposed error functional enables the computation of the Lagrange multipliers, and thus the first order derivative information, at the expense of just one model evaluation. Therefore, the calculation of the Lagrange multipliers does not require the solution of the computationally intensive adjoint problem. This leads to significant speedups for large-scale, gradient-based inverse problems.
The Mathematical Basis of the Inverse Scattering Problem for Cracks from Near-Field Data
Directory of Open Access Journals (Sweden)
Yao Mao
2015-01-01
Full Text Available We consider the acoustic scattering problem from a crack which has Dirichlet boundary condition on one side and impedance boundary condition on the other side. The inverse scattering problem in this paper tries to determine the shape of the crack and the surface impedance coefficient from the near-field measurements of the scattered waves, while the source point is placed on a closed curve. We firstly establish a near-field operator and focus on the operator’s mathematical analysis. Secondly, we obtain a uniqueness theorem for the shape and surface impedance. Finally, by using the operator’s properties and modified linear sampling method, we reconstruct the shape and surface impedance.
International Nuclear Information System (INIS)
Chen, Xudong
2010-01-01
This paper proposes a version of the subspace-based optimization method to solve the inverse scattering problem with an inhomogeneous background medium where the known inhomogeneities are bounded in a finite domain. Although the background Green's function at each discrete point in the computational domain is not directly available in an inhomogeneous background scenario, the paper uses the finite element method to simultaneously obtain the Green's function at all discrete points. The essence of the subspace-based optimization method is that part of the contrast source is determined from the spectrum analysis without using any optimization, whereas the orthogonally complementary part is determined by solving a lower dimension optimization problem. This feature significantly speeds up the convergence of the algorithm and at the same time makes it robust against noise. Numerical simulations illustrate the efficacy of the proposed algorithm. The algorithm presented in this paper finds wide applications in nondestructive evaluation, such as through-wall imaging
A hopfield-like artificial neural network for solving inverse radiation transport problems
International Nuclear Information System (INIS)
Lee, Sang Hoon
1997-02-01
In this thesis, we solve inverse radiation transport problems by an Artificial Neural Network(ANN) approach. ANNs have many interesting properties such as nonlinear, parallel, and distributed processing. Some of the promising applications of ANNs are optimization, image and signal processing, system control, etc. In some optimization problems, Hopfield Neural Network(HNN) which has one-layered and fully interconnected neurons with feed-back topology showed that it worked well with acceptable fault tolerance and efficiency. The identification of radioactive source in a medium with a limited number of external detectors is treated as an inverse radiation transport problem in this work. This kind of inverse problem is usually ill-posed and severely under-determined; however, its applications are very useful in many fields including medical diagnosis and nondestructive assay of nuclear materials. Therefore, it is desired to develop efficient and robust solution algorithms. Firstly, we study a representative ANN model which has learning ability and fault tolerance, i.e., feed-forward neural network. It has an error backpropagation learning algorithm processed by reducing error in learning patterns that are usually results of test or calculation. Although it has enough fault tolerance and efficiency, a major obstacle is 'curse of dimensionality'--required number of learning patterns and learning time increase exponentially proportional to the problem size. Therefore, in this thesis, this type of ANN is used as benchmarking the reliability of the solution. Secondly, another approach for solving inverse problems, a modified version of HNN is proposed. When diagonal elements of the interconnection matrix are not zero, HNN may become unstable. However, most problems including this identification problem contain non-zero diagonal elements when programmed on neural networks. According to Soulie et al., discrete random iterations could produce the stable minimum state
Sparse optimization for inverse problems in atmospheric modelling
Czech Academy of Sciences Publication Activity Database
Adam, Lukáš; Branda, Martin
2016-01-01
Roč. 79, č. 3 (2016), s. 256-266 ISSN 1364-8152 R&D Projects: GA MŠk(CZ) 7F14287 Institutional support: RVO:67985556 Keywords : Inverse modelling * Sparse optimization * Integer optimization * Least squares * European tracer experiment * Free Matlab codes Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.404, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/adam-0457037.pdf
An Inverse Problem Formulation Methodology for Stochastic Models
2010-05-02
form the surveillance data Infection control measures were implemented in the form of health care worker hand - hygiene before and after patients contact...manuscript derives from our interest in understanding the spread of infectious diseases in particular, nosocomial infections , in order to prevent major...given by the inverse of the parameter of the exponential distribution. A hand - hygiene policy applied to health care workers on isolated VRE colonized
Identification of the Thermophysical Properties of the Soil by Inverse Problem
Mansour , Salwa; Canot , Édouard; Muhieddine , Mohamad
2016-01-01
International audience; This paper introduces a numerical strategy to estimate the thermophysical properties of a saturated porous medium (volumetric heat capacity (ρC)s , thermal conductivity λs and porosity φ) where a phase change problem (liquid/vapor) appears due strong heating. The estimation of these properties is done by inverse problem knowing the heating curves at selected points of the medium. To solve the inverse problem, we use both the Damped Gauss Newton and the Levenberg Marqua...
Inverse problems in the design, modeling and testing of engineering systems
Alifanov, Oleg M.
1991-01-01
Formulations, classification, areas of application, and approaches to solving different inverse problems are considered for the design of structures, modeling, and experimental data processing. Problems in the practical implementation of theoretical-experimental methods based on solving inverse problems are analyzed in order to identify mathematical models of physical processes, aid in input data preparation for design parameter optimization, help in design parameter optimization itself, and to model experiments, large-scale tests, and real tests of engineering systems.
Riemann–Hilbert problem approach for two-dimensional flow inverse scattering
Energy Technology Data Exchange (ETDEWEB)
Agaltsov, A. D., E-mail: agalets@gmail.com [Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow (Russian Federation); Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr [CNRS (UMR 7641), Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau (France); IEPT RAS, 117997 Moscow (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny (Russian Federation)
2014-10-15
We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.
Riemann–Hilbert problem approach for two-dimensional flow inverse scattering
International Nuclear Information System (INIS)
Agaltsov, A. D.; Novikov, R. G.
2014-01-01
We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given
Determination of the direction to a source of antineutrinos via inverse beta decay in Double Chooz
Nikitenko, Ya.
2016-11-01
To determine the direction to a source of neutrinos (and antineutrinos) is an important problem for the physics of supernovae and of the Earth. The direction to a source of antineutrinos can be estimated through the reaction of inverse beta decay. We show that the reactor neutrino experiment Double Chooz has unique capabilities to study antineutrino signal from point-like sources. Contemporary experimental data on antineutrino directionality is given. A rigorous mathematical approach for neutrino direction studies has been developed. Exact expressions for the precision of the simple mean estimator of neutrinos' direction for normal and exponential distributions for a finite sample and for the limiting case of many events have been obtained.
Propagation of Singularities and Some Inverse Problems in Wave Propagation
National Research Council Canada - National Science Library
Symes, William W
1989-01-01
... in various useful coefficient classes, separation of scales,...We explain the essential role of travel time in the study of these problems, and show how its function may be generalized to multidimensional (i.e. non-layered) problems.
Collage-based approaches for elliptic partial differential equations inverse problems
Yodzis, Michael; Kunze, Herb
2017-01-01
The collage method for inverse problems has become well-established in the literature in recent years. Initial work developed a collage theorem, based upon Banach's fixed point theorem, for treating inverse problems for ordinary differential equations (ODEs). Amongst the subsequent work was a generalized collage theorem, based upon the Lax-Milgram representation theorem, useful for treating inverse problems for elliptic partial differential equations (PDEs). Each of these two different approaches can be applied to elliptic PDEs in one space dimension. In this paper, we explore and compare how the two different approaches perform for the estimation of the diffusivity for a steady-state heat equation.
DEFF Research Database (Denmark)
Hansen, Thomas Mejer; Cordua, Knud Skou; Holm Jacobsen, Bo
2014-01-01
forward models, can be more than an order of magnitude larger than the measurement uncertainty. We also found that the modeling error is strongly linked to the spatial variability of the assumed velocity field, i.e., the a priori velocity model.We discovered some general tools by which the modeling error...... synthetic ground-penetrating radar crosshole tomographic inverse problems. Ignoring the modeling error can lead to severe artifacts, which erroneously appear to be well resolved in the solution of the inverse problem. Accounting for the modeling error leads to a solution of the inverse problem consistent...
Solving inverse two-point boundary value problems using collage coding
Kunze, H.; Murdock, S.
2006-08-01
The method of collage coding, with its roots in fractal imaging, is the central tool in a recently established rigorous framework for solving inverse initial value problems for ordinary differential equations (Kunze and Vrscay 1999 Inverse Problems 15 745-70). We extend these ideas to solve the following inverse problem: given a function u(x) on [A, B] (which may be the interpolation of data points), determine a two-point boundary value problem on [A, B] which admits u(x) as a solution as closely as desired. The solution of such inverse problems may be useful in parameter estimation or determination of potential functional forms of the underlying differential equation. We discuss ways to improve results, including the development of a partitioning scheme. Several examples are considered.
Lawrence, Chris C.; Febbraro, Michael; Flaska, Marek; Pozzi, Sara A.; Becchetti, F. D.
2016-08-01
Verification of future warhead-dismantlement treaties will require detection of certain warhead attributes without the disclosure of sensitive design information, and this presents an unusual measurement challenge. Neutron spectroscopy—commonly eschewed as an ill-posed inverse problem—may hold special advantages for warhead verification by virtue of its insensitivity to certain neutron-source parameters like plutonium isotopics. In this article, we investigate the usefulness of unfolded neutron spectra obtained from organic-scintillator data for verifying a particular treaty-relevant warhead attribute: the presence of high-explosive and neutron-reflecting materials. Toward this end, several improvements on current unfolding capabilities are demonstrated: deuterated detectors are shown to have superior response-matrix condition to that of standard hydrogen-base scintintillators; a novel data-discretization scheme is proposed which removes important detector nonlinearities; and a technique is described for re-parameterizing the unfolding problem in order to constrain the parameter space of solutions sought, sidestepping the inverse problem altogether. These improvements are demonstrated with trial measurements and verified using accelerator-based time-of-flight calculation of reference spectra. Then, a demonstration is presented in which the elemental compositions of low-Z neutron-attenuating materials are estimated to within 10%. These techniques could have direct application in verifying the presence of high-explosive materials in a neutron-emitting test item, as well as other for treaty verification challenges.
A new optimization approach for source-encoding full-waveform inversion
Moghaddam, P.P.; Keers, H.; Herrmann, F.J.; Mulder, W.A.
2013-01-01
Waveform inversion is the method of choice for determining a highly heterogeneous subsurface structure. However, conventional waveform inversion requires that the wavefield for each source is computed separately. This makes it very expensive for realistic 3D seismic surveys. Source-encoding waveform
Multi-source waveform inversion of marine streamer data using the normalized wavefield
Choi, Yun Seok; Alkhalifah, Tariq Ali
2012-01-01
Even though the encoded multi-source approach dramatically reduces the computational cost of waveform inversion, it is generally not applicable to marine streamer data. This is because the simultaneous-sources modeled data cannot be muted to comply
The inverse problem to the evaluation of magnetic fields
Caspi, S.; Helm, M.; Laslett, L. J.; Brady, V.
1992-12-01
In the design of superconducting magnet elements, such as may be required to guide and focus ions in a particle accelerator, one frequently premises some particular current distribution and then proceeds to compute the consequent magnetic field through use of the laws of Biot and Savart or of Ampere. When working in this manner one of course may need to revise frequently the postulated current distribution before arriving at a resulting magnetic field of acceptable field quality. It therefore is of interest to consider an alternative ('inverse') procedure in which one specifies a desired character for the field required in the region interior to the winding and undertakes them to evaluate the current distribution on the specified winding surface that would provide this desired field. We may note that in undertaking such an inverse procedure we would wish, on practical grounds, to avoid the use of any 'double-layer' distributions of current on the winding surface or interface but would not demand that no fields be generated in the exterior region, so that in this respect the goal would differ in detail from that discussed by other authors, in analogy to the distribution sought in electrostatics by the so-caged Green's equivalent stratum.
Directory of Open Access Journals (Sweden)
J. S. de Villiers
2014-10-01
Full Text Available This research focuses on the inversion of geomagnetic variation field measurement to obtain source currents in the ionosphere. During a geomagnetic disturbance, the ionospheric currents create magnetic field variations that induce geoelectric fields, which drive geomagnetically induced currents (GIC in power systems. These GIC may disturb the operation of power systems and cause damage to grounded power transformers. The geoelectric fields at any location of interest can be determined from the source currents in the ionosphere through a solution of the forward problem. Line currents running east–west along given surface position are postulated to exist at a certain height above the Earth's surface. This physical arrangement results in the fields on the ground having the magnetic north and down components, and the electric east component. Ionospheric currents are modelled by inverting Fourier integrals (over the wavenumber of elementary geomagnetic fields using the Levenberg–Marquardt technique. The output parameters of the inversion model are the current strength, height and surface position of the ionospheric current system. A ground conductivity structure with five layers from Quebec, Canada, based on the Layered-Earth model is used to obtain the complex skin depth at a given angular frequency. This paper presents preliminary and inversion results based on these structures and simulated geomagnetic fields. The results show some interesting features in the frequency domain. Model parameters obtained through inversion are within 2% of simulated values. This technique has applications for modelling the currents of electrojets at the equator and auroral regions, as well as currents in the magnetosphere.
Reinwald, Michael; Bernauer, Moritz; Igel, Heiner; Donner, Stefanie
2016-10-01
With the prospects of seismic equipment being able to measure rotational ground motions in a wide frequency and amplitude range in the near future, we engage in the question of how this type of ground motion observation can be used to solve the seismic source inverse problem. In this paper, we focus on the question of whether finite-source inversion can benefit from additional observations of rotational motion. Keeping the overall number of traces constant, we compare observations from a surface seismic network with 44 three-component translational sensors (classic seismometers) with those obtained with 22 six-component sensors (with additional three-component rotational motions). Synthetic seismograms are calculated for known finite-source properties. The corresponding inverse problem is posed in a probabilistic way using the Shannon information content to measure how the observations constrain the seismic source properties. We minimize the influence of the source receiver geometry around the fault by statistically analyzing six-component inversions with a random distribution of receivers. Since our previous results are achieved with a regular spacing of the receivers, we try to answer the question of whether the results are dependent on the spatial distribution of the receivers. The results show that with the six-component subnetworks, kinematic source inversions for source properties (such as rupture velocity, rise time, and slip amplitudes) are not only equally successful (even that would be beneficial because of the substantially reduced logistics installing half the sensors) but also statistically inversions for some source properties are almost always improved. This can be attributed to the fact that the (in particular vertical) gradient information is contained in the additional motion components. We compare these effects for strike-slip and normal-faulting type sources and confirm that the increase in inversion quality for kinematic source parameters is
Cheng, Jin; Hon, Yiu-Chung; Seo, Jin Keun; Yamamoto, Masahiro
2005-01-01
The Second International Conference on Inverse Problems: Recent Theoretical Developments and Numerical Approaches was held at Fudan University, Shanghai from 16-21 June 2004. The first conference in this series was held at the City University of Hong Kong in January 2002 and it was agreed to hold the conference once every two years in a Pan-Pacific Asian country. The next conference is scheduled to be held at Hokkaido University, Sapporo, Japan in July 2006. The purpose of this series of biennial conferences is to establish and develop constant international collaboration, especially among the Pan-Pacific Asian countries. In recent decades, interest in inverse problems has been flourishing all over the globe because of both the theoretical interest and practical requirements. In particular, in Asian countries, one is witnessing remarkable new trends of research in inverse problems as well as the participation of many young talents. Considering these trends, the second conference was organized with the chairperson Professor Li Tat-tsien (Fudan University), in order to provide forums for developing research cooperation and to promote activities in the field of inverse problems. Because solutions to inverse problems are needed in various applied fields, we entertained a total of 92 participants at the second conference and arranged various talks which ranged from mathematical analyses to solutions of concrete inverse problems in the real world. This volume contains 18 selected papers, all of which have undergone peer review. The 18 papers are classified as follows: Surveys: four papers give reviews of specific inverse problems. Theoretical aspects: six papers investigate the uniqueness, stability, and reconstruction schemes. Numerical methods: four papers devise new numerical methods and their applications to inverse problems. Solutions to applied inverse problems: four papers discuss concrete inverse problems such as scattering problems and inverse problems in
Review on solving the forward problem in EEG source analysis
Directory of Open Access Journals (Sweden)
Vergult Anneleen
2007-11-01
Full Text Available Abstract Background The aim of electroencephalogram (EEG source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes. Methods While other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field. Results It starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poisson's differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter. In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poisson's equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM, the finite element method (FEM and the finite difference method (FDM. In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poisson's equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative
International Nuclear Information System (INIS)
Winiarek, Victor
2014-01-01
Uncontrolled releases of pollutant in the atmosphere may be the consequence of various situations: accidents, for instance leaks or explosions in an industrial plant, or terrorist attacks such as biological bombs, especially in urban areas. In the event of such situations, authorities' objectives are various: predict the contaminated zones to apply first countermeasures such as evacuation of concerned population; determine the source location; assess the long-term polluted areas, for instance by deposition of persistent pollutants in the soil. To achieve these objectives, numerical models can be used to model the atmospheric dispersion of pollutants. We will first present the different processes that govern the transport of pollutants in the atmosphere, then the different numerical models that are commonly used in this context. The choice between these models mainly depends of the scale and the details one seeks to take into account. We will then present several inverse modeling methods to estimate the emission as well as statistical methods to estimate prior errors, to which the inversion is very sensitive. Several case studies are presented, using synthetic data as well as real data such as the estimation of source terms from the Fukushima accident in March 2011. From our results, we estimate the Cesium-137 emission to be between 12 and 19 PBq with a standard deviation between 15 and 65% and the Iodine-131 emission to be between 190 and 380 PBq with a standard deviation between 5 and 10%. Concerning the localization of an unknown source of pollutant, two strategies can be considered. On one hand parametric methods use a limited number of parameters to characterize the source term to be reconstructed. To do so, strong assumptions are made on the nature of the source. The inverse problem is hence to estimate these parameters. On the other hand nonparametric methods attempt to reconstruct a full emission field. Several parametric and nonparametric methods are
Active Subspace Methods for Data-Intensive Inverse Problems
Energy Technology Data Exchange (ETDEWEB)
Wang, Qiqi [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
2017-04-27
The project has developed theory and computational tools to exploit active subspaces to reduce the dimension in statistical calibration problems. This dimension reduction enables MCMC methods to calibrate otherwise intractable models. The same theoretical and computational tools can also reduce the measurement dimension for calibration problems that use large stores of data.
Desmal, Abdulla; Bagci, Hakan
2014-01-01
A numerical framework that incorporates recently developed iterative shrinkage thresholding (IST) algorithms within the Born iterative method (BIM) is proposed for solving the two-dimensional inverse electromagnetic scattering problem. IST
DEFF Research Database (Denmark)
Lange, Katrine; Frydendall, Jan; Cordua, Knud Skou
2012-01-01
The frequency matching method defines a closed form expression for a complex prior that quantifies the higher order statistics of a proposed solution model to an inverse problem. While existing solution methods to inverse problems are capable of sampling the solution space while taking into account...... arbitrarily complex a priori information defined by sample algorithms, it is not possible to directly compute the maximum a posteriori model, as the prior probability of a solution model cannot be expressed. We demonstrate how the frequency matching method enables us to compute the maximum a posteriori...... solution model to an inverse problem by using a priori information based on multiple point statistics learned from training images. We demonstrate the applicability of the suggested method on a synthetic tomographic crosshole inverse problem....
Application of Lead Field Theory and Computerized Thorax Modeling for the ECG Inverse Problem
National Research Council Canada - National Science Library
Puurtinen, H
2001-01-01
.... In this study, one anatomically detailed 3D FDM model of the human thorax as a volume conductor was employed for forward and inverse estimation of ECG potentials and cardiac sources, respectively...
Dettmer, J.; Benavente, R. F.; Cummins, P. R.
2017-12-01
This work considers probabilistic, non-linear centroid moment tensor inversion of data from earthquakes at teleseismic distances. The moment tensor is treated as deviatoric and centroid location is parametrized with fully unknown latitude, longitude, depth and time delay. The inverse problem is treated as fully non-linear in a Bayesian framework and the posterior density is estimated with interacting Markov chain Monte Carlo methods which are implemented in parallel and allow for chain interaction. The source mechanism and location, including uncertainties, are fully described by the posterior probability density and complex trade-offs between various metrics are studied. These include the percent of double couple component as well as fault orientation and the probabilistic results are compared to results from earthquake catalogs. Additional focus is on the analysis of complex events which are commonly not well described by a single point source. These events are studied by jointly inverting for multiple centroid moment tensor solutions. The optimal number of sources is estimated by the Bayesian information criterion to ensure parsimonious solutions. [Supported by NSERC.
SQUIDs and inverse problem techniques in nondestructive evaluation of metals
Bruno, A C
2001-01-01
Superconducting Quantum Interference Devices coupled to gradiometers were used to defect flaws in metals. We detected flaws in aluminium samples carrying current, measuring fields at lift-off distances up to one order of magnitude larger than the size of the flaw. Configured as a susceptometer we detected surface-braking flaws in steel samples, measuring the distortion on the applied magnetic field. We also used spatial filtering techniques to enhance the visualization of the magnetic field due to the flaws. In order to assess its severity, we used the generalized inverse method and singular value decomposition to reconstruct small spherical inclusions in steel. In addition, finite elements and optimization techniques were used to image complex shaped flaws.
Solving inverse problems for biological models using the collage method for differential equations.
Capasso, V; Kunze, H E; La Torre, D; Vrscay, E R
2013-07-01
In the first part of this paper we show how inverse problems for differential equations can be solved using the so-called collage method. Inverse problems can be solved by minimizing the collage distance in an appropriate metric space. We then provide several numerical examples in mathematical biology. We consider applications of this approach to the following areas: population dynamics, mRNA and protein concentration, bacteria and amoeba cells interaction, tumor growth.
Collage-type approach to inverse problems for elliptic PDEs on perforated domains
Directory of Open Access Journals (Sweden)
Herb E. Kunze
2015-02-01
Full Text Available We present a collage-based method for solving inverse problems for elliptic partial differential equations on a perforated domain. The main results of this paper establish a link between the solution of an inverse problem on a perforated domain and the solution of the same model on a domain with no holes. The numerical examples at the end of the paper show the goodness of this approach.
Review of the inverse scattering problem at fixed energy in quantum mechanics
Sabatier, P. C.
1972-01-01
Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.
Well-posedness of inverse problems for systems with time dependent parameters
DEFF Research Database (Denmark)
Banks, H. T.; Pedersen, Michael
2009-01-01
on the data of the problem. We also consider well-posedness as well as finite element type approximations in associated inverse problems. The problem above is a weak formulation that includes models in abstract differential operator form that include plate, beam and shell equations with several important...
Abdelsalhin, Tiziano; Maselli, Andrea; Ferrari, Valeria
2018-04-01
The LIGO/Virgo Collaboration has recently announced the direct detection of gravitational waves emitted in the coalescence of a neutron star binary. This discovery allows, for the first time, to set new constraints on the behavior of matter at supranuclear density, complementary with those coming from astrophysical observations in the electromagnetic band. In this paper we demonstrate the feasibility of using gravitational signals to solve the relativistic inverse stellar problem, i.e., to reconstruct the parameters of the equation of state (EoS) from measurements of the stellar mass and tidal Love number. We perform Bayesian inference of mock data, based on different models of the star internal composition, modeled through piecewise polytropes. Our analysis shows that the detection of a small number of sources by a network of advanced interferometers would allow to put accurate bounds on the EoS parameters, and to perform a model selection among the realistic equations of state proposed in the literature.
Seismic signal simulation and study of underground nuclear sources by moment inversion
International Nuclear Information System (INIS)
Crusem, R.
1986-09-01
Some problems of underground nuclear explosions are examined from the seismological point of view. In the first part a model is developed for mean seismic propagation through the lagoon of Mururoa atoll and for calculation of synthetic seismograms (in intermediate fields: 5 to 20 km) by summation of discrete wave numbers. In the second part this ground model is used with a linear inversion method of seismic moments for estimation of elastic source terms equivalent to the nuclear source. Only the isotrope part is investigated solution stability is increased by using spectral smoothing and a minimal phase hypothesis. Some examples of applications are presented: total energy estimation of a nuclear explosion, simulation of mechanical effects induced by an underground explosion [fr
International Nuclear Information System (INIS)
Castaneda M, V. H.; Martinez B, M. R.; Solis S, L. O.; Castaneda M, R.; Leon P, A. A.; Hernandez P, C. F.; Espinoza G, J. G.; Ortiz R, J. M.; Vega C, H. R.; Mendez, R.; Gallego, E.; Sousa L, M. A.
2016-10-01
The Taguchi methodology has proved to be highly efficient to solve inverse problems, in which the values of some parameters of the model must be obtained from the observed data. There are intrinsic mathematical characteristics that make a problem known as inverse. Inverse problems appear in many branches of science, engineering and mathematics. To solve this type of problem, researches have used different techniques. Recently, the use of techniques based on Artificial Intelligence technology is being explored by researches. This paper presents the use of a software tool based on artificial neural networks of generalized regression in the solution of inverse problems with application in high energy physics, specifically in the solution of the problem of neutron spectrometry. To solve this problem we use a software tool developed in the Mat Lab programming environment, which employs a friendly user interface, intuitive and easy to use for the user. This computational tool solves the inverse problem involved in the reconstruction of the neutron spectrum based on measurements made with a Bonner spheres spectrometric system. Introducing this information, the neural network is able to reconstruct the neutron spectrum with high performance and generalization capability. The tool allows that the end user does not require great training or technical knowledge in development and/or use of software, so it facilitates the use of the program for the resolution of inverse problems that are in several areas of knowledge. The techniques of Artificial Intelligence present singular veracity to solve inverse problems, given the characteristics of artificial neural networks and their network topology, therefore, the tool developed has been very useful, since the results generated by the Artificial Neural Network require few time in comparison to other techniques and are correct results comparing them with the actual data of the experiment. (Author)
DEFF Research Database (Denmark)
Oh, Geok Lian
properties such as the elastic wave speeds and soil densities. One processing method is casting the estimation problem into an inverse problem to solve for the unknown material parameters. The forward model for the seismic signals used in the literatures include ray tracing methods that consider only...... density values of the discretized ground medium, which leads to time-consuming computations and instability behaviour of the inversion process. In addition, the geophysics inverse problem is generally ill-posed due to non-exact forward model that introduces errors. The Bayesian inversion method through...... the first arrivals of the reflected compressional P-waves from the subsurface structures, or 3D elastic wave models that model all the seismic wave components. The ray tracing forward model formulation is linear, whereas the full 3D elastic wave model leads to a nonlinear inversion problem. In this Ph...
Integral equations of the first kind, inverse problems and regularization: a crash course
International Nuclear Information System (INIS)
Groetsch, C W
2007-01-01
This paper is an expository survey of the basic theory of regularization for Fredholm integral equations of the first kind and related background material on inverse problems. We begin with an historical introduction to the field of integral equations of the first kind, with special emphasis on model inverse problems that lead to such equations. The basic theory of linear Fredholm equations of the first kind, paying particular attention to E. Schmidt's singular function analysis, Picard's existence criterion, and the Moore-Penrose theory of generalized inverses is outlined. The fundamentals of the theory of Tikhonov regularization are then treated and a collection of exercises and a bibliography are provided
FOREWORD: 5th International Workshop on New Computational Methods for Inverse Problems
Vourc'h, Eric; Rodet, Thomas
2015-11-01
This volume of Journal of Physics: Conference Series is dedicated to the scientific research presented during the 5th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2015 (http://complement.farman.ens-cachan.fr/NCMIP_2015.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 29, 2015. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011, and secondly at the initiative of Institut Farman, in May 2012, May 2013 and May 2014. The New Computational Methods for Inverse Problems (NCMIP) workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods
FOREWORD: 4th International Workshop on New Computational Methods for Inverse Problems (NCMIP2014)
2014-10-01
This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 4th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2014 (http://www.farman.ens-cachan.fr/NCMIP_2014.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 23, 2014. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 and May 2013, (http://www.farman.ens-cachan.fr/NCMIP_2012.html), (http://www.farman.ens-cachan.fr/NCMIP_2013.html). The New Computational Methods for Inverse Problems (NCMIP) Workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the
Choi, Yun Seok
2011-09-01
Full waveform inversion requires a good estimation of the source wavelet to improve our chances of a successful inversion. This is especially true for an encoded multisource time-domain implementation, which, conventionally, requires separate-source modeling, as well as the Fourier transform of wavefields. As an alternative, we have developed the source-independent time-domain waveform inversion using convolved wavefields. Specifically, the misfit function consists of the convolution of the observed wavefields with a reference trace from the modeled wavefield, plus the convolution of the modeled wavefields with a reference trace from the observed wavefield. In this case, the source wavelet of the observed and the modeled wavefields are equally convolved with both terms in the misfit function, and thus, the effects of the source wavelets are eliminated. Furthermore, because the modeled wavefields play a role of low-pass filtering, the observed wavefields in the misfit function, the frequency-selection strategy from low to high can be easily adopted just by setting the maximum frequency of the source wavelet of the modeled wavefields; and thus, no filtering is required. The gradient of the misfit function is computed by back-propagating the new residual seismograms and applying the imaging condition, similar to reverse-time migration. In the synthetic data evaluations, our waveform inversion yields inverted models that are close to the true model, but demonstrates, as predicted, some limitations when random noise is added to the synthetic data. We also realized that an average of traces is a better choice for the reference trace than using a single trace. © 2011 Society of Exploration Geophysicists.
Inverse problems in machine learning: An application to brain activity interpretation
International Nuclear Information System (INIS)
Prato, M; Zanni, L
2008-01-01
In a typical machine learning problem one has to build a model from a finite training set which is able to generalize the properties characterizing the examples of the training set to new examples. The model has to reflect as much as possible the set of training examples but, especially in real-world problems in which the data are often corrupted by different sources of noise, it has to avoid a too strict dependence on the training examples themselves. Recent studies on the relationship between this kind of learning problem and the regularization theory for ill-posed inverse problems have given rise to new regularized learning algorithms. In this paper we recall some of these learning methods and we propose an accelerated version of the classical Landweber iterative scheme which results particularly efficient from the computational viewpoint. Finally, we compare the performances of these methods with the classical Support Vector Machines learning algorithm on a real-world experiment concerning brain activity interpretation through the analysis of functional magnetic resonance imaging data.
Butler, T.; Graham, L.; Estep, D.; Dawson, C.; Westerink, J. J.
2015-04-01
The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.
The ''INVERSE PROBLEM'' to the evaluation of magnetic fields
International Nuclear Information System (INIS)
Caspi, S.; Helm, M.; Laslett, L.J.
1996-01-01
In the design of superconducting magnet elements, such as may be required to guide and focus ions in a particle accelerator, one frequently premises some particular current distribution and then proceeds to compute the consequent magnetic field through use of the laws of Biot and Savart or of Ampere. When working in this manner one of course may need to revise frequently the postulated current distribution before arriving at a resulting magnetic field of acceptable field quality. It therefore is of interest to consider an alternative (inverse) procedure in which one specifies a desired character for the field required in the region interior to the winding and undertakes then to evaluate the current distribution on the specified winding surface that would provide this desired field. By evaluating the specified potential in the region interior to the winding along the interface, the authors have determined that a relaxation solution to the potential in the region outside the winding can be converged and used to calculate wire location. They have demonstrated this method by applying a slightly modified version of the program POISSON to a periodic alternating sinusoidal quadrupole field
Micro-seismic Imaging Using a Source Independent Waveform Inversion Method
Wang, Hanchen
2016-04-18
Micro-seismology is attracting more and more attention in the exploration seismology community. The main goal in micro-seismic imaging is to find the source location and the ignition time in order to track the fracture expansion, which will help engineers monitor the reservoirs. Conventional imaging methods work fine in this field but there are many limitations such as manual picking, incorrect migration velocity and low signal to noise ratio (S/N). In traditional surface survey imaging, full waveform inversion (FWI) is widely used. The FWI method updates the velocity model by minimizing the misfit between the observed data and the predicted data. Using FWI to locate and image microseismic events allows for an automatic process (free of picking) that utilizes the full wavefield. Use the FWI technique, and overcomes the difficulties of manual pickings and incorrect velocity model for migration. However, the technique of waveform inversion of micro-seismic events faces its own problems. There is significant nonlinearity due to the unknown source location (space) and function (time). We have developed a source independent FWI of micro-seismic events to simultaneously invert for the source image, source function and velocity model. It is based on convolving reference traces with the observed and modeled data to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. To examine the accuracy of the inverted source image and velocity model the extended image for source wavelet in z-axis is extracted. Also the angle gather is calculated to check the applicability of the migration velocity. By inverting for the source image, source wavelet and the velocity model simultaneously, the proposed method produces good estimates of the source location, ignition time and the background velocity in the synthetic experiments with both parts of the Marmousi and the SEG
The algebraic method of the scattering inverse problem solution under untraditional statements
Popushnoj, M N
2001-01-01
The algebraic method of the scattering inverse problem solution under untraditional statements is proposed consistently in this review, in the framework of which some quantum theory od scattering charged particles problem were researched afterwards. The inverse problem of scattering theory of charged particles on the complex plane of the Coulomb coupling constant (CCC) is considered. A procedure of interaction potential restoration is established for the case when the energy, orbital moment quadrate and CCC are linearly dependent. The relation between one-parametric problems of the potential scattering of charged particles is investigated
Liouville's theorem and the method of the inverse problem
International Nuclear Information System (INIS)
Its, A.R.
1985-01-01
An approach to the investigation of the Zakharov-Shabat equations is developed. This approach is based on a classical theorem of Liouville and is the synthesis of ''finite-zone'' integration, the matrix Riemann problem method and the theory of isomonodromy deformations of differential equations. The effectiveness of the proposed scheme is demonstrated by developing ''dressing procedures'' for the Bullough-Dodd equation
Uniqueness of inverse scattering problem in local quantum physics
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: schroer@cbpf.br
2001-06-01
It is shown that the a Bisognano-Wichmann-Unruh inspired formulation of local quantum physics which starts from wedge-localized algebras, leads to a uniqueness proof for the scattering problem. The important mathematical tool is the thermal KMS aspect of localization and its strengthening by the requirement of crossing symmetry for generalized formfactors. (author)
Application of the unwrapped phase inversion to land data without source estimation
Choi, Yun Seok; Alkhalifah, Tariq Ali; DeVault, Bryan
2015-01-01
and the source wavelet are updated simultaneously and interact with each other. We suggest a source-independent unwrapped phase inversion approach instead of relying on source-estimation from this land data. In the source-independent approach, the phase
Rapid kinematic finite source inversion for Tsunamic Early Warning using high rate GNSS data
Chen, K.; Liu, Z.; Song, Y. T.
2017-12-01
Recently, Global Navigation Satellite System (GNSS) has been used for rapid earthquake source inversion towards tsunami early warning. In practice, two approaches, i.e., static finite source inversion based on permanent co-seismic offsets and kinematic finite source inversion using high-rate (>= 1 Hz) co-seismic displacement waveforms, are often employed to fulfill the task. The static inversion is relatively easy to be implemented and does not require additional constraints on rupture velocity, duration, and temporal variation. However, since most GNSS receivers are deployed onshore locating on one side of the subduction fault, there is very limited resolution on near-trench fault slip using GNSS in static finite source inversion. On the other hand, the high-rate GNSS displacement waveforms, which contain the timing information of earthquake rupture explicitly and static offsets implicitly, have the potential to improve near-trench resolution by reconciling with the depth-dependent megathrust rupture behaviors. In this contribution, we assess the performance of rapid kinematic finite source inversion using high-rate GNSS by three selected historical tsunamigenic cases: the 2010 Mentawai, 2011 Tohoku and 2015 Illapel events. With respect to the 2010 Mentawai case, it is a typical tsunami earthquake with most slip concentrating near the trench. The static inversion has little resolution there and incorrectly puts slip at greater depth (>10km). In contrast, the recorded GNSS displacement waveforms are deficit in high-frequency energy, the kinematic source inversion recovers a shallow slip patch (depth less than 6 km) and tsunami runups are predicted quite reasonably. For the other two events, slip from kinematic and static inversion show similar characteristics and comparable tsunami scenarios, which may be related to dense GNSS network and behavior of the rupture. Acknowledging the complexity of kinematic source inversion in real-time, we adopt the back
On uniqueness of an inverse problem in electromagnetic obstacle scattering for an impedance cylinder
International Nuclear Information System (INIS)
Nakamura, Gen; Wang, Haibing; Sleeman, Brian D
2012-01-01
We consider an inverse problem for the scattering of an obliquely incident electromagnetic wave by an impedance cylinder. In previous work, we have shown that the direct scattering problem is governed by a pair of Helmholtz equations subject to coupled oblique boundary conditions, where the wave number depends on the frequency and the incident angle with respect to the axis of the cylinder. In this paper, we are concerned with the inverse problem of uniquely identifying the cross-section of an unknown cylinder and the impedance function from the far-field patterns at fixed frequency and a range of incident angles. A uniqueness result for such an inverse scattering problem is established. Our method is based on the analyticity of solution to the direct scattering problem, which is justified by using the Lax–Phillips method together with the perturbation theory of Fredholm operators. (paper)
Uniqueness for the inverse backscattering problem for angularly controlled potentials
International Nuclear Information System (INIS)
Rakesh; Uhlmann, Gunther
2014-01-01
We consider the problem of recovering a smooth, compactly supported potential on R 3 from its backscattering data. We show that if two such potentials have the same backscattering data and the difference of the two potentials has controlled angular derivatives, then the two potentials are identical. In particular, if two potentials differ by a finite linear combination of spherical harmonics with radial coefficients and have the same backscattering data then the two potentials are identical. (paper)
Institute of Scientific and Technical Information of China (English)
ZHANG Yin; WEI Zhiyuan; ZHANG Yinping; WANG Xin
2017-01-01
Urban heating in northern China accounts for 40％ of total building energy usage.In central heating systems,heat is often transfened from heat source to users by the heat network where several heat exchangers arc installed at heat source,substations and terminals respectively.For given overall heating capacity and heat source temperarure,increasing the terminal fluid temperature is an effective way to improve the thermal performance of such cascade heat exchange network for energy saving.In this paper,the mathematical optimization model of the cascade heat exchange network with three-stage heat exchangers in series is established.Aim at maximizing the cold fluid temperature for given hot fluid temperature and overall heating capacity,the optimal heat exchange area distribution and the medium fluids' flow rates are determined through inverse problem and variation method.The preliminary results show that the heat exchange areas should be distributed equally for each heat exchanger.It also indicates that in order to improve the thernmal performance of the whole system,more heat exchange areas should be allocated to the heat exchanger where flow rate difference between two fluids is relatively small.This work is important for guiding the optimization design of practical cascade heating systems.
Solving the patient zero inverse problem by using generalized simulated annealing
Menin, Olavo H.; Bauch, Chris T.
2018-01-01
Identifying patient zero - the initially infected source of a given outbreak - is an important step in epidemiological investigations of both existing and emerging infectious diseases. Here, the use of the Generalized Simulated Annealing algorithm (GSA) to solve the inverse problem of finding the source of an outbreak is studied. The classical disease natural histories susceptible-infected (SI), susceptible-infected-susceptible (SIS), susceptible-infected-recovered (SIR) and susceptible-infected-recovered-susceptible (SIRS) in a regular lattice are addressed. Both the position of patient zero and its time of infection are considered unknown. The algorithm performance with respect to the generalization parameter q˜v and the fraction ρ of infected nodes for whom infection was ascertained is assessed. Numerical experiments show the algorithm is able to retrieve the epidemic source with good accuracy, even when ρ is small, but present no evidence to support that GSA performs better than its classical version. Our results suggest that simulated annealing could be a helpful tool for identifying patient zero in an outbreak where not all cases can be ascertained.
Solution of the Cox-Thompson inverse scattering problem using finite set of phase shifts
Apagyi, B; Scheid, W
2003-01-01
A system of nonlinear equations is presented for the solution of the Cox-Thompson inverse scattering problem (1970 J. Math. Phys. 11 805) at fixed energy. From a given finite set of phase shifts for physical angular momenta, the nonlinear equations determine related sets of asymptotic normalization constants and nonphysical (shifted) angular momenta from which all quantities of interest, including the inversion potential itself, can be calculated. As a first application of the method we use input data consisting of a finite set of phase shifts calculated from Woods-Saxon and box potentials representing interactions with diffuse or sharp surfaces, respectively. The results for the inversion potentials, their first moments and asymptotic properties are compared with those provided by the Newton-Sabatier quantum inversion procedure. It is found that in order to achieve inversion potentials of similar quality, the Cox-Thompson method requires a smaller set of phase shifts than the Newton-Sabatier procedure.
Solution of the Cox-Thompson inverse scattering problem using finite set of phase shifts
International Nuclear Information System (INIS)
Apagyi, Barnabas; Harman, Zoltan; Scheid, Werner
2003-01-01
A system of nonlinear equations is presented for the solution of the Cox-Thompson inverse scattering problem (1970 J. Math. Phys. 11 805) at fixed energy. From a given finite set of phase shifts for physical angular momenta, the nonlinear equations determine related sets of asymptotic normalization constants and nonphysical (shifted) angular momenta from which all quantities of interest, including the inversion potential itself, can be calculated. As a first application of the method we use input data consisting of a finite set of phase shifts calculated from Woods-Saxon and box potentials representing interactions with diffuse or sharp surfaces, respectively. The results for the inversion potentials, their first moments and asymptotic properties are compared with those provided by the Newton-Sabatier quantum inversion procedure. It is found that in order to achieve inversion potentials of similar quality, the Cox-Thompson method requires a smaller set of phase shifts than the Newton-Sabatier procedure
Energy Technology Data Exchange (ETDEWEB)
Krukovsky, P G [Institute of Engineering Thermophysics, National Academy of Sciences of Ukraine, Kiev (Ukraine)
1998-12-31
The description of method and software FRIEND which provide a possibility of solution of inverse and inverse design problems on the basis of existing (base) CFD-software for solution of direct problems (in particular, heat-transfer and fluid-flow problems using software PHOENICS) are presented. FRIEND is an independent additional module that widens the operational capacities of the base software unified with this module. This unifying does not require any change or addition to the base software. Interfacing of FRIEND and the base software takes place through input and output files of the base software. A brief description of the computational technique applied for the inverse problem solution, same detailed information on the interfacing of FRIEND and CFD-software and solution results for testing inverse and inverse design problems, obtained using the tandem CFD-software PHOENICS and FRIEND, are presented. (author) 9 refs.
Energy Technology Data Exchange (ETDEWEB)
Krukovsky, P.G. [Institute of Engineering Thermophysics, National Academy of Sciences of Ukraine, Kiev (Ukraine)
1997-12-31
The description of method and software FRIEND which provide a possibility of solution of inverse and inverse design problems on the basis of existing (base) CFD-software for solution of direct problems (in particular, heat-transfer and fluid-flow problems using software PHOENICS) are presented. FRIEND is an independent additional module that widens the operational capacities of the base software unified with this module. This unifying does not require any change or addition to the base software. Interfacing of FRIEND and the base software takes place through input and output files of the base software. A brief description of the computational technique applied for the inverse problem solution, same detailed information on the interfacing of FRIEND and CFD-software and solution results for testing inverse and inverse design problems, obtained using the tandem CFD-software PHOENICS and FRIEND, are presented. (author) 9 refs.
Maximum a posteriori probability estimates in infinite-dimensional Bayesian inverse problems
International Nuclear Information System (INIS)
Helin, T; Burger, M
2015-01-01
A demanding challenge in Bayesian inversion is to efficiently characterize the posterior distribution. This task is problematic especially in high-dimensional non-Gaussian problems, where the structure of the posterior can be very chaotic and difficult to analyse. Current inverse problem literature often approaches the problem by considering suitable point estimators for the task. Typically the choice is made between the maximum a posteriori (MAP) or the conditional mean (CM) estimate. The benefits of either choice are not well-understood from the perspective of infinite-dimensional theory. Most importantly, there exists no general scheme regarding how to connect the topological description of a MAP estimate to a variational problem. The recent results by Dashti and others (Dashti et al 2013 Inverse Problems 29 095017) resolve this issue for nonlinear inverse problems in Gaussian framework. In this work we improve the current understanding by introducing a novel concept called the weak MAP (wMAP) estimate. We show that any MAP estimate in the sense of Dashti et al (2013 Inverse Problems 29 095017) is a wMAP estimate and, moreover, how the wMAP estimate connects to a variational formulation in general infinite-dimensional non-Gaussian problems. The variational formulation enables to study many properties of the infinite-dimensional MAP estimate that were earlier impossible to study. In a recent work by the authors (Burger and Lucka 2014 Maximum a posteriori estimates in linear inverse problems with logconcave priors are proper bayes estimators preprint) the MAP estimator was studied in the context of the Bayes cost method. Using Bregman distances, proper convex Bayes cost functions were introduced for which the MAP estimator is the Bayes estimator. Here, we generalize these results to the infinite-dimensional setting. Moreover, we discuss the implications of our results for some examples of prior models such as the Besov prior and hierarchical prior. (paper)
International Nuclear Information System (INIS)
Bakhos, Tania; Saibaba, Arvind K.; Kitanidis, Peter K.
2015-01-01
We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method
Energy Technology Data Exchange (ETDEWEB)
Bakhos, Tania, E-mail: taniab@stanford.edu [Institute for Computational and Mathematical Engineering, Stanford University (United States); Saibaba, Arvind K. [Department of Electrical and Computer Engineering, Tufts University (United States); Kitanidis, Peter K. [Institute for Computational and Mathematical Engineering, Stanford University (United States); Department of Civil and Environmental Engineering, Stanford University (United States)
2015-10-15
We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method.
NUMERICAL SOLUTION OF SINGULAR INVERSE NODAL PROBLEM BY USING CHEBYSHEV POLYNOMIALS
NEAMATY, ABDOLALI; YILMAZ, EMRAH; AKBARPOOR, SHAHRBANOO; DABBAGHIAN, ABDOLHADI
2017-01-01
In this study, we consider Sturm-Liouville problem in two cases: the first case having no singularity and the second case having a singularity at zero. Then, we calculate the eigenvalues and the nodal points and present the uniqueness theorem for the solution of the inverse problem by using a dense subset of the nodal points in two given cases. Also, we use Chebyshev polynomials of the first kind for calculating the approximate solution of the inverse nodal problem in these cases. Finally, we...
Statistical method for resolving the photon-photoelectron-counting inversion problem
International Nuclear Information System (INIS)
Wu Jinlong; Li Tiejun; Peng, Xiang; Guo Hong
2011-01-01
A statistical inversion method is proposed for the photon-photoelectron-counting statistics in quantum key distribution experiment. With the statistical viewpoint, this problem is equivalent to the parameter estimation for an infinite binomial mixture model. The coarse-graining idea and Bayesian methods are applied to deal with this ill-posed problem, which is a good simple example to show the successful application of the statistical methods to the inverse problem. Numerical results show the applicability of the proposed strategy. The coarse-graining idea for the infinite mixture models should be general to be used in the future.
A gradient based algorithm to solve inverse plane bimodular problems of identification
Ran, Chunjiang; Yang, Haitian; Zhang, Guoqing
2018-02-01
This paper presents a gradient based algorithm to solve inverse plane bimodular problems of identifying constitutive parameters, including tensile/compressive moduli and tensile/compressive Poisson's ratios. For the forward bimodular problem, a FE tangent stiffness matrix is derived facilitating the implementation of gradient based algorithms, for the inverse bimodular problem of identification, a two-level sensitivity analysis based strategy is proposed. Numerical verification in term of accuracy and efficiency is provided, and the impacts of initial guess, number of measurement points, regional inhomogeneity, and noisy data on the identification are taken into accounts.
Inverse problem theory methods for data fitting and model parameter estimation
Tarantola, A
2002-01-01
Inverse Problem Theory is written for physicists, geophysicists and all scientists facing the problem of quantitative interpretation of experimental data. Although it contains a lot of mathematics, it is not intended as a mathematical book, but rather tries to explain how a method of acquisition of information can be applied to the actual world.The book provides a comprehensive, up-to-date description of the methods to be used for fitting experimental data, or to estimate model parameters, and to unify these methods into the Inverse Problem Theory. The first part of the book deals wi
Two numerical methods for an inverse problem for the 2-D Helmholtz equation
Gryazin, Y A; Lucas, T R
2003-01-01
Two solution methods for the inverse problem for the 2-D Helmholtz equation are developed, tested, and compared. The proposed approaches are based on a marching finite-difference scheme which requires the solution of an overdetermined system at each step. The preconditioned conjugate gradient method is used for rapid solutions of these systems and an efficient preconditioner has been developed for this class of problems. Underlying target applications include the imaging of land mines, unexploded ordinance, and pollutant plumes in environmental cleanup sites, each formulated as an inverse problem for a 2-D Helmholtz equation. The images represent the electromagnetic properties of the respective underground regions. Extensive numerical results are presented.
A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line
Its, A.; Sukhanov, V.
2016-05-01
The paper is concerned with the inverse scattering problem for the Stark operator on the line with a potential from the Schwartz class. In our study of the inverse problem, we use the Riemann-Hilbert formalism. This allows us to overcome the principal technical difficulties which arise in the more traditional approaches based on the Gel’fand-Levitan-Marchenko equations, and indeed solve the problem. We also produce a complete description of the relevant scattering data (which have not been obtained in the previous works on the Stark operator) and establish the bijection between the Schwartz class potentials and the scattering data.
Bagnardi, M.; Hooper, A. J.
2017-12-01
Inversions of geodetic observational data, such as Interferometric Synthetic Aperture Radar (InSAR) and Global Navigation Satellite System (GNSS) measurements, are often performed to obtain information about the source of surface displacements. Inverse problem theory has been applied to study magmatic processes, the earthquake cycle, and other phenomena that cause deformation of the Earth's interior and of its surface. Together with increasing improvements in data resolution, both spatial and temporal, new satellite missions (e.g., European Commission's Sentinel-1 satellites) are providing the unprecedented opportunity to access space-geodetic data within hours from their acquisition. To truly take advantage of these opportunities we must become able to interpret geodetic data in a rapid and robust manner. Here we present the open-source Geodetic Bayesian Inversion Software (GBIS; available for download at http://comet.nerc.ac.uk/gbis). GBIS is written in Matlab and offers a series of user-friendly and interactive pre- and post-processing tools. For example, an interactive function has been developed to estimate the characteristics of noise in InSAR data by calculating the experimental semi-variogram. The inversion software uses a Markov-chain Monte Carlo algorithm, incorporating the Metropolis-Hastings algorithm with adaptive step size, to efficiently sample the posterior probability distribution of the different source parameters. The probabilistic Bayesian approach allows the user to retrieve estimates of the optimal (best-fitting) deformation source parameters together with the associated uncertainties produced by errors in the data (and by scaling, errors in the model). The current version of GBIS (V1.0) includes fast analytical forward models for magmatic sources of different geometry (e.g., point source, finite spherical source, prolate spheroid source, penny-shaped sill-like source, and dipping-dike with uniform opening) and for dipping faults with uniform
Inverse Source Data-Processing Strategies for Radio-Frequency Localization in Indoor Environments
Directory of Open Access Journals (Sweden)
Gianluca Gennarelli
2017-10-01
Full Text Available Indoor positioning of mobile devices plays a key role in many aspects of our daily life. These include real-time people tracking and monitoring, activity recognition, emergency detection, navigation, and numerous location based services. Despite many wireless technologies and data-processing algorithms have been developed in recent years, indoor positioning is still a problem subject of intensive research. This paper deals with the active radio-frequency (RF source localization in indoor scenarios. The localization task is carried out at the physical layer thanks to receiving sensor arrays which are deployed on the border of the surveillance region to record the signal emitted by the source. The localization problem is formulated as an imaging one by taking advantage of the inverse source approach. Different measurement configurations and data-processing/fusion strategies are examined to investigate their effectiveness in terms of localization accuracy under both line-of-sight (LOS and non-line of sight (NLOS conditions. Numerical results based on full-wave synthetic data are reported to support the analysis.
Inverse Problems for a Parabolic Integrodifferential Equation in a Convolutional Weak Form
Directory of Open Access Journals (Sweden)
Kairi Kasemets
2013-01-01
Full Text Available We deduce formulas for the Fréchet derivatives of cost functionals of several inverse problems for a parabolic integrodifferential equation in a weak formulation. The method consists in the application of an integrated convolutional form of the weak problem and all computations are implemented in regular Sobolev spaces.
Bayes procedures for adaptive inference in inverse problems for the white noise model
Knapik, B.T.; Szabó, B.T.; van der Vaart, A.W.; van Zanten, J.H.
2016-01-01
We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies regularity. We prove that both methods we consider succeed
Observation and inverse problems in coupled cell networks
International Nuclear Information System (INIS)
Joly, Romain
2012-01-01
A coupled cell network is a model for many situations such as food webs in ecosystems, cellular metabolism and economic networks. It consists in a directed graph G, each node (or cell) representing an agent of the network and each directed arrow representing which agent acts on which. It yields a system of differential equations .x(t)=f(x(t)), where the component i of f depends only on the cells x j (t) for which the arrow j → i exists in G. In this paper, we investigate the observation problems in coupled cell networks: can one deduce the behaviour of the whole network (oscillations, stabilization, etc) by observing only one of the cells? We show that the natural observation properties hold for almost all the interactions f
International Nuclear Information System (INIS)
Choi, C. Y.; Park, C. T.; Kim, T. H.; Han, K. N.; Choe, S. H.
1995-01-01
A geometrical inverse heat conduction problem is solved for the development of Infrared Computerized-Axial-Tomography (IR CAT) Scan by using a boundary element method in conjunction with regularization procedure. In this problem, an overspecified temperature condition by infrared scanning is provided on the surface, and is used together with other conditions to solve the position of an unknown boundary (cavity). An auxiliary problem is introduced in the solution of this problem. By defining a hypothetical inner boundary for the auxiliary problem domain, the cavity is located interior to the domain and its position is determined by solving a potential problem. Boundary element method with regularization procedure is used to solve this problem, and the effects of regularization on the inverse solution method are investigated by means of numerical analysis
Inverse problem for the mean-field monomer-dimer model with attractive interaction
International Nuclear Information System (INIS)
Contucci, Pierluigi; Luzi, Rachele; Vernia, Cecilia
2017-01-01
The inverse problem method is tested for a class of monomer-dimer statistical mechanics models that contain also an attractive potential and display a mean-field critical point at a boundary of a coexistence line. The inversion is obtained by analytically identifying the parameters in terms of the correlation functions and via the maximum-likelihood method. The precision is tested in the whole phase space and, when close to the coexistence line, the algorithm is used together with a clustering method to take care of the underlying possible ambiguity of the inversion. (paper)
Choi, Yun Seok; Alkhalifah, Tariq Ali
2012-01-01
Conventional multi-source waveform inversion using an objective function based on the least-square misfit cannot be applied to marine streamer acquisition data because of inconsistent acquisition geometries between observed and modelled data
Micro-seismic imaging using a source function independent full waveform inversion method
Wang, Hanchen; Alkhalifah, Tariq Ali
2018-01-01
hand, the conventional micro-seismic source locating methods require, in many cases manual picking of traveltime arrivals, which do not only lead to manual effort and human interaction, but also prone to errors. Using full waveform inversion (FWI
THE DIDACTIC ANALYSIS OF STUDIES ON THE INVERSE PROBLEMS FOR THE DIFFERENTIAL EQUATIONS
Directory of Open Access Journals (Sweden)
В С Корнилов
2017-12-01
Full Text Available In article results of the didactic analysis of the organization and carrying out seminar classes in the inverse problems for the differential equations for students of higher educational institutions of the physical and mathematical directions of preparation are discussed. Such analysis includes a general characteristic of mathematical content of seminar occupations, the analysis of structure of seminar occupation, the analysis of realization of the developing and educational purposes, allocation of didactic units and informative means which have to be acquired by students when training each section of content of training in the inverse problems and other important psychology and pedagogical aspects. The attention to establishment of compliance to those of seminar occupations to lecture material and identification of functions in teaching and educational process which are carried out at the solution of the inverse problems, and also is paid to need to show various mathematical receptions and methods of their decision. Such didactic analysis helps not only to reveal such inverse problems at which solution students can collectively join in creative process of search of their decision, but also effectively organize control of assimilation of knowledge and abilities of students on the inverse problems for the differential equations.
Double point source W-phase inversion: Real-time implementation and automated model selection
Nealy, Jennifer; Hayes, Gavin
2015-01-01
Rapid and accurate characterization of an earthquake source is an extremely important and ever evolving field of research. Within this field, source inversion of the W-phase has recently been shown to be an effective technique, which can be efficiently implemented in real-time. An extension to the W-phase source inversion is presented in which two point sources are derived to better characterize complex earthquakes. A single source inversion followed by a double point source inversion with centroid locations fixed at the single source solution location can be efficiently run as part of earthquake monitoring network operational procedures. In order to determine the most appropriate solution, i.e., whether an earthquake is most appropriately described by a single source or a double source, an Akaike information criterion (AIC) test is performed. Analyses of all earthquakes of magnitude 7.5 and greater occurring since January 2000 were performed with extended analyses of the September 29, 2009 magnitude 8.1 Samoa earthquake and the April 19, 2014 magnitude 7.5 Papua New Guinea earthquake. The AIC test is shown to be able to accurately select the most appropriate model and the selected W-phase inversion is shown to yield reliable solutions that match published analyses of the same events.
A Bayesian setting for an inverse problem in heat transfer
Ruggeri, Fabrizio; Sawlan, Zaid A; Scavino, Marco; Tempone, Raul
2014-01-01
In this work a Bayesian setting is developed to infer the thermal conductivity, an unknown parameter that appears into heat equation. Temperature data are available on the basis of cooling experiments. The realistic assumption that the boundary data are noisy is introduced, for a given prescribed initial condition. We show how to derive the global likelihood function for the forward boundary-initial condition problem, given the values of the temperature field plus Gaussian noise. We assume that the thermal conductivity parameter can be modelled a priori through a lognormal distributed random variable or by means of a space-dependent stationary lognormal random field. In both cases, given Gaussian priors for the time-dependent Dirichlet boundary values, we marginalize out analytically the joint posterior distribution of and the random boundary conditions, TL and TR, using the linearity of the heat equation. Synthetic data are used to carry out the inference. We exploit the concentration of the posterior distribution of , using the Laplace approximation and therefore avoiding costly MCMC computations.
A Bayesian setting for an inverse problem in heat transfer
Ruggeri, Fabrizio
2014-01-06
In this work a Bayesian setting is developed to infer the thermal conductivity, an unknown parameter that appears into heat equation. Temperature data are available on the basis of cooling experiments. The realistic assumption that the boundary data are noisy is introduced, for a given prescribed initial condition. We show how to derive the global likelihood function for the forward boundary-initial condition problem, given the values of the temperature field plus Gaussian noise. We assume that the thermal conductivity parameter can be modelled a priori through a lognormal distributed random variable or by means of a space-dependent stationary lognormal random field. In both cases, given Gaussian priors for the time-dependent Dirichlet boundary values, we marginalize out analytically the joint posterior distribution of and the random boundary conditions, TL and TR, using the linearity of the heat equation. Synthetic data are used to carry out the inference. We exploit the concentration of the posterior distribution of , using the Laplace approximation and therefore avoiding costly MCMC computations.
Efficient generalized Golub-Kahan based methods for dynamic inverse problems
Chung, Julianne; Saibaba, Arvind K.; Brown, Matthew; Westman, Erik
2018-02-01
We consider efficient methods for computing solutions to and estimating uncertainties in dynamic inverse problems, where the parameters of interest may change during the measurement procedure. Compared to static inverse problems, incorporating prior information in both space and time in a Bayesian framework can become computationally intensive, in part, due to the large number of unknown parameters. In these problems, explicit computation of the square root and/or inverse of the prior covariance matrix is not possible, so we consider efficient, iterative, matrix-free methods based on the generalized Golub-Kahan bidiagonalization that allow automatic regularization parameter and variance estimation. We demonstrate that these methods for dynamic inversion can be more flexible than standard methods and develop efficient implementations that can exploit structure in the prior, as well as possible structure in the forward model. Numerical examples from photoacoustic tomography, space-time deblurring, and passive seismic tomography demonstrate the range of applicability and effectiveness of the described approaches. Specifically, in passive seismic tomography, we demonstrate our approach on both synthetic and real data. To demonstrate the scalability of our algorithm, we solve a dynamic inverse problem with approximately 43 000 measurements and 7.8 million unknowns in under 40 s on a standard desktop.
Reiter, D. T.; Rodi, W. L.
2015-12-01
Constructing 3D Earth models through the joint inversion of large geophysical data sets presents numerous theoretical and practical challenges, especially when diverse types of data and model parameters are involved. Among the challenges are the computational complexity associated with large data and model vectors and the need to unify differing model parameterizations, forward modeling methods and regularization schemes within a common inversion framework. The challenges can be addressed in part by decomposing the inverse problem into smaller, simpler inverse problems that can be solved separately, providing one knows how to merge the separate inversion results into an optimal solution of the full problem. We have formulated an approach to the decomposition of large inverse problems based on the augmented Lagrangian technique from optimization theory. As commonly done, we define a solution to the full inverse problem as the Earth model minimizing an objective function motivated, for example, by a Bayesian inference formulation. Our decomposition approach recasts the minimization problem equivalently as the minimization of component objective functions, corresponding to specified data subsets, subject to the constraints that the minimizing models be equal. A standard optimization algorithm solves the resulting constrained minimization problems by alternating between the separate solution of the component problems and the updating of Lagrange multipliers that serve to steer the individual solution models toward a common model solving the full problem. We are applying our inversion method to the reconstruction of the·crust and upper-mantle seismic velocity structure across Eurasia.· Data for the inversion comprise a large set of P and S body-wave travel times·and fundamental and first-higher mode Rayleigh-wave group velocities.
Random fixed point equations and inverse problems using "collage method" for contraction mappings
Kunze, H. E.; La Torre, D.; Vrscay, E. R.
2007-10-01
In this paper we are interested in the direct and inverse problems for the following class of random fixed point equations T(w,x(w))=x(w) where is a given operator, [Omega] is a probability space and X is a Polish metric space. The inverse problem is solved by recourse to the collage theorem for contractive maps. We then consider two applications: (i) random integral equations, and (ii) random iterated function systems with greyscale maps (RIFSM), for which noise is added to the classical IFSM.
Absolute mass scale calibration in the inverse problem of the physical theory of fireballs.
Kalenichenko, V. V.
A method of the absolute mass scale calibration is suggested for solving the inverse problem of the physical theory of fireballs. The method is based on the data on the masses of the fallen meteorites whose fireballs have been photographed in their flight. The method may be applied to those fireballs whose bodies have not experienced considerable fragmentation during their destruction in the atmosphere and have kept their form well enough. Statistical analysis of the inverse problem solution for a sufficiently representative sample makes it possible to separate a subsample of such fireballs. The data on the Lost City and Innisfree meteorites are used to obtain calibration coefficients.
Inverse Problems in Geosciences: Modelling the Rock Properties of an Oil Reservoir
DEFF Research Database (Denmark)
Lange, Katrine
. We have developed and implemented the Frequency Matching method that uses the closed form expression of the a priori probability density function to formulate an inverse problem and compute the maximum a posteriori solution to it. Other methods for computing models that simultaneously fit data...... of the subsurface of the reservoirs. Hence the focus of this work has been on acquiring models of spatial parameters describing rock properties of the subsurface using geostatistical a priori knowledge and available geophysical data. Such models are solutions to often severely under-determined, inverse problems...
Hybrid inverse problems for a system of Maxwell’s equations
International Nuclear Information System (INIS)
Bal, Guillaume; Zhou, Ting
2014-01-01
This paper concerns the quantitative step of the medical imaging modality thermo-acoustic tomography (TAT). We model the radiation propagation by a system of Maxwell’s equations. We show that the index of refraction of light and the absorption coefficient (conductivity) can be uniquely and stably reconstructed from a sufficiently large number of TAT measurements. Our method is based on verifying that the linearization of the inverse problem forms a redundant elliptic system of equations. We also observe that the reconstructions are qualitatively quite different from the setting where radiation is modeled by a scalar Helmholtz equation as in Bal G et al (2011 Inverse Problems 27 055007). (paper)
Methane combustion kinetic rate constants determination: an ill-posed inverse problem analysis
Directory of Open Access Journals (Sweden)
Bárbara D. L. Ferreira
2013-01-01
Full Text Available Methane combustion was studied by the Westbrook and Dryer model. This well-established simplified mechanism is very useful in combustion science, for computational effort can be notably reduced. In the inversion procedure to be studied, rate constants are obtained from [CO] concentration data. However, when inherent experimental errors in chemical concentrations are considered, an ill-conditioned inverse problem must be solved for which appropriate mathematical algorithms are needed. A recurrent neural network was chosen due to its numerical stability and robustness. The proposed methodology was compared against Simplex and Levenberg-Marquardt, the most used methods for optimization problems.
Fractal-Based Methods and Inverse Problems for Differential Equations: Current State of the Art
Directory of Open Access Journals (Sweden)
Herb E. Kunze
2014-01-01
Full Text Available We illustrate, in this short survey, the current state of the art of fractal-based techniques and their application to the solution of inverse problems for ordinary and partial differential equations. We review several methods based on the Collage Theorem and its extensions. We also discuss two innovative applications: the first one is related to a vibrating string model while the second one considers a collage-based approach for solving inverse problems for partial differential equations on a perforated domain.
Energy Technology Data Exchange (ETDEWEB)
Balci, Murat [Dept. of Mechanical Engineering, Bayburt University, Bayburt (Turkmenistan); Gundogdu, Omer [Dept. of Mechanical Engineering, Ataturk University, Erzurum (Turkmenistan)
2017-01-15
In this study, estimation of some physical properties of a laminated composite plate was conducted via the inverse vibration problem. Laminated composite plate was modelled and simulated to obtain vibration responses for different length-to-thickness ratio in ANSYS. Furthermore, a numerical finite element model was developed for the laminated composite utilizing the Kirchhoff plate theory and programmed in MATLAB for simulations. Optimizing the difference between these two vibration responses, inverse vibration problem was solved to obtain some of the physical properties of the laminated composite using genetic algorithms. The estimated parameters are compared with the theoretical results, and a very good correspondence was observed.
International Nuclear Information System (INIS)
Balci, Murat; Gundogdu, Omer
2017-01-01
In this study, estimation of some physical properties of a laminated composite plate was conducted via the inverse vibration problem. Laminated composite plate was modelled and simulated to obtain vibration responses for different length-to-thickness ratio in ANSYS. Furthermore, a numerical finite element model was developed for the laminated composite utilizing the Kirchhoff plate theory and programmed in MATLAB for simulations. Optimizing the difference between these two vibration responses, inverse vibration problem was solved to obtain some of the physical properties of the laminated composite using genetic algorithms. The estimated parameters are compared with the theoretical results, and a very good correspondence was observed
DEFF Research Database (Denmark)
Montoya-Martinez, Jair; Artes-Rodriguez, Antonio; Pontil, Massimiliano
2014-01-01
We consider the estimation of the Brain Electrical Sources (BES) matrix from noisy electroencephalographic (EEG) measurements, commonly named as the EEG inverse problem. We propose a new method to induce neurophysiological meaningful solutions, which takes into account the smoothness, structured...... sparsity, and low rank of the BES matrix. The method is based on the factorization of the BES matrix as a product of a sparse coding matrix and a dense latent source matrix. The structured sparse-low-rank structure is enforced by minimizing a regularized functional that includes the ℓ21-norm of the coding...... matrix and the squared Frobenius norm of the latent source matrix. We develop an alternating optimization algorithm to solve the resulting nonsmooth-nonconvex minimization problem. We analyze the convergence of the optimization procedure, and we compare, under different synthetic scenarios...
Wu, Sheng-Jhih; Chu, Moody T.
2017-08-01
An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.
International Nuclear Information System (INIS)
Wu, Sheng-Jhih; Chu, Moody T
2017-01-01
An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing–Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations. (paper)
Karve, Pranav M.
2016-12-28
We discuss a methodology for computing the optimal spatio-temporal characteristics of surface wave sources necessary for delivering wave energy to a targeted subsurface formation. The wave stimulation is applied to the target formation to enhance the mobility of particles trapped in its pore space. We formulate the associated wave propagation problem for three-dimensional, heterogeneous, semi-infinite, elastic media. We use hybrid perfectly matched layers at the truncation boundaries of the computational domain to mimic the semi-infiniteness of the physical domain of interest. To recover the source parameters, we define an inverse source problem using the mathematical framework of constrained optimization and resolve it by employing a reduced-space approach. We report the results of our numerical experiments attesting to the methodology\\'s ability to specify the spatio-temporal description of sources that maximize wave energy delivery. Copyright © 2016 John Wiley & Sons, Ltd.
The inverse problems of reconstruction in the X-rays, gamma or positron tomographic imaging systems
International Nuclear Information System (INIS)
Grangeat, P.
1999-01-01
The revolution in imagery, brought by the tomographic technic in the years 70, allows the computation of local values cartography for the attenuation or the emission activity. The reconstruction techniques thus allow the connection from integral measurements to characteristic information distribution by inversion of the measurement equations. They are a main application of the solution technic for inverse problems. In a first part the author recalls the physical principles for measures in X-rays, gamma and positron imaging. Then he presents the various problems with their associated inversion techniques. The third part is devoted to the activity sector and examples, to conclude in the last part with the forecast. (A.L.B.)
Directory of Open Access Journals (Sweden)
Ali Mohammad-Djafari
2015-06-01
Full Text Available The main content of this review article is first to review the main inference tools using Bayes rule, the maximum entropy principle (MEP, information theory, relative entropy and the Kullback–Leibler (KL divergence, Fisher information and its corresponding geometries. For each of these tools, the precise context of their use is described. The second part of the paper is focused on the ways these tools have been used in data, signal and image processing and in the inverse problems, which arise in different physical sciences and engineering applications. A few examples of the applications are described: entropy in independent components analysis (ICA and in blind source separation, Fisher information in data model selection, different maximum entropy-based methods in time series spectral estimation and in linear inverse problems and, finally, the Bayesian inference for general inverse problems. Some original materials concerning the approximate Bayesian computation (ABC and, in particular, the variational Bayesian approximation (VBA methods are also presented. VBA is used for proposing an alternative Bayesian computational tool to the classical Markov chain Monte Carlo (MCMC methods. We will also see that VBA englobes joint maximum a posteriori (MAP, as well as the different expectation-maximization (EM algorithms as particular cases.
International Nuclear Information System (INIS)
Sharma, Pavan K.; Gera, B.; Ghosh, A.K.; Kushwaha, H.S.
2010-01-01
Scalar dispersion in the atmosphere is an important area wherein different approaches are followed in development of good analytical model. The analyses based on Computational Fluid Dynamics (CFD) codes offer an opportunity of model development based on first principles of physics and hence such models have an edge over the existing models. Both forward and backward calculation methods are being developed for atmospheric dispersion around NPPs at BARC Forward modeling methods, which describe the atmospheric transport from sources to receptors, use forward-running transport and dispersion models or computational fluid dynamics models which are run many times, and the resulting dispersion field is compared to observations from multiple sensors. Backward or inverse modeling methods use only one model run in the reverse direction from the receptors to estimate the upwind sources. Inverse modeling methods include adjoint and tangent linear models, Kalman filters, and variational data assimilation, and neural network. The present paper is aimed at developing a new approach where the identified specific signatures at receptor points form the basis for source estimation or inversions. This approach is expected to reduce the large transient data sets to reduced and meaningful data sets. In fact this reduces the inherently transient data set into a time independent mean data set. Forward computation were carried out with CFD code for various case to generate a large set of data to train the ANN. Specific signature analysis was carried out to find the parameters of interest for ANN training like peak concentration, time to reach peak concentration and time to fall, the ANN was trained with data and source strength and location were predicted from ANN. Inverse problem was performed using ANN approach in long range atmospheric dispersion. An illustration of application of CFD code for atmospheric dispersion studies for a hypothetical case is also included in the paper. (author)
On the solution of the inverse scattering problem on a ray
International Nuclear Information System (INIS)
Egikyan, R.S.; Zhidkov, E.P.
1988-01-01
Quantum inverse scattering problem (ISP) is considered within the framework of two-particle scattering for local interaction case depending only on the scattering between particles. Constructing the solution of secondary integral equation solution of ISP is described in the clear image. Numerical calculations are conducted using a direct method
On the Quantum Inverse problem for the continuous Heisenberg spin chain with axial anisotropy
International Nuclear Information System (INIS)
Roy Chowdhury, A.; Chanda, P.K.
1986-06-01
We have considered the Quantum Inverse problem for the continuous form of Heisenberg spin chain with anisotropy. The form of quantum R-matrix, the commutation rules for the scattering data, and the explicit structure of the excitation spectrum are obtained. (author)
On the inverse problem of the calculus of variations in field theory
International Nuclear Information System (INIS)
Henneaux, M.
1984-01-01
The inverse problem of the calculus of variations is investigated in the case of field theory. Uniqueness of the action principle is demonstrated for the vector Laplace equation in a non-decomposable Riemannian space, as well as for the harmonic map equation. (author)
Presymplectic current and the inverse problem of the calculus of variations
Khavkine, I.
2013-01-01
The inverse problem of the calculus of variations asks whether a given system of partial differential equations (PDEs) admits a variational formulation. We show that the existence of a presymplectic form in the variational bicomplex, when horizontally closed on solutions, allows us to construct a
Control and System Theory, Optimization, Inverse and Ill-Posed Problems
1988-09-14
Justlfleatlen Distribut ion/ Availability Codes # AFOSR-87-0350 Avat’ and/or1987-1988 Dist Special *CONTROL AND SYSTEM THEORY , ~ * OPTIMIZATION, * INVERSE...considerable va- riety of research investigations within the grant areas (Control and system theory , Optimization, and Ill-posed problems]. The
Large scale inverse problems computational methods and applications in the earth sciences
Scheichl, Robert; Freitag, Melina A; Kindermann, Stefan
2013-01-01
This book is thesecond volume of three volume series recording the ""Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment"" taking place in Linz, Austria, October 3-7, 2011. The volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications.
An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology
Beretta, Elena; Cavaterra, Cecilia; Cerutti, M. Cristina; Manzoni, Andrea; Ratti, Luca
2017-10-01
In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential in the myocardial tissue. The goal is the detection of an inhomogeneity \
International Nuclear Information System (INIS)
Chaichian, M.; Kulish, P. P.
1978-04-01
Supersymmetric Liouville and sine-Gordon equations are studied. We write down for these models the system of linear equations for which the method of inverse scattering problem should be applicable. Expressions for an infinite set of conserved currents are explicitly given. Supersymmetric Baecklund transformations and generalized conservation laws are constructed. (author)
Physics-based models for measurement correlations: application to an inverse Sturm–Liouville problem
International Nuclear Information System (INIS)
Bal, Guillaume; Ren Kui
2009-01-01
In many inverse problems, the measurement operator, which maps objects of interest to available measurements, is a smoothing (regularizing) operator. Its inverse is therefore unbounded and as a consequence, only the low-frequency component of the object of interest is accessible from inevitably noisy measurements. In many inverse problems however, the neglected high-frequency component may significantly affect the measured data. Using simple scaling arguments, we characterize the influence of the high-frequency component. We then consider situations where the correlation function of such an influence may be estimated by asymptotic expansions, for instance as a random corrector in homogenization theory. This allows us to consistently eliminate the high-frequency component and derive a closed form, more accurate, inverse problem for the low-frequency component of the object of interest. We present the asymptotic expression of the correlation matrix of the eigenvalues in a Sturm–Liouville problem with unknown potential. We propose an iterative algorithm for the reconstruction of the potential from knowledge of the eigenvalues and show that using the approximate correlation matrix significantly improves the reconstructions
The black-body radiation inversion problem, its instability and a new universal function set method
International Nuclear Information System (INIS)
Ye, JiPing; Ji, FengMin; Wen, Tao; Dai, Xian-Xi; Dai, Ji-Xin; Evenson, William E.
2006-01-01
The black-body radiation inversion (BRI) problem is ill-posed and requires special techniques to achieve stable solutions. In this Letter, the universal function set method (UFS), is developed in BRI. An improved unique existence theorem is proposed. Asymptotic behavior control (ABC) is introduced. A numerical example shows that practical calculations are possible with UFS
On inverse and direct free boundary problems in the theory of plasma equilibrium in a Tokamak
International Nuclear Information System (INIS)
Demidov, A.; Petrova, V.; Silantiev, V.
1996-01-01
Theorems of existence of simply connected 'plasma' domain for the cylindrical case of the Grad-Shafranov equation Δu = F(u) are given. For the inverse problem upper and lower estimates of normal derivative of u on the boundary of the 'plasma' domain are obtained. (author)
A general approach to regularizing inverse problems with regional data using Slepian wavelets
Michel, Volker; Simons, Frederik J.
2017-12-01
Slepian functions are orthogonal function systems that live on subdomains (for example, geographical regions on the Earth’s surface, or bandlimited portions of the entire spectrum). They have been firmly established as a useful tool for the synthesis and analysis of localized (concentrated or confined) signals, and for the modeling and inversion of noise-contaminated data that are only regionally available or only of regional interest. In this paper, we consider a general abstract setup for inverse problems represented by a linear and compact operator between Hilbert spaces with a known singular-value decomposition (svd). In practice, such an svd is often only given for the case of a global expansion of the data (e.g. on the whole sphere) but not for regional data distributions. We show that, in either case, Slepian functions (associated to an arbitrarily prescribed region and the given compact operator) can be determined and applied to construct a regularization for the ill-posed regional inverse problem. Moreover, we describe an algorithm for constructing the Slepian basis via an algebraic eigenvalue problem. The obtained Slepian functions can be used to derive an svd for the combination of the regionalizing projection and the compact operator. As a result, standard regularization techniques relying on a known svd become applicable also to those inverse problems where the data are regionally given only. In particular, wavelet-based multiscale techniques can be used. An example for the latter case is elaborated theoretically and tested on two synthetic numerical examples.
SIPPI: A Matlab toolbox for sampling the solution to inverse problems with complex prior information
DEFF Research Database (Denmark)
Hansen, Thomas Mejer; Cordua, Knud Skou; Caroline Looms, Majken
2013-01-01
on the solution. The combined states of information (i.e. the solution to the inverse problem) is a probability density function typically referred to as the a posteriori probability density function. We present a generic toolbox for Matlab and Gnu Octave called SIPPI that implements a number of methods...
SIPPI: A Matlab toolbox for sampling the solution to inverse problems with complex prior information
DEFF Research Database (Denmark)
Hansen, Thomas Mejer; Cordua, Knud Skou; Looms, Majken Caroline
2013-01-01
We present an application of the SIPPI Matlab toolbox, to obtain a sample from the a posteriori probability density function for the classical tomographic inversion problem. We consider a number of different forward models, linear and non-linear, such as ray based forward models that rely...
Inverse problem of the vibrational band gap of periodically supported beam
Shi, Xiaona; Shu, Haisheng; Dong, Fuzhen; Zhao, Lei
2017-04-01
The researches of periodic structures have a long history with the main contents confined in the field of forward problem. In this paper, the inverse problem is considered and an overall frame is proposed which includes two main stages, i.e., the band gap criterion and its optimization. As a preliminary investigation, the inverse problem of the flexural vibrational band gap of a periodically supported beam is analyzed. According to existing knowledge of its forward problem, the band gap criterion is given in implicit form. Then, two cases with three independent parameters, namely the double supported case and the triple one, are studied in detail and the explicit expressions of the feasible domain are constructed by numerical fitting. Finally, the parameter optimization of the double supported case with three variables is conducted using genetic algorithm aiming for the best mean attenuation within specified frequency band.
A domain derivative-based method for solving elastodynamic inverse obstacle scattering problems
International Nuclear Information System (INIS)
Le Louër, Frédérique
2015-01-01
The present work is concerned with the shape reconstruction problem of isotropic elastic inclusions from far-field data obtained by the scattering of a finite number of time-harmonic incident plane waves. This paper aims at completing the theoretical framework which is necessary for the application of geometric optimization tools to the inverse transmission problem in elastodynamics. The forward problem is reduced to systems of boundary integral equations following the direct and indirect methods initially developed for solving acoustic transmission problems. We establish the Fréchet differentiability of the boundary to far-field operator and give a characterization of the first Fréchet derivative and its adjoint operator. Using these results we propose an inverse scattering algorithm based on the iteratively regularized Gauß–Newton method and show numerical experiments in the special case of star-shaped obstacles. (paper)
An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group
International Nuclear Information System (INIS)
Wang, S.J.
1993-04-01
An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group is formulated for the first time. One dimensional problem is treated explicitly in detail for both the finite dimensional and infinite dimensional Hilbert spaces. For the finite dimensional Hilbert space, the su(2) algebraic representation is used; while for the infinite dimensional Hilbert space, the Heisenberg-Weyl algebraic representation is employed. Fourier expansion technique is generalized to the generator space, which is suitable for analysis of irregular spectra. The polynormial operator basis is also used for complement, which is appropriate for analysis of some simple Hamiltonians. The proposed new approach is applied to solve the classical inverse Sturn-Liouville problem and to study the problems of quantum regular and irregular spectra. (orig.)
Guliyev, Namig J.
2008-01-01
International audience; Inverse problems of recovering the coefficients of Sturm–Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: 1) from the sequences of eigenvalues and norming constants; 2) from two spectra. Necessary and sufficient conditions for the solvability of these inverse problems are obtained.
Oblique projections and standard-form transformations for discrete inverse problems
DEFF Research Database (Denmark)
Hansen, Per Christian
2013-01-01
This tutorial paper considers a specific computational tool for the numerical solution of discrete inverse problems, known as the standard-form transformation, by which we can treat general Tikhonov regularization problems efficiently. In the tradition of B. N. Datta's expositions of numerical li...... linear algebra, we use the close relationship between oblique projections, pseudoinverses, and matrix computations to derive a simple geometric motivation and algebraic formulation of the standard-form transformation....
Uniqueness Theorem for the Inverse Aftereffect Problem and Representation the Nodal Points Form
Directory of Open Access Journals (Sweden)
A. Neamaty
2015-03-01
Full Text Available In this paper, we consider a boundary value problem with aftereffect on a finite interval. Then, the asymptotic behavior of the solutions, eigenvalues, the nodal points and the associated nodal length are studied. We also calculate the numerical values of the nodal points and the nodal length. Finally, we prove the uniqueness theorem for the inverse aftereffect problem by applying any dense subset of the nodal points.
Uniqueness Theorem for the Inverse Aftereffect Problem and Representation the Nodal Points Form
A. Neamaty; Sh. Akbarpoor; A. Dabbaghian
2015-01-01
In this paper, we consider a boundary value problem with aftereffect on a finite interval. Then, the asymptotic behavior of the solutions, eigenvalues, the nodal points and the associated nodal length are studied. We also calculate the numerical values of the nodal points and the nodal length. Finally, we prove the uniqueness theorem for the inverse aftereffect problem by applying any dense subset of the nodal points.
Banks, H T; Holm, Kathleen; Robbins, Danielle
2010-11-01
We computationally investigate two approaches for uncertainty quantification in inverse problems for nonlinear parameter dependent dynamical systems. We compare the bootstrapping and asymptotic theory approaches for problems involving data with several noise forms and levels. We consider both constant variance absolute error data and relative error which produces non-constant variance data in our parameter estimation formulations. We compare and contrast parameter estimates, standard errors, confidence intervals, and computational times for both bootstrapping and asymptotic theory methods.
Posterior consistency for Bayesian inverse problems through stability and regression results
International Nuclear Information System (INIS)
Vollmer, Sebastian J
2013-01-01
In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes’ formula, giving rise to the posterior distribution on the unknown input. In this setting we prove posterior consistency for nonlinear inverse problems: a sequence of data is considered, with diminishing fluctuations around a single truth and it is then of interest to show that the resulting sequence of posterior measures arising from this sequence of data concentrates around the truth used to generate the data. Posterior consistency justifies the use of the Bayesian approach very much in the same way as error bounds and convergence results for regularization techniques do. As a guiding example, we consider the inverse problem of reconstructing the diffusion coefficient from noisy observations of the solution to an elliptic PDE in divergence form. This problem is approached by splitting the forward operator into the underlying continuum model and a simpler observation operator based on the output of the model. In general, these splittings allow us to conclude posterior consistency provided a deterministic stability result for the underlying inverse problem and a posterior consistency result for the Bayesian regression problem with the push-forward prior. Moreover, we prove posterior consistency for the Bayesian regression problem based on the regularity, the tail behaviour and the small ball probabilities of the prior. (paper)
Hintermüller, Michael; Holler, Martin; Papafitsoros, Kostas
2018-06-01
In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is the appropriate lower semi-continuous envelope (relaxation) of a suitable TV type functional initially defined for sufficiently smooth functions. We study examples where this relaxation can be expressed explicitly, and we also provide refinements for weighted TV for a wide range of weights. Since an integral characterization of the relaxation in function space is, in general, not always available, we show that, for a rather general linear inverse problems setting, instead of the classical Tikhonov regularization problem, one can equivalently solve a saddle-point problem where no a priori knowledge of an explicit formulation of the structural TV functional is needed. In particular, motivated by concrete applications, we deduce corresponding results for linear inverse problems with norm and Poisson log-likelihood data discrepancy terms. Finally, we provide proof-of-concept numerical examples where we solve the saddle-point problem for weighted TV denoising as well as for MR guided PET image reconstruction.
Analysis of forward and inverse problems in chemical dynamics and spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Rabitz, H. [Princeton Univ., NJ (United States)
1993-12-01
The overall scope of this research concerns the development and application of forward and inverse analysis tools for problems in chemical dynamics and chemical kinetics. The chemical dynamics work is specifically associated with relating features in potential surfaces and resultant dynamical behavior. The analogous inverse research aims to provide stable algorithms for extracting potential surfaces from laboratory data. In the case of chemical kinetics, the focus is on the development of systematic means to reduce the complexity of chemical kinetic models. Recent progress in these directions is summarized below.
Choi, Yun Seok
2012-05-02
Conventional multi-source waveform inversion using an objective function based on the least-square misfit cannot be applied to marine streamer acquisition data because of inconsistent acquisition geometries between observed and modelled data. To apply the multi-source waveform inversion to marine streamer data, we use the global correlation between observed and modelled data as an alternative objective function. The new residual seismogram derived from the global correlation norm attenuates modelled data not supported by the configuration of observed data and thus, can be applied to multi-source waveform inversion of marine streamer data. We also show that the global correlation norm is theoretically the same as the least-square norm of the normalized wavefield. To efficiently calculate the gradient, our method employs a back-propagation algorithm similar to reverse-time migration based on the adjoint-state of the wave equation. In numerical examples, the multi-source waveform inversion using the global correlation norm results in better inversion results for marine streamer acquisition data than the conventional approach. © 2012 European Association of Geoscientists & Engineers.
From capture to simulation: connecting forward and inverse problems in fluids
Gregson, James; Ihrke, Ivo; Thuerey, Nils; Heidrich, Wolfgang
2014-01-01
We explore the connection between fluid capture, simulation and proximal methods, a class of algorithms commonly used for inverse problems in image processing and computer vision. Our key finding is that the proximal operator constraining fluid velocities to be divergence-free is directly equivalent to the pressure-projection methods commonly used in incompressible flow solvers. This observation lets us treat the inverse problem of fluid tracking as a constrained flow problem all while working in an efficient, modular framework. In addition it lets us tightly couple fluid simulation into flow tracking, providing a global prior that significantly increases tracking accuracy and temporal coherence as compared to previous techniques. We demonstrate how we can use these improved results for a variety of applications, such as re-simulation, detail enhancement, and domain modification. We furthermore give an outlook of the applications beyond fluid tracking that our proximal operator framework could enable by exploring the connection of deblurring and fluid guiding.
Solving inverse problems through a smooth formulation of multiple-point geostatistics
DEFF Research Database (Denmark)
Melnikova, Yulia
be inferred, for instance, from a conceptual geological model termed a training image.The main motivation for this study was the challenge posed by history matching, an inverse problem aimed at estimating rock properties from production data. We addressed two main difficulties of the history matching problem...... corresponding inverse problems. However, noise in data, non-linear relationships and sparse observations impede creation of realistic reservoir models. Including complex a priori information on reservoir parameters facilitates the process of obtaining acceptable solutions. Such a priori knowledge may...... strategies including both theoretical motivation and practical aspects of implementation. Finally, it is complemented by six research papers submitted, reviewed and/or published in the period 2010 - 2013....
Energy spectrum inverse problem of q -deformed harmonic oscillator and WBK approximation
International Nuclear Information System (INIS)
Sang, Nguyen Anh; Thuy, Do Thi Thu; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai
2016-01-01
Using the connection between q-deformed harmonic oscillator and Morse-like anharmonic potential we investigate the energy spectrum inverse problem. Consider some energy levels of energy spectrum of q -deformed harmonic oscillator are known, we construct the corresponding Morse-like potential then find out the deform parameter q . The application possibility of using the WKB approximation in the energy spectrum inverse problem was discussed for the cases of parabolic potential (harmonic oscillator), Morse-like potential ( q -deformed harmonic oscillator). so we consider our deformed-three-levels simple model, where the set-parameters of Morse potential and the corresponding set-parameters of level deformations are easily and explicitly defined. For practical problems, we propose the deformed- three-levels simple model, where the set-parameters of Morse potential and the corresponding set-parameters of level deformations are easily and explicitly defined. (paper)
From capture to simulation: connecting forward and inverse problems in fluids
Gregson, James
2014-07-27
We explore the connection between fluid capture, simulation and proximal methods, a class of algorithms commonly used for inverse problems in image processing and computer vision. Our key finding is that the proximal operator constraining fluid velocities to be divergence-free is directly equivalent to the pressure-projection methods commonly used in incompressible flow solvers. This observation lets us treat the inverse problem of fluid tracking as a constrained flow problem all while working in an efficient, modular framework. In addition it lets us tightly couple fluid simulation into flow tracking, providing a global prior that significantly increases tracking accuracy and temporal coherence as compared to previous techniques. We demonstrate how we can use these improved results for a variety of applications, such as re-simulation, detail enhancement, and domain modification. We furthermore give an outlook of the applications beyond fluid tracking that our proximal operator framework could enable by exploring the connection of deblurring and fluid guiding.
An investigation on the solutions for the linear inverse problem in gamma ray tomography
International Nuclear Information System (INIS)
Araujo, Bruna G.M.; Dantas, Carlos C.; Santos, Valdemir A. dos; Finkler, Christine L.L.; Oliveira, Eric F. de; Melo, Silvio B.; Santos, M. Graca dos
2009-01-01
This paper the results obtained in single beam gamma ray tomography are investigated according to direct problem formulation and the applied solution for the linear system of equations. By image reconstruction based algebraic computational algorithms are used. The sparse under and over-determined linear system of equations was analyzed. Build in functions of Matlab software were applied and optimal solutions were investigate. Experimentally a section of the tube is scanned from various positions and at different angles. The solution, to find the vector of coefficients μ, from the vector of measured p values through the W matrix inversion, constitutes an inverse problem. A industrial tomography process requires a numerical solution of the system of equations. The definition of inverse problem according to Hadmard's is considered and as well the requirement of a well posed problem to find stable solutions. The formulation of the basis function and the computational algorithm to structure the weight matrix W were analyzed. For W full rank matrix the obtained solution is unique as expected. Total Least Squares was implemented which theory and computation algorithm gives adequate treatment for the problems due to non-unique solutions of the system of equations. Stability of the solution was investigating by means of a regularization technique and the comparison shows that it improves the results. An optimal solution as a function of the image quality, computation time and minimum residuals were quantified. The corresponding reconstructed images are shown in 3D graphics in order to compare with the solution. (author)
Finite-fault source inversion using adjoint methods in 3D heterogeneous media
Somala, Surendra Nadh; Ampuero, Jean-Paul; Lapusta, Nadia
2018-04-01
Accounting for lateral heterogeneities in the 3D velocity structure of the crust is known to improve earthquake source inversion, compared to results based on 1D velocity models which are routinely assumed to derive finite-fault slip models. The conventional approach to include known 3D heterogeneity in source inversion involves pre-computing 3D Green's functions, which requires a number of 3D wave propagation simulations proportional to the number of stations or to the number of fault cells. The computational cost of such an approach is prohibitive for the dense datasets that could be provided by future earthquake observation systems. Here, we propose an adjoint-based optimization technique to invert for the spatio-temporal evolution of slip velocity. The approach does not require pre-computed Green's functions. The adjoint method provides the gradient of the cost function, which is used to improve the model iteratively employing an iterative gradient-based minimization method. The adjoint approach is shown to be computationally more efficient than the conventional approach based on pre-computed Green's functions in a broad range of situations. We consider data up to 1 Hz from a Haskell source scenario (a steady pulse-like rupture) on a vertical strike-slip fault embedded in an elastic 3D heterogeneous velocity model. The velocity model comprises a uniform background and a 3D stochastic perturbation with the von Karman correlation function. Source inversions based on the 3D velocity model are performed for two different station configurations, a dense and a sparse network with 1 km and 20 km station spacing, respectively. These reference inversions show that our inversion scheme adequately retrieves the rise time when the velocity model is exactly known, and illustrates how dense coverage improves the inference of peak slip velocities. We investigate the effects of uncertainties in the velocity model by performing source inversions based on an incorrect
A penalty method for PDE-constrained optimization in inverse problems
International Nuclear Information System (INIS)
Leeuwen, T van; Herrmann, F J
2016-01-01
Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for several right-hand sides. Such PDE-constrained problems can be solved by finding a stationary point of the Lagrangian, which entails simultaneously updating the parameters and the (adjoint) state variables. For large-scale problems, such an all-at-once approach is not feasible as it requires storing all the state variables. In this case one usually resorts to a reduced approach where the constraints are explicitly eliminated (at each iteration) by solving the PDEs. These two approaches, and variations thereof, are the main workhorses for solving PDE-constrained optimization problems arising from inverse problems. In this paper, we present an alternative method that aims to combine the advantages of both approaches. Our method is based on a quadratic penalty formulation of the constrained optimization problem. By eliminating the state variable, we develop an efficient algorithm that has roughly the same computational complexity as the conventional reduced approach while exploiting a larger search space. Numerical results show that this method indeed reduces some of the nonlinearity of the problem and is less sensitive to the initial iterate. (paper)
Micro-seismic imaging using a source function independent full waveform inversion method
Wang, Hanchen; Alkhalifah, Tariq
2018-03-01
At the heart of micro-seismic event measurements is the task to estimate the location of the source micro-seismic events, as well as their ignition times. The accuracy of locating the sources is highly dependent on the velocity model. On the other hand, the conventional micro-seismic source locating methods require, in many cases manual picking of traveltime arrivals, which do not only lead to manual effort and human interaction, but also prone to errors. Using full waveform inversion (FWI) to locate and image micro-seismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, full waveform inversion of micro-seismic events faces incredible nonlinearity due to the unknown source locations (space) and functions (time). We developed a source function independent full waveform inversion of micro-seismic events to invert for the source image, source function and the velocity model. It is based on convolving reference traces with these observed and modeled to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for the source wavelet in Z axis is extracted to check the accuracy of the inverted source image and velocity model. Also, angle gathers is calculated to assess the quality of the long wavelength component of the velocity model. By inverting for the source image, source wavelet and the velocity model simultaneously, the proposed method produces good estimates of the source location, ignition time and the background velocity for synthetic examples used here, like those corresponding to the Marmousi model and the SEG/EAGE overthrust model.
Micro-seismic imaging using a source function independent full waveform inversion method
Wang, Hanchen
2018-03-26
At the heart of micro-seismic event measurements is the task to estimate the location of the source micro-seismic events, as well as their ignition times. The accuracy of locating the sources is highly dependent on the velocity model. On the other hand, the conventional micro-seismic source locating methods require, in many cases manual picking of traveltime arrivals, which do not only lead to manual effort and human interaction, but also prone to errors. Using full waveform inversion (FWI) to locate and image micro-seismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, full waveform inversion of micro-seismic events faces incredible nonlinearity due to the unknown source locations (space) and functions (time). We developed a source function independent full waveform inversion of micro-seismic events to invert for the source image, source function and the velocity model. It is based on convolving reference traces with these observed and modeled to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for the source wavelet in Z axis is extracted to check the accuracy of the inverted source image and velocity model. Also, angle gathers is calculated to assess the quality of the long wavelength component of the velocity model. By inverting for the source image, source wavelet and the velocity model simultaneously, the proposed method produces good estimates of the source location, ignition time and the background velocity for synthetic examples used here, like those corresponding to the Marmousi model and the SEG/EAGE overthrust model.
International Nuclear Information System (INIS)
Yuan Yuan; Yi Hongliang; Shuai Yong; Wang Fuqiang; Tan Heping
2010-01-01
As a part of resolving optical properties in atmosphere radiative transfer calculations, this paper focuses on obtaining aerosol optical thicknesses (AOTs) in the visible and near infrared wave band through indirect method by gleaning the values of aerosol particle size distribution parameters. Although various inverse techniques have been applied to obtain values for these parameters, we choose a stochastic particle swarm optimization (SPSO) algorithm to perform an inverse calculation. Computational performances of different inverse methods are investigated and the influence of swarm size on the inverse problem of computation particles is examined. Next, computational efficiencies of various particle size distributions and the influences of the measured errors on computational accuracy are compared. Finally, we recover particle size distributions for atmospheric aerosols over Beijing using the measured AOT data (at wavelengths λ=0.400, 0.690, 0.870, and 1.020 μm) obtained from AERONET at different times and then calculate other AOT values for this band based on the inverse results. With calculations agreeing with measured data, the SPSO algorithm shows good practicability.
NUMERICAL ANALYSIS OF AN INVERSE PROBLEM ORIGINATED IN PHENOMENON OF POLLUTION AIR URBAN
Directory of Open Access Journals (Sweden)
Aníbal Coronel
2016-12-01
Full Text Available This paper presents the calibration study of a two - dimensional mathematical model for the problem of urban air pollution. It is mainly assumed that air pollution is afected by wind convection, diffusion and chemical reactions of pollutants. Consequently, a convection-diffusion-reaction equation is obtained as a direct problem. In the inverse problem, the determination of the diffusion is analyzed, assuming that one has an observation of the pollutants in a nite time. To solve it numerically the nite volume method is used, the least squares function is considered as cost function and the gradient is calculated with the sensitivity method.
Regularization and Bayesian methods for inverse problems in signal and image processing
Giovannelli , Jean-François
2015-01-01
The focus of this book is on "ill-posed inverse problems". These problems cannot be solved only on the basis of observed data. The building of solutions involves the recognition of other pieces of a priori information. These solutions are then specific to the pieces of information taken into account. Clarifying and taking these pieces of information into account is necessary for grasping the domain of validity and the field of application for the solutions built. For too long, the interest in these problems has remained very limited in the signal-image community. However, the community has si
Venugopal, M.; Roy, D.; Rajendran, K.; Guillas, S.; Dias, F.
2017-01-01
Numerical inversions for earthquake source parameters from tsunami wave data usually incorporate subjective elements to stabilize the search. In addition, noisy and possibly insufficient data result in instability and non-uniqueness in most deterministic inversions, which are barely acknowledged. Here, we employ the satellite altimetry data for the 2004 Sumatra–Andaman tsunami event to invert the source parameters. We also include kinematic parameters that improve the description of tsunami generation and propagation, especially near the source. Using a finite fault model that represents the extent of rupture and the geometry of the trench, we perform a new type of nonlinear joint inversion of the slips, rupture velocities and rise times with minimal a priori constraints. Despite persistently good waveform fits, large uncertainties in the joint parameter distribution constitute a remarkable feature of the inversion. These uncertainties suggest that objective inversion strategies should incorporate more sophisticated physical models of seabed deformation in order to significantly improve the performance of early warning systems. PMID:28989311
Multi-source waveform inversion of marine streamer data using the normalized wavefield
Choi, Yun Seok
2012-01-01
Even though the encoded multi-source approach dramatically reduces the computational cost of waveform inversion, it is generally not applicable to marine streamer data. This is because the simultaneous-sources modeled data cannot be muted to comply with the configuration of the marine streamer data, which causes differences in the number of stacked-traces, or energy levels, between the modeled and observed data. Since the conventional L2 norm does not account for the difference in energy levels, multi-source inversion based on the conventional L2 norm does not work for marine streamer data. In this study, we propose the L2, approximated L2, and L1 norm using the normalized wavefields for the multi-source waveform inversion of marine streamer data. Since the normalized wavefields mitigate the different energy levels between the observed and modeled wavefields, the multi-source waveform inversion using the normalized wavefields can be applied to marine streamer data. We obtain the gradient of the objective functions using the back-propagation algorithm. To conclude, the gradient of the L2 norm using the normalized wavefields is exactly the same as that of the global correlation norm. In the numerical examples, the new objective functions using the normalized wavefields generate successful results whereas conventional L2 norm does not.
Directory of Open Access Journals (Sweden)
M. Kopacz
2010-02-01
Full Text Available We combine CO column measurements from the MOPITT, AIRS, SCIAMACHY, and TES satellite instruments in a full-year (May 2004–April 2005 global inversion of CO sources at 4°×5° spatial resolution and monthly temporal resolution. The inversion uses the GEOS-Chem chemical transport model (CTM and its adjoint applied to MOPITT, AIRS, and SCIAMACHY. Observations from TES, surface sites (NOAA/GMD, and aircraft (MOZAIC are used for evaluation of the a posteriori solution. Using GEOS-Chem as a common intercomparison platform shows global consistency between the different satellite datasets and with the in situ data. Differences can be largely explained by different averaging kernels and a priori information. The global CO emission from combustion as constrained in the inversion is 1350 Tg a^{−1}. This is much higher than current bottom-up emission inventories. A large fraction of the correction results from a seasonal underestimate of CO sources at northern mid-latitudes in winter and suggests a larger-than-expected CO source from vehicle cold starts and residential heating. Implementing this seasonal variation of emissions solves the long-standing problem of models underestimating CO in the northern extratropics in winter-spring. A posteriori emissions also indicate a general underestimation of biomass burning in the GFED2 inventory. However, the tropical biomass burning constraints are not quantitatively consistent across the different datasets.
Inverse scattering problem for a magnetic field in the Glauber approximation
International Nuclear Information System (INIS)
Bogdanov, I.V.
1985-01-01
New results in the general theory of scattering are obtained. An inverse problem at fixed energy for an axisymmetric magnetic field is formulated and solved within the frames of the quantum-mechanical Glauber approximation. The solution is found in quadratures in the form of an explicit inversion algorithm reproducing a vector potential by the angular dependence of the scattering amplitude. Extreme transitions from the eikonal inversion method to the classical and Born ones are investigated. Integral and differential equations are derived for the eikonal amplitude that ensure the real value of the vector potential and its energy independence. Magnetoelectric analogies the existence of equivalent axisymmetric electric and magnetic fields scattering charged particles in the same manner both in the Glauber and Born approximation are established. The mentioned analogies permit to simulate ion-potential scattering by potential one that is of interest from the practical viewpoint. Three-dimensional (excentral) eikonal inverse problems for the electric and magnetic fields are discussed. The results of the paper can be used in electron optics
Microseismic imaging using a source-independent full-waveform inversion method
Wang, Hanchen
2016-09-06
Using full waveform inversion (FWI) to locate microseismic and image microseismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, waveform inversion of microseismic events faces incredible nonlinearity due to the unknown source location (space) and function (time). We develop a source independent FWI of microseismic events to invert for the source image, source function and the velocity model. It is based on convolving reference traces with the observed and modeled data to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for source wavelet in z axis is extracted to check the accuracy of the inverted source image and velocity model. Also the angle gather is calculated to see if the velocity model is correct. By inverting for all the source image, source wavelet and the velocity model, the proposed method produces good estimates of the source location, ignition time and the background velocity for part of the SEG overthrust model.
Microseismic imaging using a source-independent full-waveform inversion method
Wang, Hanchen
2016-01-01
Using full waveform inversion (FWI) to locate microseismic and image microseismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, waveform inversion of microseismic events faces incredible nonlinearity due to the unknown source location (space) and function (time). We develop a source independent FWI of microseismic events to invert for the source image, source function and the velocity model. It is based on convolving reference traces with the observed and modeled data to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for source wavelet in z axis is extracted to check the accuracy of the inverted source image and velocity model. Also the angle gather is calculated to see if the velocity model is correct. By inverting for all the source image, source wavelet and the velocity model, the proposed method produces good estimates of the source location, ignition time and the background velocity for part of the SEG overthrust model.
Inverse problems with Poisson data: statistical regularization theory, applications and algorithms
International Nuclear Information System (INIS)
Hohage, Thorsten; Werner, Frank
2016-01-01
Inverse problems with Poisson data arise in many photonic imaging modalities in medicine, engineering and astronomy. The design of regularization methods and estimators for such problems has been studied intensively over the last two decades. In this review we give an overview of statistical regularization theory for such problems, the most important applications, and the most widely used algorithms. The focus is on variational regularization methods in the form of penalized maximum likelihood estimators, which can be analyzed in a general setup. Complementing a number of recent convergence rate results we will establish consistency results. Moreover, we discuss estimators based on a wavelet-vaguelette decomposition of the (necessarily linear) forward operator. As most prominent applications we briefly introduce Positron emission tomography, inverse problems in fluorescence microscopy, and phase retrieval problems. The computation of a penalized maximum likelihood estimator involves the solution of a (typically convex) minimization problem. We also review several efficient algorithms which have been proposed for such problems over the last five years. (topical review)
Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F.
2018-04-01
We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.
Li, Zhiyuan; Yamamoto, Masahiro
2014-01-01
This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace transform, we reduce the uniqueness for our inverse problems to the uniqueness of expansions of some special function and complete the proof.
Variational approach to direct and inverse problems of atmospheric pollution studies
Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey
2016-04-01
We present the development of a variational approach for solving interrelated problems of atmospheric hydrodynamics and chemistry concerning air pollution transport and transformations. The proposed approach allows us to carry out complex studies of different-scale physical and chemical processes using the methods of direct and inverse modeling [1-3]. We formulate the problems of risk/vulnerability and uncertainty assessment, sensitivity studies, variational data assimilation procedures [4], etc. A computational technology of constructing consistent mathematical models and methods of their numerical implementation is based on the variational principle in the weak constraint formulation specifically designed to account for uncertainties in models and observations. Algorithms for direct and inverse modeling are designed with the use of global and local adjoint problems. Implementing the idea of adjoint integrating factors provides unconditionally monotone and stable discrete-analytic approximations for convection-diffusion-reaction problems [5,6]. The general framework is applied to the direct and inverse problems for the models of transport and transformation of pollutants in Siberian and Arctic regions. The work has been partially supported by the RFBR grant 14-01-00125 and RAS Presidium Program I.33P. References: 1. V. Penenko, A.Baklanov, E. Tsvetova and A. Mahura . Direct and inverse problems in a variational concept of environmental modeling //Pure and Applied Geoph.(2012) v.169: 447-465. 2. V. V. Penenko, E. A. Tsvetova, and A. V. Penenko Development of variational approach for direct and inverse problems of atmospheric hydrodynamics and chemistry, Izvestiya, Atmospheric and Oceanic Physics, 2015, Vol. 51, No. 3, p. 311-319, DOI: 10.1134/S0001433815030093. 3. V.V. Penenko, E.A. Tsvetova, A.V. Penenko. Methods based on the joint use of models and observational data in the framework of variational approach to forecasting weather and atmospheric composition
Zielke, Olaf; McDougall, Damon; Mai, Martin; Babuska, Ivo
2014-05-01
Seismic, often augmented with geodetic data, are frequently used to invert for the spatio-temporal evolution of slip along a rupture plane. The resulting images of the slip evolution for a single event, inferred by different research teams, often vary distinctly, depending on the adopted inversion approach and rupture model parameterization. This observation raises the question, which of the provided kinematic source inversion solutions is most reliable and most robust, and — more generally — how accurate are fault parameterization and solution predictions? These issues are not included in "standard" source inversion approaches. Here, we present a statistical inversion approach to constrain kinematic rupture parameters from teleseismic body waves. The approach is based a) on a forward-modeling scheme that computes synthetic (body-)waves for a given kinematic rupture model, and b) on the QUESO (Quantification of Uncertainty for Estimation, Simulation, and Optimization) library that uses MCMC algorithms and Bayes theorem for sample selection. We present Bayesian inversions for rupture parameters in synthetic earthquakes (i.e. for which the exact rupture history is known) in an attempt to identify the cross-over at which further model discretization (spatial and temporal resolution of the parameter space) is no longer attributed to a decreasing misfit. Identification of this cross-over is of importance as it reveals the resolution power of the studied data set (i.e. teleseismic body waves), enabling one to constrain kinematic earthquake rupture histories of real earthquakes at a resolution that is supported by data. In addition, the Bayesian approach allows for mapping complete posterior probability density functions of the desired kinematic source parameters, thus enabling us to rigorously assess the uncertainties in earthquake source inversions.
Inverse problems for ODEs using contraction maps and suboptimality of the 'collage method'
Kunze, H. E.; Hicken, J. E.; Vrscay, E. R.
2004-06-01
Broad classes of inverse problems in differential and integral equations can be cast in the following framework: the optimal approximation of a target x of a suitable metric space X by the fixed point \\bar x of a contraction map T on X. The 'collage method' attempts to solve such inverse problems by finding an operator Tc that maps the target x as close as possible to itself. In the case of ODEs, the appropriate contraction maps are integral Picard operators. In practice, the target solutions possibly arise from an interpolation of experimental data points. In this paper, we investigate the suboptimality of the collage method. A simple inequality that provides upper bounds on the improvement over collage coding is presented and some examples are studied. We conclude that, at worst, the collage method provides an excellent starting point for further optimization, in contrast to more traditional searching methods that must first select a good starting point.
Kunze, H. E.; La Torre, D.; Vrscay, E. R.
2009-01-01
In this paper we are concerned with differential equations with random coefficients which will be considered as random fixed point equations of the form T([omega],x([omega]))=x([omega]), [omega][set membership, variant][Omega]. Here T:[Omega]×X-->X is a random integral operator, is a probability space and X is a complete metric space. We consider the following inverse problem for such equations: Given a set of realizations of the fixed point of T (possibly the interpolations of different observational data sets), determine the operator T or the mean value of its random components, as appropriate. We solve the inverse problem for this class of equations by using the collage theorem for contraction mappings.
Inverse problems with non-trivial priors: efficient solution through sequential Gibbs sampling
DEFF Research Database (Denmark)
Hansen, Thomas Mejer; Cordua, Knud Skou; Mosegaard, Klaus
2012-01-01
Markov chain Monte Carlo methods such as the Gibbs sampler and the Metropolis algorithm can be used to sample solutions to non-linear inverse problems. In principle, these methods allow incorporation of prior information of arbitrary complexity. If an analytical closed form description of the prior...... is available, which is the case when the prior can be described by a multidimensional Gaussian distribution, such prior information can easily be considered. In reality, prior information is often more complex than can be described by the Gaussian model, and no closed form expression of the prior can be given....... We propose an algorithm, called sequential Gibbs sampling, allowing the Metropolis algorithm to efficiently incorporate complex priors into the solution of an inverse problem, also for the case where no closed form description of the prior exists. First, we lay out the theoretical background...
International Nuclear Information System (INIS)
Kaltenbacher, Barbara; Kirchner, Alana; Vexler, Boris
2011-01-01
Parameter identification problems for partial differential equations usually lead to nonlinear inverse problems. A typical property of such problems is their instability, which requires regularization techniques, like, e.g., Tikhonov regularization. The main focus of this paper will be on efficient methods for determining a suitable regularization parameter by using adaptive finite element discretizations based on goal-oriented error estimators. A well-established method for the determination of a regularization parameter is the discrepancy principle where the residual norm, considered as a function i of the regularization parameter, should equal an appropriate multiple of the noise level. We suggest to solve the resulting scalar nonlinear equation by an inexact Newton method, where in each iteration step, a regularized problem is solved at a different discretization level. The proposed algorithm is an extension of the method suggested in Griesbaum A et al (2008 Inverse Problems 24 025025) for linear inverse problems, where goal-oriented error estimators for i and its derivative are used for adaptive refinement strategies in order to keep the discretization level as coarse as possible to save computational effort but fine enough to guarantee global convergence of the inexact Newton method. This concept leads to a highly efficient method for determining the Tikhonov regularization parameter for nonlinear ill-posed problems. Moreover, we prove that with the so-obtained regularization parameter and an also adaptively discretized Tikhonov minimizer, usual convergence and regularization results from the continuous setting can be recovered. As a matter of fact, it is shown that it suffices to use stationary points of the Tikhonov functional. The efficiency of the proposed method is demonstrated by means of numerical experiments. (paper)
Directory of Open Access Journals (Sweden)
В С Корнилов
2016-12-01
Full Text Available The article presents scientific and methodical aspects of forming the content of education inverse problems for differential equations for students of higher educational institutions of physical, mathematical and natural science training areas. The goals are formulated and the principles of training are the content of learning inverse problems for differential equations. Attention is drawn to the particular issues of teaching courses inverse problems. Describes the classification criteria and target modules that play the role of tools to create and analyze the model and curriculum, forming learning content inverse problems for differential equations. The content classification features and target modules. Formulate conclusions that learning the inverse problems for differential equations has scientific, educational and humanitarian potential of students and as a result of this training they gain the fundamental knowledge in the applied and computational mathematics, and also develop scientific worldview, applied, environmental, information thinking.
Uniqueness in the inverse boundary value problem for piecewise homogeneous anisotropic elasticity
Cârstea, Cătălin I.; Honda, Naofumi; Nakamura, Gen
2016-01-01
Consider a three dimensional piecewise homogeneous anisotropic elastic medium $\\Omega$ which is a bounded domain consisting of a finite number of bounded subdomains $D_\\alpha$, with each $D_\\alpha$ a homogeneous elastic medium. One typical example is a finite element model with elements with curvilinear interfaces for an ansiotropic elastic medium. Assuming the $D_\\alpha$ are known and Lipschitz, we are concerned with the uniqueness in the inverse boundary value problem of identifying the ani...
Digital Repository Service at National Institute of Oceanography (India)
Tripathy, G.R.; Das, Anirban.
used methods, the Least Square Regression (LSR) and Inverse Modeling (IM), to determine the contributions of (i) solutes from different sources to global river water, and (ii) various rocks to a glacial till. The purpose of this exercise is to compare...
A New Wave Equation Based Source Location Method with Full-waveform Inversion
Wu, Zedong; Alkhalifah, Tariq Ali
2017-01-01
with illumination artifacts. We develop a waveform inversion approach with an additional penalty term in the objective function to reward the focusing of the source image. This penalty term is relaxed early to allow for data fitting, and avoid cycle skipping, using
Source Identification in Structural Acoustics with an Inverse Frequency Response Function Technique
Visser, Rene
2002-01-01
Inverse source identification based on acoustic measurements is essential for the investigation and understanding of sound fields generated by structural vibrations of various devices and machinery. Acoustic pressure measurements performed on a grid in the nearfield of a surface can be used to
Visco-elastic controlled-source full waveform inversion without surface waves
Paschke, Marco; Krause, Martin; Bleibinhaus, Florian
2016-04-01
We developed a frequency-domain visco-elastic full waveform inversion for onshore seismic experiments with topography. The forward modeling is based on a finite-difference time-domain algorithm by Robertsson that uses the image-method to ensure a stress-free condition at the surface. The time-domain data is Fourier-transformed at every point in the model space during the forward modeling for a given set of frequencies. The motivation for this approach is the reduced amount of memory when computing kernels, and the straightforward implementation of the multiscale approach. For the inversion, we calculate the Frechet derivative matrix explicitly, and we implement a Levenberg-Marquardt scheme that allows for computing the resolution matrix. To reduce the size of the Frechet derivative matrix, and to stabilize the inversion, an adapted inverse mesh is used. The node spacing is controlled by the velocity distribution and the chosen frequencies. To focus the inversion on body waves (P, P-coda, and S) we mute the surface waves from the data. Consistent spatiotemporal weighting factors are applied to the wavefields during the Fourier transform to obtain the corresponding kernels. We test our code with a synthetic study using the Marmousi model with arbitrary topography. This study also demonstrates the importance of topography and muting surface waves in controlled-source full waveform inversion.
Greedy solution of ill-posed problems: error bounds and exact inversion
International Nuclear Information System (INIS)
Denis, L; Lorenz, D A; Trede, D
2009-01-01
The orthogonal matching pursuit (OMP) is a greedy algorithm to solve sparse approximation problems. Sufficient conditions for exact recovery are known with and without noise. In this paper we investigate the applicability of the OMP for the solution of ill-posed inverse problems in general, and in particular for two deconvolution examples from mass spectrometry and digital holography, respectively. In sparse approximation problems one often has to deal with the problem of redundancy of a dictionary, i.e. the atoms are not linearly independent. However, one expects them to be approximatively orthogonal and this is quantified by the so-called incoherence. This idea cannot be transferred to ill-posed inverse problems since here the atoms are typically far from orthogonal. The ill-posedness of the operator probably causes the correlation of two distinct atoms to become huge, i.e. that two atoms look much alike. Therefore, one needs conditions which take the structure of the problem into account and work without the concept of coherence. In this paper we develop results for the exact recovery of the support of noisy signals. In the two examples, mass spectrometry and digital holography, we show that our results lead to practically relevant estimates such that one may check a priori if the experimental setup guarantees exact deconvolution with OMP. Especially in the example from digital holography, our analysis may be regarded as a first step to calculate the resolution power of droplet holography
Hansen, T. M.; Cordua, K. S.
2017-12-01
Probabilistically formulated inverse problems can be solved using Monte Carlo-based sampling methods. In principle, both advanced prior information, based on for example, complex geostatistical models and non-linear forward models can be considered using such methods. However, Monte Carlo methods may be associated with huge computational costs that, in practice, limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical forward response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival traveltime inversion of crosshole ground penetrating radar data. An accurate forward model, based on 2-D full-waveform modeling followed by automatic traveltime picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the accurate and computationally expensive forward model, and also considerably faster and more accurate (i.e. with better resolution), than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of non-linear and non-Gaussian inverse problems that have to be solved using Monte Carlo sampling techniques.
Evangeliou, Nikolaos; Hamburger, Thomas; Cozic, Anne; Balkanski, Yves; Stohl, Andreas
2017-07-01
This paper describes the results of an inverse modeling study for the determination of the source term of the radionuclides 134Cs, 137Cs and 131I released after the Chernobyl accident. The accident occurred on 26 April 1986 in the Former Soviet Union and released about 1019 Bq of radioactive materials that were transported as far away as the USA and Japan. Thereafter, several attempts to assess the magnitude of the emissions were made that were based on the knowledge of the core inventory and the levels of the spent fuel. More recently, when modeling tools were further developed, inverse modeling techniques were applied to the Chernobyl case for source term quantification. However, because radioactivity is a sensitive topic for the public and attracts a lot of attention, high-quality measurements, which are essential for inverse modeling, were not made available except for a few sparse activity concentration measurements far from the source and far from the main direction of the radioactive fallout. For the first time, we apply Bayesian inversion of the Chernobyl source term using not only activity concentrations but also deposition measurements from the most recent public data set. These observations refer to a data rescue attempt that started more than 10 years ago, with a final goal to provide available measurements to anyone interested. In regards to our inverse modeling results, emissions of 134Cs were estimated to be 80 PBq or 30-50 % higher than what was previously published. From the released amount of 134Cs, about 70 PBq were deposited all over Europe. Similar to 134Cs, emissions of 137Cs were estimated as 86 PBq, on the same order as previously reported results. Finally, 131I emissions of 1365 PBq were found, which are about 10 % less than the prior total releases. The inversion pushes the injection heights of the three radionuclides to higher altitudes (up to about 3 km) than previously assumed (≈ 2.2 km) in order to better match both concentration
Directory of Open Access Journals (Sweden)
N. Evangeliou
2017-07-01
Full Text Available This paper describes the results of an inverse modeling study for the determination of the source term of the radionuclides 134Cs, 137Cs and 131I released after the Chernobyl accident. The accident occurred on 26 April 1986 in the Former Soviet Union and released about 1019 Bq of radioactive materials that were transported as far away as the USA and Japan. Thereafter, several attempts to assess the magnitude of the emissions were made that were based on the knowledge of the core inventory and the levels of the spent fuel. More recently, when modeling tools were further developed, inverse modeling techniques were applied to the Chernobyl case for source term quantification. However, because radioactivity is a sensitive topic for the public and attracts a lot of attention, high-quality measurements, which are essential for inverse modeling, were not made available except for a few sparse activity concentration measurements far from the source and far from the main direction of the radioactive fallout. For the first time, we apply Bayesian inversion of the Chernobyl source term using not only activity concentrations but also deposition measurements from the most recent public data set. These observations refer to a data rescue attempt that started more than 10 years ago, with a final goal to provide available measurements to anyone interested. In regards to our inverse modeling results, emissions of 134Cs were estimated to be 80 PBq or 30–50 % higher than what was previously published. From the released amount of 134Cs, about 70 PBq were deposited all over Europe. Similar to 134Cs, emissions of 137Cs were estimated as 86 PBq, on the same order as previously reported results. Finally, 131I emissions of 1365 PBq were found, which are about 10 % less than the prior total releases. The inversion pushes the injection heights of the three radionuclides to higher altitudes (up to about 3 km than previously assumed (≈ 2.2 km in order
Spectral inversion of an indefinite Sturm-Liouville problem due to Richardson
International Nuclear Information System (INIS)
Shanley, Paul E
2009-01-01
We study an indefinite Sturm-Liouville problem due to Richardson whose complicated eigenvalue dependence on a parameter has been a puzzle for decades. In atomic physics a process exists that inverts the usual Schroedinger situation of an energy eigenvalue depending on a coupling parameter into the so-called Sturmian problem where the coupling parameter becomes the eigenvalue which then depends on the energy. We observe that the Richardson equation is of the Sturmian type. This means that the Richardson and its related Schroedinger eigenvalue functions are inverses of each other and that the Richardson spectrum is therefore no longer a puzzle
Metropolis-Hastings Algorithms in Function Space for Bayesian Inverse Problems
Ernst, Oliver
2015-01-07
We consider Markov Chain Monte Carlo methods adapted to a Hilbert space setting. Such algorithms occur in Bayesian inverse problems where the solution is a probability measure on a function space according to which one would like to integrate or sample. We focus on Metropolis-Hastings algorithms and, in particular, we introduce and analyze a generalization of the existing pCN-proposal. This new proposal allows to exploit the geometry or anisotropy of the target measure which in turn might improve the statistical efficiency of the corresponding MCMC method. Numerical experiments for a real-world problem confirm the improvement.
Metropolis-Hastings Algorithms in Function Space for Bayesian Inverse Problems
Ernst, Oliver
2015-01-01
We consider Markov Chain Monte Carlo methods adapted to a Hilbert space setting. Such algorithms occur in Bayesian inverse problems where the solution is a probability measure on a function space according to which one would like to integrate or sample. We focus on Metropolis-Hastings algorithms and, in particular, we introduce and analyze a generalization of the existing pCN-proposal. This new proposal allows to exploit the geometry or anisotropy of the target measure which in turn might improve the statistical efficiency of the corresponding MCMC method. Numerical experiments for a real-world problem confirm the improvement.
Estimation of the thermal properties in alloys as an inverse problem
International Nuclear Information System (INIS)
Zueco, J.; Alhama, F.
2005-01-01
This paper provides an efficient numerical method for estimating the thermal conductivity and heat capacity of alloys, as a function of the temperature, starting from temperature measurements (including errors) in heating and cooling processes. The proposed procedure is a modification of the known function estimation technique, typical of the inverse problem field, in conjunction with the network simulation method (already checked in many non-lineal problems) as the numerical tool. Estimations only require a point of measurement. The methodology is applied for determining these thermal properties in alloys within ranges of temperature where allotropic changes take place. These changes are characterized by sharp temperature dependencies. (Author) 13 refs
The inverse problem of the calculus of variations for discrete systems
Barbero-Liñán, María; Farré Puiggalí, Marta; Ferraro, Sebastián; Martín de Diego, David
2018-05-01
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also provide a transition between the discrete and the continuous problems and propose variationality as an interesting geometric property to take into account in the design and computer simulation of numerical integrators for constrained systems. For instance, nonholonomic mechanics is generally non variational but some special cases admit an alternative variational description. We apply some standard nonholonomic integrators to such an example to study which ones conserve this property.
Directory of Open Access Journals (Sweden)
S.N. Nnamchi
2010-01-01
Full Text Available Determination of the thermal conductivity and the specific heat capacity of neem seeds (Azadirachta indica A. Juss usingthe inverse method is the main subject of this work. One-dimensional formulation of heat conduction problem in a spherewas used. Finite difference method was adopted for the solution of the heat conduction problem. The thermal conductivityand the specific heat capacity were determined by least square method in conjunction with Levenberg-Marquardt algorithm.The results obtained compare favourably with those obtained experimentally. These results are useful in the analysis ofneem seeds drying and leaching processes.
International Nuclear Information System (INIS)
Sakhnovich, Alexander
2008-01-01
A Borg–Marchenko-type uniqueness theorem (in terms of the Weyl function) is obtained here for the system auxiliary to the N-wave equation. A procedure to solve the inverse problem is used for this purpose. The asymptotic condition on the Weyl function, under which the inverse problem is uniquely solvable, is completed by a new and simple sufficient condition on the potential, which implies this asymptotic condition. The evolution of the Weyl function is discussed and the solution of an initial-boundary-value problem for the N-wave equation follows. Explicit solutions of an inverse problem are obtained. The system with a shifted argument is treated
On parameterization of the inverse problem for estimating aquifer properties using tracer data
International Nuclear Information System (INIS)
Kowalsky, M. B.; Finsterle, Stefan A.; Williams, Kenneth H.; Murray, Christopher J.; Commer, Michael; Newcomer, Darrell R.; Englert, Andreas L.; Steefel, Carl I.; Hubbard, Susan
2012-01-01
We consider a field-scale tracer experiment conducted in 2007 in a shallow uranium-contaminated aquifer at Rifle, Colorado. In developing a reliable approach for inferring hydrological properties at the site through inverse modeling of the tracer data, decisions made on how to parameterize heterogeneity (i.e., how to represent a heterogeneous distribution using a limited number of parameters that are amenable to estimation) are of paramount importance. We present an approach for hydrological inversion of the tracer data and explore, using a 2D synthetic example at first, how parameterization affects the solution, and how additional characterization data could be incorporated to reduce uncertainty. Specifically, we examine sensitivity of the results to the configuration of pilot points used in a geostatistical parameterization, and to the sampling frequency and measurement error of the concentration data. A reliable solution of the inverse problem is found when the pilot point configuration is carefully implemented. In addition, we examine the use of a zonation parameterization, in which the geometry of the geological facies is known (e.g., from geophysical data or core data), to reduce the non-uniqueness of the solution and the number of unknown parameters to be estimated. When zonation information is only available for a limited region, special treatment in the remainder of the model is necessary, such as using a geostatistical parameterization. Finally, inversion of the actual field data is performed using 2D and 3D models, and results are compared with slug test data.
International Nuclear Information System (INIS)
Mareschal, M.
1975-01-01
The major thrust of this dissertation was to test an original method for resolving the current system associated with polar magnetic substorms from ground based magnetic observations. This method is based on a general technique of inversion reviewed by Wiggins in 1972 and appears to give quite satisfactory results, at least, when the current system considered is simulated by a three-dimensional current system consisting of field-aligned currents flowing down to the ionosphere, westward in the ionosphere, and back up again to the magnetosphere. Conclusions suggest that, for the purpose of inverting polar magnetic substorm data with the use of the three-dimensional model of current, the Earth's induction effects can be simulated by introducing a perfectly conducting layer inside the Earth. However, the depth of this equivalent conductor should be allowed to vary with the source frequency as the substorm develops with time. To determine how satisfactorily each model parameter could be expected to be resolved during the process of inversion, a study of the magnetic disturbance variations under specific parameter variations was then performed. The results of that study were encouraging enough to foster the inversion of an actual polar magnetic substorm data, the event of June 15, 1970. Despite the success of the enterprise, it seems reasonable to suggest that the technique of inversion should be further tested before being systematically used to resolve polar magnetic substorms
Directory of Open Access Journals (Sweden)
A. Richter
2009-11-01
Full Text Available Tropospheric glyoxal and formaldehyde columns retrieved from the SCIAMACHY satellite instrument in 2005 are used with the IMAGESv2 global chemistry-transport model and its adjoint in a two-compound inversion scheme designed to estimate the continental source of glyoxal. The formaldehyde observations provide an important constraint on the production of glyoxal from isoprene in the model, since the degradation of isoprene constitutes an important source of both glyoxal and formaldehyde. Current modelling studies underestimate largely the observed glyoxal satellite columns, pointing to the existence of an additional land glyoxal source of biogenic origin. We include an extra glyoxal source in the model and we explore its possible distribution and magnitude through two inversion experiments. In the first case, the additional source is represented as a direct glyoxal emission, and in the second, as a secondary formation through the oxidation of an unspecified glyoxal precursor. Besides this extra source, the inversion scheme optimizes the primary glyoxal and formaldehyde emissions, as well as their secondary production from other identified non-methane volatile organic precursors of anthropogenic, pyrogenic and biogenic origin.
In the first inversion experiment, the additional direct source, estimated at 36 Tg/yr, represents 38% of the global continental source, whereas the contribution of isoprene is equally important (30%, the remainder being accounted for by anthropogenic (20% and pyrogenic fluxes. The inversion succeeds in reducing the underestimation of the glyoxal columns by the model, but it leads to a severe overestimation of glyoxal surface concentrations in comparison with in situ measurements. In the second scenario, the inferred total global continental glyoxal source is estimated at 108 Tg/yr, almost two times higher than the global a priori source. The extra secondary source is the largest contribution to the global glyoxal
Approximation in generalized Hardy classes and resolution of inverse problems for tokamaks
International Nuclear Information System (INIS)
Fisher, Y.
2011-11-01
This thesis concerns both the theoretical and constructive resolution of inverse problems for isotropic diffusion equation in planar domains, simply and doubly connected. From partial Cauchy boundary data (potential, flux), we look for those quantities on the remaining part of the boundary, where no information is available, as well as inside the domain. The proposed approach proceeds by considering solutions to the diffusion equation as real parts of complex valued solutions to some conjugated Beltrami equation. These particular generalized analytic functions allow to introduce Hardy classes, where the inverse problem is stated as a best constrained approximation issue (bounded extrema problem), and thereby is regularized. Hence, existence and smoothness properties, together with density results of traces on the boundary, ensure well-posedness. An application is studied, to a free boundary problem for a magnetically confined plasma in the tokamak Tore Supra (CEA Cadarache France). The resolution of the approximation problem on a suitable basis of functions (toroidal harmonics) leads to a qualification criterion for the estimated plasma boundary. A descent algorithm makes it decrease, and refines the estimations. The method does not require any integration of the solution in the overall domain. It furnishes very accurate numerical results, and could be extended to other devices, like JET or ITER. (author)
Schmitt, R. J. P.; Bizzi, S.; Kondolf, G. M.; Rubin, Z.; Castelletti, A.
2016-12-01
Field and laboratory evidence indicates that the spatial distribution of transport in both alluvial and bedrock rivers is an adaptation to sediment supply. Sediment supply, in turn, depends on spatial distribution and properties (e.g., grain sizes and supply rates) of individual sediment sources. Analyzing the distribution of transport capacity in a river network could hence clarify the spatial distribution and properties of sediment sources. Yet, challenges include a) identifying magnitude and spatial distribution of transport capacity for each of multiple grain sizes being simultaneously transported, and b) estimating source grain sizes and supply rates, both at network scales. Herein, we approach the problem of identifying the spatial distribution of sediment sources and the resulting network sediment fluxes in a major, poorly monitored tributary (80,000 km2) of the Mekong. Therefore, we apply the CASCADE modeling framework (Schmitt et al. (2016)). CASCADE calculates transport capacities and sediment fluxes for multiple grainsizes on the network scale based on remotely-sensed morphology and modelled hydrology. CASCADE is run in an inverse Monte Carlo approach for 7500 random initializations of source grain sizes. In all runs, supply of each source is inferred from the minimum downstream transport capacity for the source grain size. Results for each realization are compared to sparse available sedimentary records. Only 1 % of initializations reproduced the sedimentary record. Results for these realizations revealed a spatial pattern in source supply rates, grain sizes, and network sediment fluxes that correlated well with map-derived patterns in lithology and river-morphology. Hence, we propose that observable river hydro-morphology contains information on upstream source properties that can be back-calculated using an inverse modeling approach. Such an approach could be coupled to more detailed models of hillslope processes in future to derive integrated models
Energy Technology Data Exchange (ETDEWEB)
Fraguela Collar, Andres; Oliveros Oliveros, Jose J.; Ivanovich Grebennikov, Alexandre [Benemerita Universidad Autonoma de Puebla, Puebla (Mexico)
2001-04-01
Techniques of the potential theory have been used to analyze the properties of the operator where the sources of current produced by electric activity in the cerebral cortex is associated with the measurements on the scalp of the electric potential generated by these sources. A medium conductor model which take in account the circle convolution of the brain has been used to prove the uniqueness of solution of the inverse problem of recuperation of activity cortical sources from electroencephalographic measurement on the scalp. This result of uniqueness is very important because we can to use algorithms of regularization. An other state the problem is presented to elaborate numerical solutions of the inverse problem using a set of discrete measurement. The stability of algorithms is showed in some examples. [Spanish] Tecnicas de la teoria de potencial han sido utilizadas para analizar las propiedades del operador que a las fuentes de corriente asociadas a la actividad electrica de las neuronas en la corteza cerebral, le hace corresponder la medicion de potencial electrico generado por dichas fuentes sobre el cuero cabelludo. Un modelo de medio conductor que toma en consideracion las circonvoluciones del cerebro ha sido utilizado para probar la unidad de solucion del problema inverso de recuperacion de las fuentes de actividad cortical a partir de las mediciones electroencefalograficas. Este resultado de unidad es fundamental ya que nos permite aplicar los metodos de regularizacion. Es presentado otro planteamiento del problema que nos permite construir soluciones numericas del problema inverso usando los datos de entrada discretos. La estabilidad de los algoritmos es ilustrada en algunos ejemplos numericos.
Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems
International Nuclear Information System (INIS)
Haber, E; Horesh, L; Tenorio, L
2010-01-01
Design of experiments for discrete ill-posed problems is a relatively new area of research. While there has been some limited work concerning the linear case, little has been done to study design criteria and numerical methods for ill-posed nonlinear problems. We present an algorithmic framework for nonlinear experimental design with an efficient numerical implementation. The data are modeled as indirect, noisy observations of the model collected via a set of plausible experiments. An inversion estimate based on these data is obtained by a weighted Tikhonov regularization whose weights control the contribution of the different experiments to the data misfit term. These weights are selected by minimization of an empirical estimate of the Bayes risk that is penalized to promote sparsity. This formulation entails a bilevel optimization problem that is solved using a simple descent method. We demonstrate the viability of our design with a problem in electromagnetic imaging based on direct current resistivity and magnetotelluric data
Estimation of G-renewal process parameters as an ill-posed inverse problem
International Nuclear Information System (INIS)
Krivtsov, V.; Yevkin, O.
2013-01-01
Statistical estimation of G-renewal process parameters is an important estimation problem, which has been considered by many authors. We view this problem from the standpoint of a mathematically ill-posed, inverse problem (the solution is not unique and/or is sensitive to statistical error) and propose a regularization approach specifically suited to the G-renewal process. Regardless of the estimation method, the respective objective function usually involves parameters of the underlying life-time distribution and simultaneously the restoration parameter. In this paper, we propose to regularize the problem by decoupling the estimation of the aforementioned parameters. Using a simulation study, we show that the resulting estimation/extrapolation accuracy of the proposed method is considerably higher than that of the existing methods
6th International Workshop on New Computational Methods for Inverse Problems
International Nuclear Information System (INIS)
2016-01-01
Foreword This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 6 th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2016 (http://complement.farman.ens-cachan.fr/NCMIP 2016.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 20, 2016. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011, and secondly at the initiative of Institut Farman, in May 2012, May 2013, May 2014 and May 2015. The New Computational Methods for Inverse Problems (NCMIP) workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists in estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one- day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel
Kovalets, Ivan V.; Efthimiou, George C.; Andronopoulos, Spyros; Venetsanos, Alexander G.; Argyropoulos, Christos D.; Kakosimos, Konstantinos E.
2018-05-01
In this work, we present an inverse computational method for the identification of the location, start time, duration and quantity of emitted substance of an unknown air pollution source of finite time duration in an urban environment. We considered a problem of transient pollutant dispersion under stationary meteorological fields, which is a reasonable assumption for the assimilation of available concentration measurements within 1 h from the start of an incident. We optimized the calculation of the source-receptor function by developing a method which requires integrating as many backward adjoint equations as the available measurement stations. This resulted in high numerical efficiency of the method. The source parameters are computed by maximizing the correlation function of the simulated and observed concentrations. The method has been integrated into the CFD code ADREA-HF and it has been tested successfully by performing a series of source inversion runs using the data of 200 individual realizations of puff releases, previously generated in a wind tunnel experiment.
Marinin, I. V.; Kabanikhin, S. I.; Krivorotko, O. I.; Karas, A.; Khidasheli, D. G.
2012-04-01
We consider new techniques and methods for earthquake and tsunami related problems, particularly - inverse problems for the determination of tsunami source parameters, numerical simulation of long wave propagation in soil and water and tsunami risk estimations. In addition, we will touch upon the issue of database management and destruction scenario visualization. New approaches and strategies, as well as mathematical tools and software are to be shown. The long joint investigations by researchers of the Institute of Mathematical Geophysics and Computational Mathematics SB RAS and specialists from WAPMERR and Informap have produced special theoretical approaches, numerical methods, and software tsunami and earthquake modeling (modeling of propagation and run-up of tsunami waves on coastal areas), visualization, risk estimation of tsunami, and earthquakes. Algorithms are developed for the operational definition of the origin and forms of the tsunami source. The system TSS numerically simulates the source of tsunami and/or earthquakes and includes the possibility to solve the direct and the inverse problem. It becomes possible to involve advanced mathematical results to improve models and to increase the resolution of inverse problems. Via TSS one can construct maps of risks, the online scenario of disasters, estimation of potential damage to buildings and roads. One of the main tools for the numerical modeling is the finite volume method (FVM), which allows us to achieve stability with respect to possible input errors, as well as to achieve optimum computing speed. Our approach to the inverse problem of tsunami and earthquake determination is based on recent theoretical results concerning the Dirichlet problem for the wave equation. This problem is intrinsically ill-posed. We use the optimization approach to solve this problem and SVD-analysis to estimate the degree of ill-posedness and to find the quasi-solution. The software system we developed is intended to
Ambient Seismic Source Inversion in a Heterogeneous Earth: Theory and Application to the Earth's Hum
Ermert, Laura; Sager, Korbinian; Afanasiev, Michael; Boehm, Christian; Fichtner, Andreas
2017-11-01
The sources of ambient seismic noise are extensively studied both to better understand their influence on ambient noise tomography and related techniques, and to infer constraints on their excitation mechanisms. Here we develop a gradient-based inversion method to infer the space-dependent and time-varying source power spectral density of the Earth's hum from cross correlations of continuous seismic data. The precomputation of wavefields using spectral elements allows us to account for both finite-frequency sensitivity and for three-dimensional Earth structure. Although similar methods have been proposed previously, they have not yet been applied to data to the best of our knowledge. We apply this method to image the seasonally varying sources of Earth's hum during North and South Hemisphere winter. The resulting models suggest that hum sources are localized, persistent features that occur at Pacific coasts or shelves and in the North Atlantic during North Hemisphere winter, as well as South Pacific coasts and several distinct locations in the Southern Ocean in South Hemisphere winter. The contribution of pelagic sources from the central North Pacific cannot be constrained. Besides improving the accuracy of noise source locations through the incorporation of finite-frequency effects and 3-D Earth structure, this method may be used in future cross-correlation waveform inversion studies to provide initial source models and source model updates.
International Nuclear Information System (INIS)
Klibanov, Michael V; Pantong, Natee; Fiddy, Michael A; Schenk, John; Beilina, Larisa
2010-01-01
A globally convergent algorithm by the first and third authors for a 3D hyperbolic coefficient inverse problem is verified on experimental data measured in the picosecond scale regime. Quantifiable images of dielectric abnormalities are obtained. The total measurement timing of a 100 ps pulse for one detector location was 1.2 ns with 20 ps (=0.02 ns) time step between two consecutive readings. Blind tests have consistently demonstrated an accurate imaging of refractive indexes of dielectric abnormalities. At the same time, it is shown that a modified gradient method is inapplicable to this kind of experimental data. This inverse algorithm is also applicable to other types of imaging modalities, e.g. acoustics. Potential applications are in airport security, imaging of land mines, imaging of defects in non-distractive testing, etc
Solution of the inverse scattering problem at fixed energy with non-physical S matrix elements
International Nuclear Information System (INIS)
Eberspaecher, M.; Amos, K.; Apagyi, B.
1999-12-01
The quantum mechanical inverse elastic scattering problem is solved with the modified Newton-Sabatier method. A set of S matrix elements calculated from a realistic analytic optical model potential serves as input data. It is demonstrated that the quality of the inversion potential can be improved by including non-physical S matrix elements to half, quarter and eighth valued partial waves if the original set does not contain enough information to determine the interaction potential. We demonstrate that results can be very sensitive to the choice of those non-physical S matrix values both with the analytic potential model and in a real application in which the experimental cross section for the symmetrical scattering system of 12 C+ 12 C at E=7.998 MeV is analyzed
Use of Genetic Algorithms to solve Inverse Problems in Relativistic Hydrodynamics
Guzmán, F. S.; González, J. A.
2018-04-01
We present the use of Genetic Algorithms (GAs) as a strategy to solve inverse problems associated with models of relativistic hydrodynamics. The signal we consider to emulate an observation is the density of a relativistic gas, measured at a point where a shock is traveling. This shock is generated numerically out of a Riemann problem with mildly relativistic conditions. The inverse problem we propose is the prediction of the initial conditions of density, velocity and pressure of the Riemann problem that gave origin to that signal. For this we use the density, velocity and pressure of the gas at both sides of the discontinuity, as the six genes of an organism, initially with random values within a tolerance. We then prepare an initial population of N of these organisms and evolve them using methods based on GAs. In the end, the organism with the best fitness of each generation is compared to the signal and the process ends when the set of initial conditions of the organisms of a later generation fit the Signal within a tolerance.
An inverse spectral problem related to the Geng-Xue two-component peakon equation
Lundmark, Hans
2016-01-01
The authors solve a spectral and an inverse spectral problem arising in the computation of peakon solutions to the two-component PDE derived by Geng and Xue as a generalization of the Novikov and Degasperisâe"Procesi equations. Like the spectral problems for those equations, this one is of a âeoediscrete cubic stringâe typeâe"a nonselfadjoint generalization of a classical inhomogeneous stringâe"but presents some interesting novel features: there are two Lax pairs, both of which contribute to the correct complete spectral data, and the solution to the inverse problem can be expressed using quantities related to Cauchy biorthogonal polynomials with two different spectral measures. The latter extends the range of previous applications of Cauchy biorthogonal polynomials to peakons, which featured either two identical, or two closely related, measures. The method used to solve the spectral problem hinges on the hidden presence of oscillatory kernels of Gantmacherâe"Krein type, implying that the spectrum of...
Tian, X.; Zhang, Y.
2018-03-01
Herglotz variational principle, in which the functional is defined by a differential equation, generalizes the classical ones defining the functional by an integral. The principle gives a variational principle description of nonconservative systems even when the Lagrangian is independent of time. This paper focuses on studying the Noether's theorem and its inverse of a Birkhoffian system in event space based on the Herglotz variational problem. Firstly, according to the Herglotz variational principle of a Birkhoffian system, the principle of a Birkhoffian system in event space is established. Secondly, its parametric equations and two basic formulae for the variation of Pfaff-Herglotz action of a Birkhoffian system in event space are obtained. Furthermore, the definition and criteria of Noether symmetry of the Birkhoffian system in event space based on the Herglotz variational problem are given. Then, according to the relationship between the Noether symmetry and conserved quantity, the Noether's theorem is derived. Under classical conditions, Noether's theorem of a Birkhoffian system in event space based on the Herglotz variational problem reduces to the classical ones. In addition, Noether's inverse theorem of the Birkhoffian system in event space based on the Herglotz variational problem is also obtained. In the end of the paper, an example is given to illustrate the application of the results.