PREFACE: First International Congress of the International Association of Inverse Problems (IPIA): Applied Inverse Problems 2007: Theoretical and Computational Aspects

Science.gov (United States)

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

Solving inversion problems with neural networks

Science.gov (United States)

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.

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

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)

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 logarithmic potential problem

CERN Document Server

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.

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.

The application of neural network techniques to magnetic and optical inverse problems

International Nuclear Information System (INIS)

Jones, H.V.

2000-12-01

The processing power of the computer has increased at unimaginable rates over the last few decades. However, even today's fastest computer can take several hours to find solutions to some mathematical problems; and there are instances where a high powered supercomputer may be impractical, with the need for near instant solutions just as important (such as in an on-line testing system). This led us to believe that such complex problems could be solved using a novel approach, whereby the system would have prior knowledge about the expected solutions through a process of learning. One method of approaching this kind of problem is through the use of machine learning. Just as a human can be trained and is able to learn from past experiences, a machine is can do just the same. This is the concept of neural networks. The research which was conducted involves the investigation of various neural network techniques, and their applicability to solve some known complex inverse problems in the field of magnetic and optical recording. In some cases a comparison is also made to more conventional methods of solving the problems, from which it was possible to outline some key advantages of using a neural network approach. We initially investigated the application of neural networks to transverse susceptibility data in order to determine anisotropy distributions. This area of research is proving to be very important, as it gives us information about the switching field distribution, which then determines the minimum transition width achievable in a medium, and affects the overwrite characteristics of the media. Secondly, we investigated a similar situation, but applied to an optical problem. This involved the determination of important compact disc parameters from the diffraction pattern of a laser from a disc. This technique was then intended for use in an on-line testing system. Finally we investigated another area of neural networks with the analysis of magnetisation maps and

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.

Method and software to solution of inverse and inverse design fluid flow and heat transfer problems is compatible with CFD-software

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.

Method and software to solution of inverse and inverse design fluid flow and heat transfer problems is compatible with CFD-software

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.

Direct Problems and Inverse Problems in Biometric Systems

OpenAIRE

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...

Application of the kernel method to the inverse geosounding problem.

Science.gov (United States)

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.

Data-Driven Model Order Reduction for Bayesian Inverse Problems

KAUST Repository

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

Automatic differentiation in geophysical inverse problems

Science.gov (United States)

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.

Topological inversion for solution of geodesy-constrained geophysical problems

Science.gov (United States)

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

Optimization and inverse problems in electromagnetism

CERN Document Server

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 and Ill-posed Problems Theory and Applications

CERN Document Server

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.

SQUIDs and inverse problem techniques in nondestructive evaluation of metals

CERN Document Server

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.

Inverse problems for Maxwell's equations

CERN Document Server

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.

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)

Three-Dimensional Inverse Transport Solver Based on Compressive Sensing Technique

Science.gov (United States)

Cheng, Yuxiong; Wu, Hongchun; Cao, Liangzhi; Zheng, Youqi

2013-09-01

According to the direct exposure measurements from flash radiographic image, a compressive sensing-based method for three-dimensional inverse transport problem is presented. The linear absorption coefficients and interface locations of objects are reconstructed directly at the same time. It is always very expensive to obtain enough measurements. With limited measurements, compressive sensing sparse reconstruction technique orthogonal matching pursuit is applied to obtain the sparse coefficients by solving an optimization problem. A three-dimensional inverse transport solver is developed based on a compressive sensing-based technique. There are three features in this solver: (1) AutoCAD is employed as a geometry preprocessor due to its powerful capacity in graphic. (2) The forward projection matrix rather than Gauss matrix is constructed by the visualization tool generator. (3) Fourier transform and Daubechies wavelet transform are adopted to convert an underdetermined system to a well-posed system in the algorithm. Simulations are performed and numerical results in pseudo-sine absorption problem, two-cube problem and two-cylinder problem when using compressive sensing-based solver agree well with the reference value.

Solution of axisymmetric transient inverse heat conduction problems using parameter estimation and multi block methods

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)

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.

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.

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.)

Data-Driven Model Order Reduction for Bayesian Inverse Problems

KAUST Repository

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.

Software tool for resolution of inverse problems using artificial intelligence techniques: an application in neutron spectrometry; Herramienta en software para resolucion de problemas inversos mediante tecnicas de inteligencia artificial: una aplicacion en espectrometria neutronica

Energy Technology Data Exchange (ETDEWEB)

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. [Universidad Autonoma de Zacatecas, 98000 Zacatecas, Zac. (Mexico); Mendez, R. [CIEMAT, Departamento de Metrologia de Radiaciones Ionizantes, Laboratorio de Patrones Neutronicos, Av. Complutense 22, 28040 Madrid (Spain); Gallego, E. [Universidad Politecnica de Madrid, Departamento de Ingenieria Nuclear, C. Jose Gutierrez Abascal 2, 28006 Madrid (Spain); Sousa L, M. A. [Comision Nacional de Energia Nuclear, Centro de Investigacion de Tecnologia Nuclear, Av. Pte. Antonio Carlos 6627, Pampulha, 31270-901 Belo Horizonte, Minas Gerais (Brazil)

2016-10-15

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)

NON-INVASIVE INVERSE PROBLEM IN CIVIL ENGINEERING

Directory of Open Access Journals (Sweden)

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.

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

Estimates of error introduced when one-dimensional inverse heat transfer techniques are applied to multi-dimensional problems

International Nuclear Information System (INIS)

Lopez, C.; Koski, J.A.; Razani, A.

2000-01-01

A study of the errors introduced when one-dimensional inverse heat conduction techniques are applied to problems involving two-dimensional heat transfer effects was performed. The geometry used for the study was a cylinder with similar dimensions as a typical container used for the transportation of radioactive materials. The finite element analysis code MSC P/Thermal was used to generate synthetic test data that was then used as input for an inverse heat conduction code. Four different problems were considered including one with uniform flux around the outer surface of the cylinder and three with non-uniform flux applied over 360 deg C, 180 deg C, and 90 deg C sections of the outer surface of the cylinder. The Sandia One-Dimensional Direct and Inverse Thermal (SODDIT) code was used to estimate the surface heat flux of all four cases. The error analysis was performed by comparing the results from SODDIT and the heat flux calculated based on the temperature results obtained from P/Thermal. Results showed an increase in error of the surface heat flux estimates as the applied heat became more localized. For the uniform case, SODDIT provided heat flux estimates with a maximum error of 0.5% whereas for the non-uniform cases, the maximum errors were found to be about 3%, 7%, and 18% for the 360 deg C, 180 deg C, and 90 deg C cases, respectively

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

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

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

A conditioning technique for matrix inversion for Wilson fermions

International Nuclear Information System (INIS)

DeGrand, T.A.

1988-01-01

I report a simple technique for conditioning conjugate gradient or conjugate residue matrix inversion as applied to the lattice gauge theory problem of computing the propagator of Wilson fermions. One form of the technique provides about a factor of three speedup over an unconditioned algorithm while running at the same speed as an unconditioned algorithm. I illustrate the method as it is applied to a conjugate residue algorithm. (orig.)

Filtering techniques for efficient inversion of two-dimensional Nuclear Magnetic Resonance data

Science.gov (United States)

Bortolotti, V.; Brizi, L.; Fantazzini, P.; Landi, G.; Zama, F.

2017-10-01

The inversion of two-dimensional Nuclear Magnetic Resonance (NMR) data requires the solution of a first kind Fredholm integral equation with a two-dimensional tensor product kernel and lower bound constraints. For the solution of this ill-posed inverse problem, the recently presented 2DUPEN algorithm [V. Bortolotti et al., Inverse Problems, 33(1), 2016] uses multiparameter Tikhonov regularization with automatic choice of the regularization parameters. In this work, I2DUPEN, an improved version of 2DUPEN that implements Mean Windowing and Singular Value Decomposition filters, is deeply tested. The reconstruction problem with filtered data is formulated as a compressed weighted least squares problem with multi-parameter Tikhonov regularization. Results on synthetic and real 2D NMR data are presented with the main purpose to deeper analyze the separate and combined effects of these filtering techniques on the reconstructed 2D distribution.

Solving Inverse Kinematics – A New Approach to the Extended Jacobian Technique

Directory of Open Access Journals (Sweden)

M. Šoch

2005-01-01

Full Text Available This paper presents a brief summary of current numerical algorithms for solving the Inverse Kinematics problem. Then a new approach based on the Extended Jacobian technique is compared with the current Jacobian Inversion method. The presented method is intended for use in the field of computer graphics for animation of articulated structures. 

Microlocal analysis of a seismic linearized inverse problem

NARCIS (Netherlands)

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

Decomposing Large Inverse Problems with an Augmented Lagrangian Approach: Application to Joint Inversion of Body-Wave Travel Times and Surface-Wave Dispersion Measurements

Science.gov (United States)

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.

Introduction to inverse problems for differential equations

CERN Document Server

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...

Obtaining sparse distributions in 2D inverse problems

OpenAIRE

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...

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.)

From inverse problems to learning: a Statistical Mechanics approach

Science.gov (United States)

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.

Efficient Monte Carlo sampling of inverse problems using a neural network-based forward—applied to GPR crosshole traveltime inversion

Science.gov (United States)

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.

Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

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

Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

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.

Size Estimates in Inverse Problems

KAUST Repository

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.

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.

On two-spectra inverse problems

OpenAIRE

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.

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)

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

Trimming and procrastination as inversion techniques

Science.gov (United States)

Backus, George E.

1996-12-01

By examining the processes of truncating and approximating the model space (trimming it), and by committing to neither the objectivist nor the subjectivist interpretation of probability (procrastinating), we construct a formal scheme for solving linear and non-linear geophysical inverse problems. The necessary prior information about the correct model xE can be either a collection of inequalities or a probability measure describing where xE was likely to be in the model space X before the data vector y0 was measured. The results of the inversion are (1) a vector z0 that estimates some numerical properties zE of xE; (2) an estimate of the error δz = z0 - zE. As y0 is finite dimensional, so is z0, and hence in principle inversion cannot describe all of xE. The error δz is studied under successively more specialized assumptions about the inverse problem, culminating in a complete analysis of the linear inverse problem with a prior quadratic bound on xE. Our formalism appears to encompass and provide error estimates for many of the inversion schemes current in geomagnetism, and would be equally applicable in geodesy and seismology if adequate prior information were available there. As an idealized example we study the magnetic field at the core-mantle boundary, using satellite measurements of field elements at sites assumed to be almost uniformly distributed on a single spherical surface. Magnetospheric currents are neglected and the crustal field is idealized as a random process with rotationally invariant statistics. We find that an appropriate data compression diagonalizes the variance matrix of the crustal signal and permits an analytic trimming of the idealized problem.

FOREWORD: 5th International Workshop on New Computational Methods for Inverse Problems

Science.gov (United States)

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

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

Approximation of Bayesian Inverse Problems for PDEs

OpenAIRE

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...

One-dimensional nonlinear inverse heat conduction technique

International Nuclear Information System (INIS)

Hills, R.G.; Hensel, E.C. Jr.

1986-01-01

The one-dimensional nonlinear problem of heat conduction is considered. A noniterative space-marching finite-difference algorithm is developed to estimate the surface temperature and heat flux from temperature measurements at subsurface locations. The trade-off between resolution and variance of the estimates of the surface conditions is discussed quantitatively. The inverse algorithm is stabilized through the use of digital filters applied recursively. The effect of the filters on the resolution and variance of the surface estimates is quantified. Results are presented which indicate that the technique is capable of handling noisy measurement data

Formulas in inverse and ill-posed problems

CERN Document Server

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.

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.

Inverse radiative transfer problems in two-dimensional heterogeneous media; Problemas inversos em transferencia radiativa em meios heterogeneos bidimensionais

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)

Recovery of material parameters of soft hyperelastic tissue by an inverse spectral technique

KAUST Repository

Gou, Kun

2012-07-01

An inverse spectral method is developed for recovering a spatially inhomogeneous shear modulus for soft tissue. The study is motivated by a novel use of the intravascular ultrasound technique to image arteries. The arterial wall is idealized as a nonlinear isotropic cylindrical hyperelastic body. A boundary value problem is formulated for the response of the arterial wall within a specific class of quasistatic deformations reflective of the response due to imposed blood pressure. Subsequently, a boundary value problem is developed via an asymptotic construction modeling intravascular ultrasound interrogation which generates small amplitude, high frequency time harmonic vibrations superimposed on the static finite deformation. This leads to a system of second order ordinary Sturm-Liouville boundary value problems that are then employed to reconstruct the shear modulus through a nonlinear inverse spectral technique. Numerical examples are demonstrated to show the viability of the method. © 2012 Elsevier Ltd. All rights reserved.

Detection of Cavities by Inverse Heat Conduction Boundary Element Method Using Minimal Energy Technique

International Nuclear Information System (INIS)

Choi, C. Y.

1997-01-01

A geometrical inverse heat conduction problem is solved for the infrared scanning cavity detection by the boundary element method using minimal energy technique. By minimizing the kinetic energy of temperature field, boundary element equations are converted to the quadratic programming problem. A hypothetical inner boundary is defined such that the actual cavity is located interior to the domain. Temperatures at hypothetical inner boundary are determined to meet the constraints of measurement error of surface temperature obtained by infrared scanning, and then boundary element analysis is performed for the position of an unknown boundary (cavity). Cavity detection algorithm is provided, and the effects of minimal energy technique on the inverse solution method are investigated by means of numerical analysis

A general approach to regularizing inverse problems with regional data using Slepian wavelets

Science.gov (United States)

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.

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...

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.

PREFACE: Inverse Problems in Applied Sciences—towards breakthrough

Science.gov (United States)

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

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)

Inverse Modelling Problems in Linear Algebra Undergraduate Courses

Science.gov (United States)

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…

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.

An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

Science.gov (United States)

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 \

From capture to simulation: connecting forward and inverse problems in fluids

KAUST Repository

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.

From capture to simulation: connecting forward and inverse problems in fluids

KAUST Repository

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 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.

One-dimensional inverse problems of mathematical physics

CERN Document Server

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 in Geodynamics Using Machine Learning Algorithms

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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.

Size Estimates in Inverse Problems

KAUST Repository

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

Inverse problems in vision and 3D tomography

CERN Document Server

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

Inverse problems basics, theory and applications in geophysics

CERN Document Server

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.

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...

FOREWORD: 4th International Workshop on New Computational Methods for Inverse Problems (NCMIP2014)

Science.gov (United States)

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

Solving inverse two-point boundary value problems using collage coding

Science.gov (United States)

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.

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.

Inverse problems in ordinary differential equations and applications

CERN Document Server

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.

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

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.

Applications of elliptic Carleman inequalities to Cauchy and inverse problems

CERN Document Server

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.

Source localization in electromyography using the inverse potential problem

Science.gov (United States)

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

Analyses of Effects of Cutting Parameters on Cutting Edge Temperature Using Inverse Heat Conduction Technique

Directory of Open Access Journals (Sweden)

Marcelo Ribeiro dos Santos

2014-01-01

Full Text Available During machining energy is transformed into heat due to plastic deformation of the workpiece surface and friction between tool and workpiece. High temperatures are generated in the region of the cutting edge, which have a very important influence on wear rate of the cutting tool and on tool life. This work proposes the estimation of heat flux at the chip-tool interface using inverse techniques. Factors which influence the temperature distribution at the AISI M32C high speed steel tool rake face during machining of a ABNT 12L14 steel workpiece were also investigated. The temperature distribution was predicted using finite volume elements. A transient 3D numerical code using irregular and nonstaggered mesh was developed to solve the nonlinear heat diffusion equation. To validate the software, experimental tests were made. The inverse problem was solved using the function specification method. Heat fluxes at the tool-workpiece interface were estimated using inverse problems techniques and experimental temperatures. Tests were performed to study the effect of cutting parameters on cutting edge temperature. The results were compared with those of the tool-work thermocouple technique and a fair agreement was obtained.

Inverse source problems in elastodynamics

Science.gov (United States)

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.

Integral geometry and inverse problems for hyperbolic equations

CERN Document Server

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...

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

A technique for increasing the accuracy of the numerical inversion of the Laplace transform with applications

Science.gov (United States)

Berger, B. S.; Duangudom, S.

1973-01-01

A technique is introduced which extends the range of useful approximation of numerical inversion techniques to many cycles of an oscillatory function without requiring either the evaluation of the image function for many values of s or the computation of higher-order terms. The technique consists in reducing a given initial value problem defined over some interval into a sequence of initial value problems defined over a set of subintervals. Several numerical examples demonstrate the utility of the method.

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.

The philosophical aspect of learning inverse problems of mathematical physics

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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.

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

Methods and Algorithms for Solving Inverse Problems for Fractional Advection-Dispersion Equations

KAUST Repository

Aldoghaither, Abeer

2015-11-12

observations. An analytic solution for the non-homogeneous case is derived and existence and uniqueness of the solution are established. In addition, the uniqueness and stability of the inverse problem is studied. Moreover, the modulating functions-based method is used to solve the problem and it is compared to a standard Tikhono-based optimization technique.

Inverse Raman effect: applications and detection techniques

Energy Technology Data Exchange (ETDEWEB)

Hughes, L.J. Jr.

1980-08-01

The processes underlying the inverse Raman effect are qualitatively described by comparing it to the more familiar phenomena of conventional and stimulated Raman scattering. An experession is derived for the inverse Raman absorption coefficient, and its relationship to the stimulated Raman gain is obtained. The power requirements of the two fields are examined qualitatively and quantitatively. The assumption that the inverse Raman absorption coefficient is constant over the interaction length is examined. Advantages of the technique are discussed and a brief survey of reported studies is presented.

Inverse Raman effect: applications and detection techniques

International Nuclear Information System (INIS)

Hughes, L.J. Jr.

1980-08-01

The processes underlying the inverse Raman effect are qualitatively described by comparing it to the more familiar phenomena of conventional and stimulated Raman scattering. An experession is derived for the inverse Raman absorption coefficient, and its relationship to the stimulated Raman gain is obtained. The power requirements of the two fields are examined qualitatively and quantitatively. The assumption that the inverse Raman absorption coefficient is constant over the interaction length is examined. Advantages of the technique are discussed and a brief survey of reported studies is presented

Inverse kinematics problem in robotics using neural networks

Science.gov (United States)

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.

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

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.

Geostatistical regularization operators for geophysical inverse problems on irregular meshes

Science.gov (United States)

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.

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

Carleman estimates and applications to inverse problems for hyperbolic systems

CERN Document Server

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...

Machine Learning and Inverse Problem in Geodynamics

Science.gov (United States)

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

Direct and inverse source problems for a space fractional advection dispersion equation

KAUST Repository

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.

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)

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)

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

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.)

Collage-based approaches for elliptic partial differential equations inverse problems

Science.gov (United States)

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.

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 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

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

Science.gov (United States)

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.

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

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)

Time reversal imaging, Inverse problems and Adjoint Tomography}

Science.gov (United States)

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.

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)

Efficient generalized Golub-Kahan based methods for dynamic inverse problems

Science.gov (United States)

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.

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)

Determining the metallicity of the solar envelope using seismic inversion techniques

Science.gov (United States)

Buldgen, G.; Salmon, S. J. A. J.; Noels, A.; Scuflaire, R.; Dupret, M. A.; Reese, D. R.

2017-11-01

The solar metallicity issue is a long-lasting problem of astrophysics, impacting multiple fields and still subject to debate and uncertainties. While spectroscopy has mostly been used to determine the solar heavy elements abundance, helioseismologists attempted providing a seismic determination of the metallicity in the solar convective envelope. However, the puzzle remains since two independent groups provided two radically different values for this crucial astrophysical parameter. We aim at providing an independent seismic measurement of the solar metallicity in the convective envelope. Our main goal is to help provide new information to break the current stalemate amongst seismic determinations of the solar heavy element abundance. We start by presenting the kernels, the inversion technique and the target function of the inversion we have developed. We then test our approach in multiple hare-and-hounds exercises to assess its reliability and accuracy. We then apply our technique to solar data using calibrated solar models and determine an interval of seismic measurements for the solar metallicity. We show that our inversion can indeed be used to estimate the solar metallicity thanks to our hare-and-hounds exercises. However, we also show that further dependencies in the physical ingredients of solar models lead to a low accuracy. Nevertheless, using various physical ingredients for our solar models, we determine metallicity values between 0.008 and 0.014.

Cohesive phase-field fracture and a PDE constrained optimization approach to fracture inverse problems

Energy Technology Data Exchange (ETDEWEB)

Tupek, Michael R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2016-06-30

In recent years there has been a proliferation of modeling techniques for forward predictions of crack propagation in brittle materials, including: phase-field/gradient damage models, peridynamics, cohesive-zone models, and G/XFEM enrichment techniques. However, progress on the corresponding inverse problems has been relatively lacking. Taking advantage of key features of existing modeling approaches, we propose a parabolic regularization of Barenblatt cohesive models which borrows extensively from previous phase-field and gradient damage formulations. An efficient explicit time integration strategy for this type of nonlocal fracture model is then proposed and justified. In addition, we present a C++ computational framework for computing in- put parameter sensitivities efficiently for explicit dynamic problems using the adjoint method. This capability allows for solving inverse problems involving crack propagation to answer interesting engineering questions such as: 1) what is the optimal design topology and material placement for a heterogeneous structure to maximize fracture resistance, 2) what loads must have been applied to a structure for it to have failed in an observed way, 3) what are the existing cracks in a structure given various experimental observations, etc. In this work, we focus on the first of these engineering questions and demonstrate a capability to automatically and efficiently compute optimal designs intended to minimize crack propagation in structures.

Numerical solution to a multi-dimensional linear inverse heat conduction problem by a splitting-based conjugate gradient method

International Nuclear Information System (INIS)

Dinh Nho Hao; Nguyen Trung Thanh; Sahli, Hichem

2008-01-01

In this paper we consider a multi-dimensional inverse heat conduction problem with time-dependent coefficients in a box, which is well-known to be severely ill-posed, by a variational method. The gradient of the functional to be minimized is obtained by aids of an adjoint problem and the conjugate gradient method with a stopping rule is then applied to this ill-posed optimization problem. To enhance the stability and the accuracy of the numerical solution to the problem we apply this scheme to the discretized inverse problem rather than to the continuous one. The difficulties with large dimensions of discretized problems are overcome by a splitting method which only requires the solution of easy-to-solve one-dimensional problems. The numerical results provided by our method are very good and the techniques seem to be very promising.

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

Eigenvectors phase correction in inverse modal problem

Science.gov (United States)

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.

An inverse boundary value problem for the Schroedinger operator with vector potentials in two dimensions

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

Inverse problem for particle size distributions of atmospheric aerosols using stochastic particle swarm optimization

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.

Bilinear Inverse Problems: Theory, Algorithms, and Applications

Science.gov (United States)

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

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

Inverse Problems in Systems Biology: A Critical Review.

Science.gov (United States)

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.

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

Adaptive discretizations for the choice of a Tikhonov regularization parameter in nonlinear inverse problems

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)

Direct and inverse source problems for a space fractional advection dispersion equation

KAUST Repository

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

An inverse Sturm–Liouville problem with a fractional derivative

KAUST Repository

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

An inverse problem for a one-dimensional time-fractional diffusion problem

KAUST Repository

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 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)

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

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)

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.

Wavelet-sparsity based regularization over time in the inverse problem of electrocardiography.

Science.gov (United States)

Cluitmans, Matthijs J M; Karel, Joël M H; Bonizzi, Pietro; Volders, Paul G A; Westra, Ronald L; Peeters, Ralf L M

2013-01-01

Noninvasive, detailed assessment of electrical cardiac activity at the level of the heart surface has the potential to revolutionize diagnostics and therapy of cardiac pathologies. Due to the requirement of noninvasiveness, body-surface potentials are measured and have to be projected back to the heart surface, yielding an ill-posed inverse problem. Ill-posedness ensures that there are non-unique solutions to this problem, resulting in a problem of choice. In the current paper, it is proposed to restrict this choice by requiring that the time series of reconstructed heart-surface potentials is sparse in the wavelet domain. A local search technique is introduced that pursues a sparse solution, using an orthogonal wavelet transform. Epicardial potentials reconstructed from this method are compared to those from existing methods, and validated with actual intracardiac recordings. The new technique improves the reconstructions in terms of smoothness and recovers physiologically meaningful details. Additionally, reconstruction of activation timing seems to be improved when pursuing sparsity of the reconstructed signals in the wavelet domain.

Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo

Science.gov (United States)

Bui-Thanh, T.; Girolami, M.

2014-11-01

We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint

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.

An Inverse Eigenvalue Problem for a Vibrating String with Two Dirichlet Spectra

KAUST Repository

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

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...

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...

Identification of the Thermophysical Properties of the Soil by Inverse Problem

OpenAIRE

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

Science.gov (United States)

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.

MAP estimators and their consistency in Bayesian nonparametric inverse problems

KAUST Repository

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 an asymptotic technique of solution of the inverse problem of helioseismology

International Nuclear Information System (INIS)

Brodskij, M.A.; Vorontsov, S.V.

1987-01-01

The technique for the solution of the universe problem for the solar 5-min. oscillations is proposed, which provides an independent determination of the second speed as a function of depth in solar interior and the frequency dependence of the effective phase shift for the reflection of the trapped acoustic waves from the outer layers. The preliminary numerical results are presented

Objective mapping of observed sub-surface mesoscale cold core eddy in the Bay of Bengal by stochastic inverse technique with tomographically simulated travel times

Digital Repository Service at National Institute of Oceanography (India)

Murty, T.V.R.; Rao, M.M.M.; Sadhuram, Y.; Sridevi, B.; Maneesha, K.; SujithKumar, S.; Prasanna, P.L.; Murthy, K.S.R.

of Bengal during south-west monsoon season and explore possibility to reconstruct the acoustic profile of the eddy by Stochastic Inverse Technique. A simulation experiment on forward and inverse problems for observed sound velocity perturbation field has...

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

Science.gov (United States)

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

Introduction to the 30th volume of Inverse Problems

Science.gov (United States)

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

A fast algorithm for parabolic PDE-based inverse problems based on Laplace transforms and flexible Krylov solvers

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

A fast algorithm for parabolic PDE-based inverse problems based on Laplace transforms and flexible Krylov solvers

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.

Control of plasma profile in microwave discharges via inverse-problem approach

Directory of Open Access Journals (Sweden)

Yasuyoshi Yasaka

2013-12-01

Full Text Available In the manufacturing process of semiconductors, plasma processing is an essential technology, and the plasma used in the process is required to be of high density, low temperature, large diameter, and high uniformity. This research focuses on the microwave-excited plasma that meets these needs, and the research target is a spatial profile control. Two novel techniques are introduced to control the uniformity; one is a segmented slot antenna that can change radial distribution of the radiated field during operation, and the other is a hyper simulator that can predict microwave power distribution necessary for a desired radial density profile. The control system including these techniques provides a method of controlling radial profiles of the microwave plasma via inverse-problem approach, and is investigated numerically and experimentally.

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

Variational methods for direct/inverse problems of atmospheric dynamics and chemistry

Science.gov (United States)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the

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.

Coefficient Inverse Problem for Poisson's Equation in a Cylinder

NARCIS (Netherlands)

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

NUMERICAL SOLUTION OF SINGULAR INVERSE NODAL PROBLEM BY USING CHEBYSHEV POLYNOMIALS

OpenAIRE

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...

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 ...

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

PREFACE: The Second International Conference on Inverse Problems: Recent Theoretical Developments and Numerical Approaches

Science.gov (United States)

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

Escript: Open Source Environment For Solving Large-Scale Geophysical Joint Inversion Problems in Python

Science.gov (United States)

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

Total variation regularization of the 3-D gravity inverse problem using a randomized generalized singular value decomposition

Science.gov (United States)

Vatankhah, Saeed; Renaut, Rosemary A.; Ardestani, Vahid E.

2018-04-01

We present a fast algorithm for the total variation regularization of the 3-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved better than when using a conventional minimum-structure inversion. The associated problem formulation for the regularization is nonlinear but can be solved using an iteratively reweighted least-squares algorithm. For small-scale problems the regularized least-squares problem at each iteration can be solved using the generalized singular value decomposition. This is not feasible for large-scale, or even moderate-scale, problems. Instead we introduce the use of a randomized generalized singular value decomposition in order to reduce the dimensions of the problem and provide an effective and efficient solution technique. For further efficiency an alternating direction algorithm is used to implement the total variation weighting operator within the iteratively reweighted least-squares algorithm. Presented results for synthetic examples demonstrate that the novel randomized decomposition provides good accuracy for reduced computational and memory demands as compared to use of classical approaches.

Comparative interpretations of renormalization inversion technique for reconstructing unknown emissions from measured atmospheric concentrations

Science.gov (United States)

Singh, Sarvesh Kumar; Kumar, Pramod; Rani, Raj; Turbelin, Grégory

2017-04-01

The study highlights a theoretical comparison and various interpretations of a recent inversion technique, called renormalization, developed for the reconstruction of unknown tracer emissions from their measured concentrations. The comparative interpretations are presented in relation to the other inversion techniques based on principle of regularization, Bayesian, minimum norm, maximum entropy on mean, and model resolution optimization. It is shown that the renormalization technique can be interpreted in a similar manner to other techniques, with a practical choice of a priori information and error statistics, while eliminating the need of additional constraints. The study shows that the proposed weight matrix and weighted Gram matrix offer a suitable deterministic choice to the background error and measurement covariance matrices, respectively, in the absence of statistical knowledge about background and measurement errors. The technique is advantageous since it (i) utilizes weights representing a priori information apparent to the monitoring network, (ii) avoids dependence on background source estimates, (iii) improves on alternative choices for the error statistics, (iv) overcomes the colocalization problem in a natural manner, and (v) provides an optimally resolved source reconstruction. A comparative illustration of source retrieval is made by using the real measurements from a continuous point release conducted in Fusion Field Trials, Dugway Proving Ground, Utah.

Differential equations inverse and direct problems

CERN Document Server

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

Solving of L0 norm constrained EEG inverse problem.

Science.gov (United States)

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.

Magnetic resonance separation imaging using a divided inversion recovery technique (DIRT).

Science.gov (United States)

Goldfarb, James W

2010-04-01

The divided inversion recovery technique is an MRI separation method based on tissue T(1) relaxation differences. When tissue T(1) relaxation times are longer than the time between inversion pulses in a segmented inversion recovery pulse sequence, longitudinal magnetization does not pass through the null point. Prior to additional inversion pulses, longitudinal magnetization may have an opposite polarity. Spatial displacement of tissues in inversion recovery balanced steady-state free-precession imaging has been shown to be due to this magnetization phase change resulting from incomplete magnetization recovery. In this paper, it is shown how this phase change can be used to provide image separation. A pulse sequence parameter, the time between inversion pulses (T180), can be adjusted to provide water-fat or fluid separation. Example water-fat and fluid separation images of the head, heart, and abdomen are presented. The water-fat separation performance was investigated by comparing image intensities in short-axis divided inversion recovery technique images of the heart. Fat, blood, and fluid signal was suppressed to the background noise level. Additionally, the separation performance was not affected by main magnetic field inhomogeneities.

Solution of the Inverse Problem for Thin Film Patterning by Electrohydrodynamic Forces

Science.gov (United States)

Zhou, Chengzhe; Troian, Sandra

2017-11-01

Micro- and nanopatterning techniques for applications ranging from optoelectronics to biofluidics have multiplied in number over the past decade to include adaptations of mature technologies as well as novel lithographic techniques based on periodic spatial modulation of surface stresses. We focus here on one such technique which relies on shape changes in nanofilms responding to a patterned counter-electrode. The interaction of a patterned electric field with the polarization charges at the liquid interface causes a patterned electrostatic pressure counterbalanced by capillary pressure which leads to 3D protrusions whose shape and evolution can be terminated as needed. All studies to date, however, have investigated the evolution of the liquid film in response to a preset counter-electrode pattern. In this talk, we present solution of the inverse problem for the thin film equation governing the electrohydrodynamic response by treating the system as a transient control problem. Optimality conditions are derived and an efficient corresponding solution algorithm is presented. We demonstrate such implementation of film control to achieve periodic, free surface shapes ranging from simple circular cap arrays to more complex square and sawtooth patterns.

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

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

Inverse problem for in vivo NMR spatial localization

Energy Technology Data Exchange (ETDEWEB)

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.

An efficient Bayesian inference approach to inverse problems based on an adaptive sparse grid collocation method

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

Inverse Problem in Self-assembly

Science.gov (United States)

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.

The algebraic method of the scattering inverse problem solution under untraditional statements

CERN Document Server

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

Inverse problem theory methods for data fitting and model parameter estimation

CERN Document Server

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

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.

Solving probabilistic inverse problems rapidly with prior samples

NARCIS (Netherlands)

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

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.

Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrodinger equation

OpenAIRE

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.

A Frequency Matching Method: Solving Inverse Problems by Use of Geologically Realistic Prior Information

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....

Warhead verification as inverse problem: Applications of neutron spectrum unfolding from organic-scintillator measurements

Science.gov (United States)

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 Concept for Atmospheric Reentry Optimal Guidance: An Inverse Problem Inspired Approach

Directory of Open Access Journals (Sweden)

Davood Abbasi

2013-01-01

Full Text Available This paper presents a new concept for atmospheric reentry online optimal guidance and control using a method called MARE G&C that exploits the different time scale featured by reentry dynamics. The new technique reaches a quasi-analytical solution and simplified computations, even considering both lift-to-drag ratio and aerodynamic roll as control variables; in addition, the paper offers a solution for the challenging path constraints issue, getting inspiration from the inverse problem methodology. The final resulting algorithm seems suitable for onboard predictive guidance, a new need for future space missions.

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.

Eddy current imaging. Limits of the born approximation and advantages of an exact solution to the inverse problem

International Nuclear Information System (INIS)

Hamman, E.; Zorgati, R.

1995-01-01

Eddy current non-destructive testing is used by EDF to detect flaws affecting conductive objects such as steam generator tubes. With a view to obtaining ever more accurate information on equipment integrity, thereby facilitating diagnosis, studies aimed at using measurements to reconstruct an image of the flaw have been proceeding now for about ten years. In this context, our approach to eddy current imaging is based on inverse problem formalism. The direct problem, involving a mathematical model linking measurements provided by a probe with variables characterizing the defect, is dealt with elsewhere. Using the model results, we study the possibility of inverting it, i.e. of reconstructing an image of the flaw from the measurements. We first give an overview of the different inversion techniques, representative of the state of the art and all based on linearization of the inverse problem by means of the Born approximation. The model error resulting from an excessive Born approximation nevertheless severely limits the quantity of the images which can be obtained. In order to counteract this often critical error and extend the eddy current imaging application field, we have to del with the non-linear inverse problem. A method derived from recent research is proposed and implemented to ensure consistency with the exact model. Based on an 'optimization' type approach and provided with a convergence theorem, the method is highly efficient. (authors). 17 refs., 7 figs., 1 append

Inverse Optimization and Forecasting Techniques Applied to Decision-making in Electricity Markets

DEFF Research Database (Denmark)

Saez Gallego, Javier

patterns that the load traditionally exhibited. On the other hand, this thesis is motivated by the decision-making processes of market players. In response to these challenges, this thesis provides mathematical models for decision-making under uncertainty in electricity markets. Demand-side bidding refers......This thesis deals with the development of new mathematical models that support the decision-making processes of market players. It addresses the problems of demand-side bidding, price-responsive load forecasting and reserve determination. From a methodological point of view, we investigate a novel...... approach to model the response of aggregate price-responsive load as a constrained optimization model, whose parameters are estimated from data by using inverse optimization techniques. The problems tackled in this dissertation are motivated, on one hand, by the increasing penetration of renewable energy...

Stabilizing inverse problems by internal data. II: non-local internal data and generic linearized uniqueness

KAUST Repository

Kuchment, Peter

2015-05-10

© 2015, Springer Basel. In the previous paper (Kuchment and Steinhauer in Inverse Probl 28(8):084007, 2012), the authors introduced a simple procedure that allows one to detect whether and explain why internal information arising in several novel coupled physics (hybrid) imaging modalities could turn extremely unstable techniques, such as optical tomography or electrical impedance tomography, into stable, good-resolution procedures. It was shown that in all cases of interest, the Fréchet derivative of the forward mapping is a pseudo-differential operator with an explicitly computable principal symbol. If one can set up the imaging procedure in such a way that the symbol is elliptic, this would indicate that the problem was stabilized. In the cases when the symbol is not elliptic, the technique suggests how to change the procedure (e.g., by adding extra measurements) to achieve ellipticity. In this article, we consider the situation arising in acousto-optical tomography (also called ultrasound modulated optical tomography), where the internal data available involves the Green’s function, and thus depends globally on the unknown parameter(s) of the equation and its solution. It is shown that the technique of (Kuchment and Steinhauer in Inverse Probl 28(8):084007, 2012) can be successfully adopted to this situation as well. A significant part of the article is devoted to results on generic uniqueness for the linearized problem in a variety of situations, including those arising in acousto-electric and quantitative photoacoustic tomography.

A theoretical formulation of the electrophysiological inverse problem on the sphere.

Science.gov (United States)

Riera, Jorge J; Valdés, Pedro A; Tanabe, Kunio; Kawashima, Ryuta

2006-04-07

The construction of three-dimensional images of the primary current density (PCD) produced by neuronal activity is a problem of great current interest in the neuroimaging community, though being initially formulated in the 1970s. There exist even now enthusiastic debates about the authenticity of most of the inverse solutions proposed in the literature, in which low resolution electrical tomography (LORETA) is a focus of attention. However, in our opinion, the capabilities and limitations of the electro and magneto encephalographic techniques to determine PCD configurations have not been extensively explored from a theoretical framework, even for simple volume conductor models of the head. In this paper, the electrophysiological inverse problem for the spherical head model is cast in terms of reproducing kernel Hilbert spaces (RKHS) formalism, which allows us to identify the null spaces of the implicated linear integral operators and also to define their representers. The PCD are described in terms of a continuous basis for the RKHS, which explicitly separates the harmonic and non-harmonic components. The RKHS concept permits us to bring LORETA into the scope of the general smoothing splines theory. A particular way of calculating the general smoothing splines is illustrated, avoiding a brute force discretization prematurely. The Bayes information criterion is used to handle dissimilarities in the signal/noise ratios and physical dimensions of the measurement modalities, which could affect the estimation of the amount of smoothness required for that class of inverse solution to be well specified. In order to validate the proposed method, we have estimated the 3D spherical smoothing splines from two data sets: electric potentials obtained from a skull phantom and magnetic fields recorded from subjects performing an experiment of human faces recognition.

Continuity of the direct and inverse problems in one-dimensional scattering theory and numerical solution of the inverse problem

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

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)

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)

An inverse problem strategy based on forward model evaluations: Gradient-based optimization without adjoint solves

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.

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.

A gradient based algorithm to solve inverse plane bimodular problems of identification

Science.gov (United States)

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.

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

Scalable posterior approximations for large-scale Bayesian inverse problems via likelihood-informed parameter and state reduction

Science.gov (United States)

Cui, Tiangang; Marzouk, Youssef; Willcox, Karen

2016-06-01

Two major bottlenecks to the solution of large-scale Bayesian inverse problems are the scaling of posterior sampling algorithms to high-dimensional parameter spaces and the computational cost of forward model evaluations. Yet incomplete or noisy data, the state variation and parameter dependence of the forward model, and correlations in the prior collectively provide useful structure that can be exploited for dimension reduction in this setting-both in the parameter space of the inverse problem and in the state space of the forward model. To this end, we show how to jointly construct low-dimensional subspaces of the parameter space and the state space in order to accelerate the Bayesian solution of the inverse problem. As a byproduct of state dimension reduction, we also show how to identify low-dimensional subspaces of the data in problems with high-dimensional observations. These subspaces enable approximation of the posterior as a product of two factors: (i) a projection of the posterior onto a low-dimensional parameter subspace, wherein the original likelihood is replaced by an approximation involving a reduced model; and (ii) the marginal prior distribution on the high-dimensional complement of the parameter subspace. We present and compare several strategies for constructing these subspaces using only a limited number of forward and adjoint model simulations. The resulting posterior approximations can rapidly be characterized using standard sampling techniques, e.g., Markov chain Monte Carlo. Two numerical examples demonstrate the accuracy and efficiency of our approach: inversion of an integral equation in atmospheric remote sensing, where the data dimension is very high; and the inference of a heterogeneous transmissivity field in a groundwater system, which involves a partial differential equation forward model with high dimensional state and parameters.

Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing

Science.gov (United States)

Chu, W. P.

1985-01-01

The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.

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....

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...

Review of the inverse scattering problem at fixed energy in quantum mechanics

Science.gov (United States)

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.

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)

FOREWORD: 2nd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2012)

Science.gov (United States)

Blanc-Féraud, Laure; Joubert, Pierre-Yves

2012-09-01

Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 2nd International Workshop on New Computational Methods for Inverse Problems, (NCMIP 2012). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 15 May 2012, at the initiative of Institut Farman. The first edition of NCMIP also took place in Cachan, France, within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/). The 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 finance. 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, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition

FOREWORD: 3rd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2013)

Science.gov (United States)

Blanc-Féraud, Laure; Joubert, Pierre-Yves

2013-10-01

Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 3rd International Workshop on New Computational Methods for Inverse Problems, NCMIP 2013 (http://www.farman.ens-cachan.fr/NCMIP_2013.html). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 22 May 2013, at the initiative of Institut Farman. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 (http://www.farman.ens-cachan.fr/NCMIP_2012.html). The 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

Time-reversal and Bayesian inversion

Science.gov (United States)

Debski, Wojciech

2017-04-01

Probabilistic inversion technique is superior to the classical optimization-based approach in all but one aspects. It requires quite exhaustive computations which prohibit its use in huge size inverse problems like global seismic tomography or waveform inversion to name a few. The advantages of the approach are, however, so appealing that there is an ongoing continuous afford to make the large inverse task as mentioned above manageable with the probabilistic inverse approach. One of the perspective possibility to achieve this goal relays on exploring the internal symmetry of the seismological modeling problems in hand - a time reversal and reciprocity invariance. This two basic properties of the elastic wave equation when incorporating into the probabilistic inversion schemata open a new horizons for Bayesian inversion. In this presentation we discuss the time reversal symmetry property, its mathematical aspects and propose how to combine it with the probabilistic inverse theory into a compact, fast inversion algorithm. We illustrate the proposed idea with the newly developed location algorithm TRMLOC and discuss its efficiency when applied to mining induced seismic data.

Accounting for imperfect forward modeling in geophysical inverse problems — Exemplified for crosshole tomography

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...

LinvPy : a Python package for linear inverse problems

OpenAIRE

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.

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

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

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...

MAP estimators and their consistency in Bayesian nonparametric inverse problems

KAUST Repository

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)

Nonlinear problems in fluid dynamics and inverse scattering: Nonlinear waves and inverse scattering

Science.gov (United States)

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.

INTRODUCTION Introduction to the conference proceeding of the Workshop on Electromagnetic Inverse ProblemsThe University of Manchester, UK, 15-18 June, 2009

Science.gov (United States)

Dorn, Oliver; Lionheart, Bill

2010-11-01

any successful inversion, whereas the other three papers discuss novel inversion techniques for specific applications. In the first contribution, with the title A Novel Simplified Mathematical Model for Antennas used in Medical Imaging Applications, the authors M J Fernando, M Elsdon, K Busawon and D Smith discuss a new technique for modelling the current across a monopole antenna from which the radiation fields of the antenna can be calculated very efficiently in specific medical imaging applications. This new technique is then tested on two examples, a quarter wavelength and a three quarter wavelength monopole antenna. The next contribution, with the title An investigation into the use of a mixture model for simulating the electrical properties of soil with varying effective saturation levels for sub-soil imaging using ECT by R R Hayes, P A Newill, F J W Podd, T A York, B D Grieve and O Dorn, considers the development of a new visualization tool for monitoring soil moisture content surrounding certain seed breeder plants. An electrical capacitance tomography technique is employed for verifying how efficiently each plant utilises the water and nutrients available in the surrounding soil. The goal of this study is to help in developing and identifying new drought tolerant food crops. In the third contribution Combination of Maximin and Kriging Prediction Methods for Eddy-Current Testing Database Generation by S Bilicz, M Lambert, E Vazquez and S Gyimóthy, a novel database generation technique is proposed for its use in solving inverse eddy-current testing problems. For avoiding expensive repeated forward simulations during the creation of this database, a kriging interpolation technique is employed for filling uniformly the data output space with sample points. Mathematically this is achieved by using a maximin formalism. The paper 2.5D inversion of CSEM data in a vertically anisotropic earth by C Ramananjaona and L MacGregor considers controlled

Applications of multiscale waveform inversion to marine data using a flooding technique and dynamic early-arrival windows

KAUST Repository

Boonyasiriwat, Chaiwoot

2010-11-01

A recently developed time-domain multiscale waveform tomography (MWT) method is applied to synthetic and field marine data. Although the MWT method was already applied to synthetic data, the synthetic data application leads to a development of a hybrid method between waveform tomography and the salt flooding technique commonly use in subsalt imaging. This hybrid method can overcome a convergence problem encountered by inversion with a traveltime velocity tomogram and successfully provides an accurate and highly resolved velocity tomogram for the 2D SEG/EAGE salt model. In the application of MWT to the field data, the inversion process is carried out using a multiscale method with a dynamic early-arrival muting window to mitigate the local minima problem of waveform tomography and elastic effects. With the modified MWT method, reasonably accurate results as verified by comparison of migration images and common image gathers were obtained. The hybrid method with the salt flooding technique is not used in this field data example because there is no salt in the subsurface according to our interpretation. However, we believe it is applicable to field data applications. © 2010 Society of Exploration Geophysicists.

An inverse hyperbolic heat conduction problem in estimating surface heat flux by the conjugate gradient method

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

A limited memory BFGS method for a nonlinear inverse problem in digital breast tomosynthesis

Science.gov (United States)

Landi, G.; Loli Piccolomini, E.; Nagy, J. G.

2017-09-01

Digital breast tomosynthesis (DBT) is an imaging technique that allows the reconstruction of a pseudo three-dimensional image of the breast from a finite number of low-dose two-dimensional projections obtained by different x-ray tube angles. An issue that is often ignored in DBT is the fact that an x-ray beam is polyenergetic, i.e. it is composed of photons with different levels of energy. The polyenergetic model requires solving a large-scale, nonlinear inverse problem, which is more expensive than the typically used simplified, linear monoenergetic model. However, the polyenergetic model is much less susceptible to beam hardening artifacts, which show up as dark streaks and cupping (i.e. background nonuniformities) in the reconstructed image. In addition, it has been shown that the polyenergetic model can be exploited to obtain additional quantitative information about the material of the object being imaged. In this paper we consider the multimaterial polyenergetic DBT model, and solve the nonlinear inverse problem with a limited memory BFGS quasi-Newton method. Regularization is enforced at each iteration using a diagonally modified approximation of the Hessian matrix, and by truncating the iterations.

Inverse problem of radiofrequency sounding of ionosphere

Science.gov (United States)

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.

Inverse Problems and Uncertainty Quantification

KAUST Repository

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

KAUST Repository

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

KAUST Repository

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.

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.

Inverse problem of the vibrational band gap of periodically supported beam

Science.gov (United States)

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.

Applying inversion techniques to derive source currents and geoelectric fields for geomagnetically induced current calculations

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.

Forward modeling. Route to electromagnetic inversion

Energy Technology Data Exchange (ETDEWEB)

Groom, R; Walker, P [PetRos EiKon Incorporated, Ontario (Canada)

1996-05-01

Inversion of electromagnetic data is a topical subject in the literature, and much time has been devoted to understanding the convergence properties of various inverse methods. The relative lack of success of electromagnetic inversion techniques is partly attributable to the difficulties in the kernel forward modeling software. These difficulties come in two broad classes: (1) Completeness and robustness, and (2) convergence, execution time and model simplicity. If such problems exist in the forward modeling kernel, it was demonstrated that inversion can fail to generate reasonable results. It was suggested that classical inversion techniques, which are based on minimizing a norm of the error between data and the simulated data, will only be successful when these difficulties in forward modeling kernels are properly dealt with. 4 refs., 5 figs.

Intersections, ideals, and inversion

International Nuclear Information System (INIS)

Vasco, D.W.

1998-01-01

Techniques from computational algebra provide a framework for treating large classes of inverse problems. In particular, the discretization of many types of integral equations and of partial differential equations with undetermined coefficients lead to systems of polynomial equations. The structure of the solution set of such equations may be examined using algebraic techniques.. For example, the existence and dimensionality of the solution set may be determined. Furthermore, it is possible to bound the total number of solutions. The approach is illustrated by a numerical application to the inverse problem associated with the Helmholtz equation. The algebraic methods are used in the inversion of a set of transverse electric (TE) mode magnetotelluric data from Antarctica. The existence of solutions is demonstrated and the number of solutions is found to be finite, bounded from above at 50. The best fitting structure is dominantly one dimensional with a low crustal resistivity of about 2 ohm-m. Such a low value is compatible with studies suggesting lower surface wave velocities than found in typical stable cratons

Intersections, ideals, and inversion

Energy Technology Data Exchange (ETDEWEB)

Vasco, D.W.

1998-10-01

Techniques from computational algebra provide a framework for treating large classes of inverse problems. In particular, the discretization of many types of integral equations and of partial differential equations with undetermined coefficients lead to systems of polynomial equations. The structure of the solution set of such equations may be examined using algebraic techniques.. For example, the existence and dimensionality of the solution set may be determined. Furthermore, it is possible to bound the total number of solutions. The approach is illustrated by a numerical application to the inverse problem associated with the Helmholtz equation. The algebraic methods are used in the inversion of a set of transverse electric (TE) mode magnetotelluric data from Antarctica. The existence of solutions is demonstrated and the number of solutions is found to be finite, bounded from above at 50. The best fitting structure is dominantly onedimensional with a low crustal resistivity of about 2 ohm-m. Such a low value is compatible with studies suggesting lower surface wave velocities than found in typical stable cratons.

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)

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

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

Real Variable Inversion of Laplace Transforms: An Application in Plasma Physics.

Science.gov (United States)

Bohn, C. L.; Flynn, R. W.

1978-01-01

Discusses the nature of Laplace transform techniques and explains an alternative to them: the Widder's real inversion. To illustrate the power of this new technique, it is applied to a difficult inversion: the problem of Landau damping. (GA)

Variational approach to direct and inverse problems of atmospheric pollution studies

Science.gov (United States)

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

Inverse problems for partial differential equations

CERN Document Server

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...

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...

A variational Bayesian method to inverse problems with impulsive noise

KAUST Repository

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.

Solving inverse problems for biological models using the collage method for differential equations.

Science.gov (United States)

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.

SCIENTIFIC AND METHODICAL ASPECTS OF FORMATION OF SUBJECT CONTENT OF TRAINING COURSESFOR INVERSE PROBLEMS FOR DIFFERENTIAL EQUATIONS

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.

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...

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

An inverse diffusivity problem for the helium production–diffusion equation

International Nuclear Information System (INIS)

Bao, Gang; Xu, Xiang

2012-01-01

Thermochronology is a technique for the extraction of information about the thermal history of rocks. Such information is crucial for determining the depth below the surface at which rocks were located at a given time (Bao G et al 2011 Commun. Comput. Phys. 9 129). Mathematically, extracting the time–temperature path can be formulated as an inverse diffusivity problem for the helium production–diffusion equation which is the underlying process of thermochronology. In this paper, to reconstruct the diffusivity which depends on space only and accounts for the structural information of rocks, a local Hölder conditional stability is obtained by a Carleman estimate. A uniqueness result is also proven for extracting the thermal history, i.e. identifying the time-dependant part of the diffusion coefficient, provided that it is analytical with respect to time. Numerical examples are presented to illustrate the validity and effectiveness of the proposed regularization scheme. (paper)

Rapid processing of data based on high-performance algorithms for solving inverse problems and 3D-simulation of the tsunami and earthquakes

Science.gov (United States)

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

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

Solving the inverse heat conduction problem using NVLink capable Power architecture

Directory of Open Access Journals (Sweden)

Sándor Szénási

2017-11-01

Full Text Available The accurate knowledge of Heat Transfer Coefficients is essential for the design of precise heat transfer operations. The determination of these values requires Inverse Heat Transfer Calculations, which are usually based on heuristic optimisation techniques, like Genetic Algorithms or Particle Swarm Optimisation. The main bottleneck of these heuristics is the high computational demand of the cost function calculation, which is usually based on heat transfer simulations producing the thermal history of the workpiece at given locations. This Direct Heat Transfer Calculation is a well parallelisable process, making it feasible to implement an efficient GPU kernel for this purpose. This paper presents a novel step forward: based on the special requirements of the heuristics solving the inverse problem (executing hundreds of simulations in a parallel fashion at the end of each iteration, it is possible to gain a higher level of parallelism using multiple graphics accelerators. The results show that this implementation (running on 4 GPUs is about 120 times faster than a traditional CPU implementation using 20 cores. The latest developments of the GPU-based High Power Computations area were also analysed, like the new NVLink connection between the host and the devices, which tries to solve the long time existing data transfer handicap of GPU programming.

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

Science.gov (United States)

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.

The development of computational algorithms for manipulator inverse kinematics

International Nuclear Information System (INIS)

Sasaki, Shinobu

1989-10-01

A solution technique of the inverse kinematics for multi-joint robot manipulators has been considered to be one of the most cumbersome treatment due to non-linearity properties inclusive of trigonometric functions. The most traditional approach is to use the Jacobian matrix on linearization assumptions. This iterative technique, however, is attended with numerical problems having significant influences on the solution characteristics such as initial guess dependence and singularities. Taking these facts into consideration, new approaches have been proposed from different standpoints, which are based on polynomial transformation of kinematic model, the minimization technique in mathematical programming, vector-geometrical concept, and the separation of joint variables associated with the optimization problem. In terms of computer simulations, each approach was identified to be a useful algorithm which leads to theoretically accurate solutions to complicated inverse problems. In this way, the short-term goal of our studies on manipulator inverse problem in the R and D project of remote handling technology was accomplished with success, and consequently the present report sums up the results of basic studies on this matter. (author)

An inverse Sturm–Liouville problem with a fractional derivative

KAUST Repository

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.

Basis set expansion for inverse problems in plasma diagnostic analysis

Science.gov (United States)

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.

Large-scale inverse model analyses employing fast randomized data reduction

Science.gov (United States)

Lin, Youzuo; Le, Ellen B.; O'Malley, Daniel; Vesselinov, Velimir V.; Bui-Thanh, Tan

2017-08-01

When the number of observations is large, it is computationally challenging to apply classical inverse modeling techniques. We have developed a new computationally efficient technique for solving inverse problems with a large number of observations (e.g., on the order of 107 or greater). Our method, which we call the randomized geostatistical approach (RGA), is built upon the principal component geostatistical approach (PCGA). We employ a data reduction technique combined with the PCGA to improve the computational efficiency and reduce the memory usage. Specifically, we employ a randomized numerical linear algebra technique based on a so-called "sketching" matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis. In this way, the computational and memory costs for RGA scale with the information content rather than the size of the calibration data. Our algorithm is coded in Julia and implemented in the MADS open-source high-performance computational framework (http://mads.lanl.gov). We apply our new inverse modeling method to invert for a synthetic transmissivity field. Compared to a standard geostatistical approach (GA), our method is more efficient when the number of observations is large. Most importantly, our method is capable of solving larger inverse problems than the standard GA and PCGA approaches. Therefore, our new model inversion method is a powerful tool for solving large-scale inverse problems. The method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity.

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.

A direct sampling method to an inverse medium scattering problem

KAUST Repository

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

Inverse Problems in a Bayesian Setting

KAUST Repository

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

KAUST Repository

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.

FOREWORD: Tackling inverse problems in a Banach space environment: from theory to applications Tackling inverse problems in a Banach space environment: from theory to applications

Science.gov (United States)

Schuster, Thomas; Hofmann, Bernd; Kaltenbacher, Barbara

2012-10-01

Inverse problems can usually be modelled as operator equations in infinite-dimensional spaces with a forward operator acting between Hilbert or Banach spaces—a formulation which quite often also serves as the basis for defining and analyzing solution methods. The additional amount of structure and geometric interpretability provided by the concept of an inner product has rendered these methods amenable to a convergence analysis, a fact which has led to a rigorous and comprehensive study of regularization methods in Hilbert spaces over the last three decades. However, for numerous problems such as x-ray diffractometry, certain inverse scattering problems and a number of parameter identification problems in PDEs, the reasons for using a Hilbert space setting seem to be based on conventions rather than an appropriate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, non-Hilbertian regularization and data fidelity terms incorporating a priori information on solution and noise, such as general Lp-norms, TV-type norms, or the Kullback-Leibler divergence, have recently become very popular. These facts have motivated intensive investigations on regularization methods in Banach spaces, a topic which has emerged as a highly active research field within the area of inverse problems. Meanwhile some of the most well-known regularization approaches, such as Tikhonov-type methods requiring the solution of extremal problems, and iterative ones like the Landweber method, the Gauss-Newton method, as well as the approximate inverse method, have been investigated for linear and nonlinear operator equations in Banach spaces. Convergence with rates has been proven and conditions on the solution smoothness and on the structure of nonlinearity have been formulated. Still, beyond the existing results a large number of challenging open questions have arisen, due to the more involved handling of general Banach spaces and the larger variety

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)

Inverse transient thermoelastic deformations in thin circular plates

Indian Academy of Sciences (India)

Bessel's functions with the help of the integral transform technique. Thermoelastic deformations are discussed with the help of temperature and are illustrated numer- ically. Keywords. Inverse transient; thermoelastic deformation. 1. Introduction. The inverse thermoelastic problem consists of determination of the temperature, ...

A mathematical framework for inverse wave problems in heterogeneous media

NARCIS (Netherlands)

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

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.

Inverse problems in complex material design: Applications to non-crystalline solids

Science.gov (United States)

Biswas, Parthapratim; Drabold, David; Elliott, Stephen

The design of complex amorphous materials is one of the fundamental problems in disordered condensed-matter science. While impressive developments of ab-initio simulation methods during the past several decades have brought tremendous success in understanding materials property from micro- to mesoscopic length scales, a major drawback is that they fail to incorporate existing knowledge of the materials in simulation methodologies. Since an essential feature of materials design is the synergy between experiment and theory, a properly developed approach to design materials should be able to exploit all available knowledge of the materials from measured experimental data. In this talk, we will address the design of complex disordered materials as an inverse problem involving experimental data and available empirical information. We show that the problem can be posed as a multi-objective non-convex optimization program, which can be addressed using a number of recently-developed bio-inspired global optimization techniques. In particular, we will discuss how a population-based stochastic search procedure can be used to determine the structure of non-crystalline solids (e.g. a-SiH, a-SiO2, amorphous graphene, and Fe and Ni clusters). The work is partially supported by NSF under Grant Nos. DMR 1507166 and 1507670.

Fast wavelet based sparse approximate inverse preconditioner

Energy Technology Data Exchange (ETDEWEB)

Wan, W.L. [Univ. of California, Los Angeles, CA (United States)

1996-12-31

Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.

A variational Bayesian method to inverse problems with impulsive noise

KAUST Repository

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

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)

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....

Two numerical methods for an inverse problem for the 2-D Helmholtz equation

CERN Document Server

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.

Use of Genetic Algorithms to solve Inverse Problems in Relativistic Hydrodynamics

Science.gov (United States)

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.

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

Control and System Theory, Optimization, Inverse and Ill-Posed Problems

Science.gov (United States)

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

Random fixed point equations and inverse problems using "collage method" for contraction mappings

Science.gov (United States)

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.

Level set methods for inverse scattering—some recent developments

International Nuclear Information System (INIS)

Dorn, Oliver; Lesselier, Dominique

2009-01-01

We give an update on recent techniques which use a level set representation of shapes for solving inverse scattering problems, completing in that matter the exposition made in (Dorn and Lesselier 2006 Inverse Problems 22 R67) and (Dorn and Lesselier 2007 Deformable Models (New York: Springer) pp 61–90), and bringing it closer to the current state of the art

Inverse problem in hydrogeology

Science.gov (United States)

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

A function space framework for structural total variation regularization with applications in inverse problems

Science.gov (United States)

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.

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

Numerical Methods for Bayesian Inverse Problems

KAUST Repository

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.

Numerical Methods for Bayesian Inverse Problems

KAUST Repository

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.

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.

Interferogram analysis using the Abel inversion technique

International Nuclear Information System (INIS)

Yusof Munajat; Mohamad Kadim Suaidi

2000-01-01

High speed and high resolution optical detection system were used to capture the image of acoustic waves propagation. The freeze image in the form of interferogram was analysed to calculate the transient pressure profile of the acoustic waves. The interferogram analysis was based on the fringe shift and the application of the Abel inversion technique. An easier approach was made by mean of using MathCAD program as a tool in the programming; yet powerful enough to make such calculation, plotting and transfer of file. (Author)

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

Science.gov (United States)

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).

Anisotropic magnetotelluric inversion using a mutual information constraint

Science.gov (United States)

Mandolesi, E.; Jones, A. G.

2012-12-01

In recent years, several authors pointed that the electrical conductivity of many subsurface structures cannot be described properly by a scalar field. With the development of field devices and techniques, data quality improved to the point that the anisotropy in conductivity of rocks (microscopic anisotropy) and tectonic structures (macroscopic anisotropy) cannot be neglected. Therefore a correct use of high quality data has to include electrical anisotropy and a correct interpretation of anisotropic data characterizes directly a non-negligible part of the subsurface. In this work we test an inversion routine that takes advantage of the classic Levenberg-Marquardt (LM) algorithm to invert magnetotelluric (MT) data generated from a bi-dimensional (2D) anisotropic domain. The LM method is routinely used in inverse problems due its performance and robustness. In non-linear inverse problems -such the MT problem- the LM method provides a spectacular compromise betwee quick and secure convergence at the price of the explicit computation and storage of the sensitivity matrix. Regularization in inverse MT problems has been used extensively, due to the necessity to constrain model space and to reduce the ill-posedness of the anisotropic MT problem, which makes MT inversions extremely challenging. In order to reduce non-uniqueness of the MT problem and to reach a model compatible with other different tomographic results from the same target region, we used a mutual information (MI) based constraint. MI is a basic quantity in information theory that can be used to define a metric between images, and it is routinely used in fields as computer vision, image registration and medical tomography, to cite some applications. We -thus- inverted for the model that best fits the anisotropic data and that is the closest -in a MI sense- to a tomographic model of the target area. The advantage of this technique is that the tomographic model of the studied region may be produced by any

Atmospheric inverse modeling via sparse reconstruction

Science.gov (United States)

Hase, Nils; Miller, Scot M.; Maaß, Peter; Notholt, Justus; Palm, Mathias; Warneke, Thorsten

2017-10-01

Many applications in atmospheric science involve ill-posed inverse problems. A crucial component of many inverse problems is the proper formulation of a priori knowledge about the unknown parameters. In most cases, this knowledge is expressed as a Gaussian prior. This formulation often performs well at capturing smoothed, large-scale processes but is often ill equipped to capture localized structures like large point sources or localized hot spots. Over the last decade, scientists from a diverse array of applied mathematics and engineering fields have developed sparse reconstruction techniques to identify localized structures. In this study, we present a new regularization approach for ill-posed inverse problems in atmospheric science. It is based on Tikhonov regularization with sparsity constraint and allows bounds on the parameters. We enforce sparsity using a dictionary representation system. We analyze its performance in an atmospheric inverse modeling scenario by estimating anthropogenic US methane (CH4) emissions from simulated atmospheric measurements. Different measures indicate that our sparse reconstruction approach is better able to capture large point sources or localized hot spots than other methods commonly used in atmospheric inversions. It captures the overall signal equally well but adds details on the grid scale. This feature can be of value for any inverse problem with point or spatially discrete sources. We show an example for source estimation of synthetic methane emissions from the Barnett shale formation.

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.

A highly efficient Shannon wavelet inverse Fourier technique for pricing European options

NARCIS (Netherlands)

L. Ortiz Gracia (Luis); C.W. Oosterlee (Cornelis)

2016-01-01

htmlabstractIn the search for robust, accurate, and highly efficient financial option valuation techniques, we here present the SWIFT method (Shannon wavelets inverse Fourier technique), based on Shannon wavelets. SWIFT comes with control over approximation errors made by means of

Using Inverse Problem Methods with Surveillance Data in Pneumococcal Vaccination

Science.gov (United States)

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

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)

A Highly Efficient Shannon Wavelet Inverse Fourier Technique for Pricing European Options

NARCIS (Netherlands)

Ortiz-Gracia, Luis; Oosterlee, C.W.

2016-01-01

In the search for robust, accurate, and highly efficient financial option valuation techniques, we here present the SWIFT method (Shannon wavelets inverse Fourier technique), based on Shannon wavelets. SWIFT comes with control over approximation errors made by means of sharp quantitative error

Weyl functions, the inverse problem and special solutions for the system auxiliary to the nonlinear optics equation

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

A general approach to posterior contraction in nonparametric inverse problems

NARCIS (Netherlands)

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

A model reduction approach for the variational estimation of vascular compliance by solving an inverse fluid–structure interaction problem

International Nuclear Information System (INIS)

Bertagna, Luca; Veneziani, Alessandro

2014-01-01

Scientific computing has progressively become an important tool for research in cardiovascular diseases. The role of quantitative analyses based on numerical simulations has moved from ‘proofs of concept’ to patient-specific investigations, thanks to a strong integration between imaging and computational tools. However, beyond individual geometries, numerical models require the knowledge of parameters that are barely retrieved from measurements, especially in vivo. For this reason, recently cardiovascular mathematics considered data assimilation procedures for extracting the knowledge of patient-specific parameters from measures and images. In this paper, we consider specifically the quantification of vascular compliance, i.e. the parameter quantifying the tendency of arterial walls to deform under blood stress. Following up a previous paper, where a variational data assimilation procedure was proposed, based on solving an inverse fluid–structure interaction problem, here we consider model reduction techniques based on a proper orthogonal decomposition approach to accomplish the solution of the inverse problem in a computationally efficient way. (paper)

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)

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.

Uniqueness for inverse problems of determining orders of multi-term time-fractional derivatives of diffusion equation

OpenAIRE

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.

Invert 1.0: A program for solving the nonlinear inverse heat conduction problem for one-dimensional solids

International Nuclear Information System (INIS)

Snider, D.M.

1981-02-01

INVERT 1.0 is a digital computer program written in FORTRAN IV which calculates the surface heat flux of a one-dimensional solid using an interior-measured temperature and a physical description of the solid. By using two interior-measured temperatures, INVERT 1.0 can provide a solution for the heat flux at two surfaces, the heat flux at a boundary and the time dependent power, or the heat flux at a boundary and the time varying thermal conductivity of a material composing the solid. The analytical solution to inversion problem is described for the one-dimensional cylinder, sphere, or rectangular slab. The program structure, input instructions, and sample problems demonstrating the accuracy of the solution technique are included

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.

Boundary Element Solution of Geometrical Inverse Heat Conduction Problems for Development of IR CAT Scan

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

Rank deficiency and Tikhonov regularization in the inverse problem for gravitational-wave bursts

International Nuclear Information System (INIS)

Rakhmanov, M

2006-01-01

Coherent techniques for searches of gravitational-wave bursts effectively combine data from several detectors, taking into account differences in their responses. The efforts are now focused on the maximum likelihood principle as the most natural way to combine data, which can also be used without prior knowledge of the signal. Recent studies however have shown that straightforward application of the maximum likelihood method to gravitational waves with unknown waveforms can lead to inconsistencies and unphysical results such as discontinuity in the residual functional, or divergence of the variance of the estimated waveforms for some locations in the sky. So far the solutions to these problems have been based on rather different physical arguments. Following these investigations, we now find that all these inconsistencies stem from the rank deficiency of the underlying network response matrix. In this paper we show that the detection of gravitational-wave bursts with a network of interferometers belongs to the category of ill-posed problems. We then apply the method of Tikhonov regularization to resolve the rank deficiency and introduce a minimal regulator which yields a well-conditioned solution to the inverse problem for all locations on the sky

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

Alternating minimisation for glottal inverse filtering

International Nuclear Information System (INIS)

Bleyer, Ismael Rodrigo; Lybeck, Lasse; Auvinen, Harri; Siltanen, Samuli; Airaksinen, Manu; Alku, Paavo

2017-01-01

A new method is proposed for solving the glottal inverse filtering (GIF) problem. The goal of GIF is to separate an acoustical speech signal into two parts: the glottal airflow excitation and the vocal tract filter. To recover such information one has to deal with a blind deconvolution problem. This ill-posed inverse problem is solved under a deterministic setting, considering unknowns on both sides of the underlying operator equation. A stable reconstruction is obtained using a double regularization strategy, alternating between fixing either the glottal source signal or the vocal tract filter. This enables not only splitting the nonlinear and nonconvex problem into two linear and convex problems, but also allows the use of the best parameters and constraints to recover each variable at a time. This new technique, called alternating minimization glottal inverse filtering (AM-GIF), is compared with two other approaches: Markov chain Monte Carlo glottal inverse filtering (MCMC-GIF), and iterative adaptive inverse filtering (IAIF), using synthetic speech signals. The recent MCMC-GIF has good reconstruction quality but high computational cost. The state-of-the-art IAIF method is computationally fast but its accuracy deteriorates, particularly for speech signals of high fundamental frequency ( F 0). The results show the competitive performance of the new method: With high F 0, the reconstruction quality is better than that of IAIF and close to MCMC-GIF while reducing the computational complexity by two orders of magnitude. (paper)

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

Inverse kinematic-based robot control

Science.gov (United States)

Wolovich, W. A.; Flueckiger, K. F.

1987-01-01

A fundamental problem which must be resolved in virtually all non-trivial robotic operations is the well-known inverse kinematic question. More specifically, most of the tasks which robots are called upon to perform are specified in Cartesian (x,y,z) space, such as simple tracking along one or more straight line paths or following a specified surfacer with compliant force sensors and/or visual feedback. In all cases, control is actually implemented through coordinated motion of the various links which comprise the manipulator; i.e., in link space. As a consequence, the control computer of every sophisticated anthropomorphic robot must contain provisions for solving the inverse kinematic problem which, in the case of simple, non-redundant position control, involves the determination of the first three link angles, theta sub 1, theta sub 2, and theta sub 3, which produce a desired wrist origin position P sub xw, P sub yw, and P sub zw at the end of link 3 relative to some fixed base frame. Researchers outline a new inverse kinematic solution and demonstrate its potential via some recent computer simulations. They also compare it to current inverse kinematic methods and outline some of the remaining problems which will be addressed in order to render it fully operational. Also discussed are a number of practical consequences of this technique beyond its obvious use in solving the inverse kinematic question.

Bayes procedures for adaptive inference in inverse problems for the white noise model

NARCIS (Netherlands)

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

Inverse eigenvalue problems for Sturm-Liouville equations with spectral parameter linearly contained in one of the boundary conditions

OpenAIRE

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.

Inversion of seismic data: how to take the correlated nature of noise into account; Inversion de donnees sismiques: prise en compte de la nature correlee du bruit

Energy Technology Data Exchange (ETDEWEB)

Renard, F.

2003-01-01

The goal of seismic inversion is to recover an Earth model that best fits some observed data. To reach that goal, we have to minimize an objective function that measures the amplitude of the misfits according to a norm to be chosen in data space. In general, the used norm is the L2 norm. Unfortunately, such a norm is not adapted to data corrupted by correlated noise: the noise is in that case inverted as signal and the inversion results are unacceptable. The goal of this thesis is to obtain satisfactory results to the inverse problem in that situation. For this purpose, we study two inverse problems: reflection tomography and waveform inversion. In reflection tomography, we propose a new formulation of the continuum inverse problem which relies on a H1 norm in data space. This allows us to account for the correlated nature of the noise that corrupts the kinematic information. However, this norm does not give more satisfactory results than the ones obtained with the classical formalism. This is why, for sake of simplicity, we recommend to use this classical formalism. Then we try to understand how to properly sample the kinematic information so as to obtain an accurate approximation of the continuum inverse problem. In waveform inversion, we propose to directly invert data corrupted by some correlated noise. A first idea consists in rejecting the noise in the residues. In that goal, we can use a semi-norm to formulate the inverse problem. This technique gives very good results, except when the data are corrupted by random noise. Thus we propose a second method which consists in retrieving, by solving an inverse problem, the signal and the noise whose sum best fits the data. This technique gives very satisfactory results, even if some random noise pollutes the data, and is moreover solved, thanks to an original algorithm, in a very efficient way. (author)

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.

Intrinsic nonlinearity and method of disturbed observations in inverse problems of celestial mechanics

Science.gov (United States)

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

A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line

Science.gov (United States)

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.

Fast Markov chain Monte Carlo sampling for sparse Bayesian inference in high-dimensional inverse problems using L1-type priors

International Nuclear Information System (INIS)

Lucka, Felix

2012-01-01

Sparsity has become a key concept for solving of high-dimensional inverse problems using variational regularization techniques. Recently, using similar sparsity-constraints in the Bayesian framework for inverse problems by encoding them in the prior distribution has attracted attention. Important questions about the relation between regularization theory and Bayesian inference still need to be addressed when using sparsity promoting inversion. A practical obstacle for these examinations is the lack of fast posterior sampling algorithms for sparse, high-dimensional Bayesian inversion. Accessing the full range of Bayesian inference methods requires being able to draw samples from the posterior probability distribution in a fast and efficient way. This is usually done using Markov chain Monte Carlo (MCMC) sampling algorithms. In this paper, we develop and examine a new implementation of a single component Gibbs MCMC sampler for sparse priors relying on L1-norms. We demonstrate that the efficiency of our Gibbs sampler increases when the level of sparsity or the dimension of the unknowns is increased. This property is contrary to the properties of the most commonly applied Metropolis–Hastings (MH) sampling schemes. We demonstrate that the efficiency of MH schemes for L1-type priors dramatically decreases when the level of sparsity or the dimension of the unknowns is increased. Practically, Bayesian inversion for L1-type priors using MH samplers is not feasible at all. As this is commonly believed to be an intrinsic feature of MCMC sampling, the performance of our Gibbs sampler also challenges common beliefs about the applicability of sample based Bayesian inference. (paper)

Presymplectic current and the inverse problem of the calculus of variations

NARCIS (Netherlands)

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

An inverse spectral problem related to the Geng-Xue two-component peakon equation

CERN Document Server

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...

Direct sampling methods for inverse elastic scattering problems

Science.gov (United States)

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.

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

Development of a Preventive HIV Vaccine Requires Solving Inverse Problems Which Is Unattainable by Rational Vaccine Design

Directory of Open Access Journals (Sweden)

Marc H. V. Van Regenmortel

2018-01-01

Full Text Available Hypotheses and theories are essential constituents of the scientific method. Many vaccinologists are unaware that the problems they try to solve are mostly inverse problems that consist in imagining what could bring about a desired outcome. An inverse problem starts with the result and tries to guess what are the multiple causes that could have produced it. Compared to the usual direct scientific problems that start with the causes and derive or calculate the results using deductive reasoning and known mechanisms, solving an inverse problem uses a less reliable inductive approach and requires the development of a theoretical model that may have different solutions or none at all. Unsuccessful attempts to solve inverse problems in HIV vaccinology by reductionist methods, systems biology and structure-based reverse vaccinology are described. The popular strategy known as rational vaccine design is unable to solve the multiple inverse problems faced by HIV vaccine developers. The term “rational” is derived from “rational drug design” which uses the 3D structure of a biological target for designing molecules that will selectively bind to it and inhibit its biological activity. In vaccine design, however, the word “rational” simply means that the investigator is concentrating on parts of the system for which molecular information is available. The economist and Nobel laureate Herbert Simon introduced the concept of “bounded rationality” to explain why the complexity of the world economic system makes it impossible, for instance, to predict an event like the financial crash of 2007–2008. Humans always operate under unavoidable constraints such as insufficient information, a limited capacity to process huge amounts of data and a limited amount of time available to reach a decision. Such limitations always prevent us from achieving the complete understanding and optimization of a complex system that would be needed to achieve a truly

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

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)

Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models

Science.gov (United States)

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 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)

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)

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

Full-Physics Inverse Learning Machine for Satellite Remote Sensing Retrievals

Science.gov (United States)

Loyola, D. G.

2017-12-01

The satellite remote sensing retrievals are usually ill-posed inverse problems that are typically solved by finding a state vector that minimizes the residual between simulated data and real measurements. The classical inversion methods are very time-consuming as they require iterative calls to complex radiative-transfer forward models to simulate radiances and Jacobians, and subsequent inversion of relatively large matrices. In this work we present a novel and extremely fast algorithm for solving inverse problems called full-physics inverse learning machine (FP-ILM). The FP-ILM algorithm consists of a training phase in which machine learning techniques are used to derive an inversion operator based on synthetic data generated using a radiative transfer model (which expresses the "full-physics" component) and the smart sampling technique, and an operational phase in which the inversion operator is applied to real measurements. FP-ILM has been successfully applied to the retrieval of the SO2 plume height during volcanic eruptions and to the retrieval of ozone profile shapes from UV/VIS satellite sensors. Furthermore, FP-ILM will be used for the near-real-time processing of the upcoming generation of European Sentinel sensors with their unprecedented spectral and spatial resolution and associated large increases in the amount of data.

Joint inversion of geophysical data using petrophysical clustering and facies deformation wth the level set technique

Science.gov (United States)

Revil, A.

2015-12-01

Geological expertise and petrophysical relationships can be brought together to provide prior information while inverting multiple geophysical datasets. The merging of such information can result in more realistic solution in the distribution of the model parameters, reducing ipse facto the non-uniqueness of the inverse problem. We consider two level of heterogeneities: facies, described by facies boundaries and heteroegenities inside each facies determined by a correlogram. In this presentation, we pose the geophysical inverse problem in terms of Gaussian random fields with mean functions controlled by petrophysical relationships and covariance functions controlled by a prior geological cross-section, including the definition of spatial boundaries for the geological facies. The petrophysical relationship problem is formulated as a regression problem upon each facies. The inversion of the geophysical data is performed in a Bayesian framework. We demonstrate the usefulness of this strategy using a first synthetic case for which we perform a joint inversion of gravity and galvanometric resistivity data with the stations located at the ground surface. The joint inversion is used to recover the density and resistivity distributions of the subsurface. In a second step, we consider the possibility that the facies boundaries are deformable and their shapes are inverted as well. We use the level set approach to perform such deformation preserving prior topological properties of the facies throughout the inversion. With the help of prior facies petrophysical relationships and topological characteristic of each facies, we make posterior inference about multiple geophysical tomograms based on their corresponding geophysical data misfits. The method is applied to a second synthetic case showing that we can recover the heterogeneities inside the facies, the mean values for the petrophysical properties, and, to some extent, the facies boundaries using the 2D joint inversion of

DEVELOPMENT OF SCIENTIFIC AND INFORMATIVE POTENTIAL OF STUDENTS IN THE TEACHING OF THE INVERSE PROBLEMS FOR DIFFERENTIAL EQUATIONS

Directory of Open Access Journals (Sweden)

Виктор Семенович Корнилов

2017-12-01

Full Text Available In article attention that when training in the inverse problems for differential equations at students scientific and cognitive potential develops is paid. Students realize that mathematical models of the inverse problems for differential equations find the application in economy, the industries, ecology, sociology, biology, chemistry, mathematician, physics, in researches of the processes and the phenomena occurring in water and earth’s environment, air and space.Attention of the reader that in training activity to the inverse problems for differential equations at students the scientific outlook, logical, algorithmic, information thinking, creative activity, independence and ingenuity develop is focused. Students acquire skills to apply knowledge of many physical and mathematical disciplines, to carry out the analysis of the received decision of the reverse task and to formulate logical outputs of application-oriented character. Solving the inverse problems for differential equations, students acquire new knowledge in the field of applied and calculus mathematics, informatics, natural sciences and other knowledge.

Metropolis-Hastings Algorithms in Function Space for Bayesian Inverse Problems

KAUST Repository

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

KAUST Repository

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.

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...

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

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

Sequential Inverse Problems Bayesian Principles and the Logistic Map Example

Science.gov (United States)

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.

Analytic Lorentz integral transform of an arbitrary response function and its application to the inversion problem

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)

Multi-frequency direct sampling method in inverse scattering problem

Science.gov (United States)

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.

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

Absolute mass scale calibration in the inverse problem of the physical theory of fireballs.

Science.gov (United States)

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.

Estimation of physical properties of laminated composites via the method of inverse vibration problem

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.

Estimation of physical properties of laminated composites via the method of inverse vibration problem

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

A 2D forward and inverse code for streaming potential problems

Science.gov (United States)

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.

An inverse problem for a one-dimensional time-fractional diffusion problem

KAUST Repository

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.

Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

Science.gov (United States)

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.

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)

Development and investigation of an inverse problem solution algorithm for determination of Ap stars magnetic field geometry

International Nuclear Information System (INIS)

Piskunov, N.E.

1985-01-01

Mathematical formulation of the inverse problem of determination of magnetic field geometry from the polarization profiles of spectral lines is gven. The solving algorithm is proposed. A set of model calculations has shown the effectiveness of the algorithm, the high precision of magnetic star model parameters obtained and also the advantages of the inverse problem method over the commonly used method of interpretation of effective field curves

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

Inverse heat transfer problem in digital temperature control in plate fin and tube heat exchangers

Science.gov (United States)

Taler, Dawid; Sury, Adam

2011-12-01

The aim of the paper is a steady-state inverse heat transfer problem for plate-fin and tube heat exchangers. The objective of the process control is to adjust the number of fan revolutions per minute so that the water temperature at the heat exchanger outlet is equal to a preset value. Two control techniques were developed. The first is based on the presented mathematical model of the heat exchanger while the second is a digital proportional-integral-derivative (PID) control. The first procedure is very stable. The digital PID controller becomes unstable if the water volumetric flow rate changes significantly. The developed techniques were implemented in digital control system of the water exit temperature in a plate fin and tube heat exchanger. The measured exit temperature of the water was very close to the set value of the temperature if the first method was used. The experiments showed that the PID controller works also well but becomes frequently unstable.

A robust spatial filtering technique for multisource localization and geoacoustic inversion.

Science.gov (United States)

Stotts, S A

2005-07-01

Geoacoustic inversion and source localization using beamformed data from a ship of opportunity has been demonstrated with a bottom-mounted array. An alternative approach, which lies within a class referred to as spatial filtering, transforms element level data into beam data, applies a bearing filter, and transforms back to element level data prior to performing inversions. Automation of this filtering approach is facilitated for broadband applications by restricting the inverse transform to the degrees of freedom of the array, i.e., the effective number of elements, for frequencies near or below the design frequency. A procedure is described for nonuniformly spaced elements that guarantees filter stability well above the design frequency. Monitoring energy conservation with respect to filter output confirms filter stability. Filter performance with both uniformly spaced and nonuniformly spaced array elements is discussed. Vertical (range and depth) and horizontal (range and bearing) ambiguity surfaces are constructed to examine filter performance. Examples that demonstrate this filtering technique with both synthetic data and real data are presented along with comparisons to inversion results using beamformed data. Examinations of cost functions calculated within a simulated annealing algorithm reveal the efficacy of the approach.

Anisotropic three-dimensional inversion of CSEM data using finite-element techniques on unstructured grids

Science.gov (United States)

Wang, Feiyan; Morten, Jan Petter; Spitzer, Klaus

2018-05-01

In this paper, we present a recently developed anisotropic 3-D inversion framework for interpreting controlled-source electromagnetic (CSEM) data in the frequency domain. The framework integrates a high-order finite-element forward operator and a Gauss-Newton inversion algorithm. Conductivity constraints are applied using a parameter transformation. We discretize the continuous forward and inverse problems on unstructured grids for a flexible treatment of arbitrarily complex geometries. Moreover, an unstructured mesh is more desirable in comparison to a single rectilinear mesh for multisource problems because local grid refinement will not significantly influence the mesh density outside the region of interest. The non-uniform spatial discretization facilitates parametrization of the inversion domain at a suitable scale. For a rapid simulation of multisource EM data, we opt to use a parallel direct solver. We further accelerate the inversion process by decomposing the entire data set into subsets with respect to frequencies (and transmitters if memory requirement is affordable). The computational tasks associated with each data subset are distributed to different processes and run in parallel. We validate the scheme using a synthetic marine CSEM model with rough bathymetry, and finally, apply it to an industrial-size 3-D data set from the Troll field oil province in the North Sea acquired in 2008 to examine its robustness and practical applicability.

Indoor detection of passive targets recast as an inverse scattering problem

Science.gov (United States)

Gottardi, G.; Moriyama, T.

2017-10-01

The wireless local area networks represent an alternative to custom sensors and dedicated surveillance systems for target indoor detection. The availability of the channel state information has opened the exploitation of the spatial and frequency diversity given by the orthogonal frequency division multiplexing. Such a fine-grained information can be used to solve the detection problem as an inverse scattering problem. The goal of the detection is to reconstruct the properties of the investigation domain, namely to estimate if the domain is empty or occupied by targets, starting from the measurement of the electromagnetic perturbation of the wireless channel. An innovative inversion strategy exploiting both the frequency and the spatial diversity of the channel state information is proposed. The target-dependent features are identified combining the Kruskal-Wallis test and the principal component analysis. The experimental validation points out the detection performance of the proposed method when applied to an existing wireless link of a WiFi architecture deployed in a real indoor scenario. False detection rates lower than 2 [%] have been obtained.

Inverse Problem for Two-Dimensional Discrete Schr`dinger Equation

CERN Document Server

Serdyukova, S I

2000-01-01

For two-dimensional discrete Schroedinger equation the boundary-value problem in rectangle M times N with zero boundary conditions is solved. It's stated in this work, that inverse problem reduces to reconstruction of C symmetric five-diagonal matrix with given spectrum and given first k(M,N), 1<-kproblem to the end in the process of concrete calculations. Deriving and solving the huge polynomial systems had been perfor...

A Joint Method of Envelope Inversion Combined with Hybrid-domain Full Waveform Inversion

Science.gov (United States)

CUI, C.; Hou, W.

2017-12-01

Full waveform inversion (FWI) aims to construct high-precision subsurface models by fully using the information in seismic records, including amplitude, travel time, phase and so on. However, high non-linearity and the absence of low frequency information in seismic data lead to the well-known cycle skipping problem and make inversion easily fall into local minima. In addition, those 3D inversion methods that are based on acoustic approximation ignore the elastic effects in real seismic field, and make inversion harder. As a result, the accuracy of final inversion results highly relies on the quality of initial model. In order to improve stability and quality of inversion results, multi-scale inversion that reconstructs subsurface model from low to high frequency are applied. But, the absence of very low frequencies (time domain and inversion in the frequency domain. To accelerate the inversion, we adopt CPU/GPU heterogeneous computing techniques. There were two levels of parallelism. In the first level, the inversion tasks are decomposed and assigned to each computation node by shot number. In the second level, GPU multithreaded programming is used for the computation tasks in each node, including forward modeling, envelope extraction, DFT (discrete Fourier transform) calculation and gradients calculation. Numerical tests demonstrated that the combined envelope inversion + hybrid-domain FWI could obtain much faithful and accurate result than conventional hybrid-domain FWI. The CPU/GPU heterogeneous parallel computation could improve the performance speed.

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

The dose-volume constraint satisfaction problem for inverse treatment planning with field segments

International Nuclear Information System (INIS)

Michalski, Darek; Xiao, Ying; Censor, Yair; Galvin, James M

2004-01-01

The prescribed goals of radiation treatment planning are often expressed in terms of dose-volume constraints. We present a novel formulation of a dose-volume constraint satisfaction search for the discretized radiation therapy model. This approach does not rely on any explicit cost function. Inverse treatment planning uses the aperture-based approach with predefined, according to geometric rules, segmental fields. The solver utilizes the simultaneous version of the cyclic subgradient projection algorithm. This is a deterministic iterative method designed for solving the convex feasibility problems. A prescription is expressed with the set of inequalities imposed on the dose at the voxel resolution. Additional constraint functions control the compliance with selected points of the expected cumulative dose-volume histograms. The performance of this method is tested on prostate and head-and-neck cases. The relationships with other models and algorithms of similar conceptual origin are discussed. The demonstrated advantages of the method are: the equivalence of the algorithmic and prescription parameters, the intuitive setup of free parameters, and the improved speed of the method as compared to similar iterative as well as other techniques. The technique reported here will deliver approximate solutions for inconsistent prescriptions

Inverse problems for random differential equations using the collage method for random contraction mappings

Science.gov (United States)

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.

Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations

Science.gov (United States)

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.

Invisibility problem in acoustics, electromagnetism and heat transfer. Inverse design method

Science.gov (United States)

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.

A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems

Directory of Open Access Journals (Sweden)

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.

Solution of the Cox-Thompson inverse scattering problem using finite set of phase shifts

CERN Document Server

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

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.

Beamforming Through Regularized Inverse Problems in Ultrasound Medical Imaging.

Science.gov (United States)

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.

Total-variation based velocity inversion with Bregmanized operator splitting algorithm

Science.gov (United States)

Zand, Toktam; Gholami, Ali

2018-04-01

Many problems in applied geophysics can be formulated as a linear inverse problem. The associated problems, however, are large-scale and ill-conditioned. Therefore, regularization techniques are needed to be employed for solving them and generating a stable and acceptable solution. We consider numerical methods for solving such problems in this paper. In order to tackle the ill-conditioning of the problem we use blockiness as a prior information of the subsurface parameters and formulate the problem as a constrained total variation (TV) regularization. The Bregmanized operator splitting (BOS) algorithm as a combination of the Bregman iteration and the proximal forward backward operator splitting method is developed to solve the arranged problem. Two main advantages of this new algorithm are that no matrix inversion is required and that a discrepancy stopping criterion is used to stop the iterations, which allow efficient solution of large-scale problems. The high performance of the proposed TV regularization method is demonstrated using two different experiments: 1) velocity inversion from (synthetic) seismic data which is based on Born approximation, 2) computing interval velocities from RMS velocities via Dix formula. Numerical examples are presented to verify the feasibility of the proposed method for high-resolution velocity inversion.

Uniqueness Theorem for the Inverse Aftereffect Problem and Representation the Nodal Points Form

OpenAIRE

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.

Regularization and Bayesian methods for inverse problems in signal and image processing

CERN Document Server

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

On an inverse source problem for enhanced oil recovery by wave motion maximization in reservoirs

KAUST Repository

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

Optimization method for an evolutional type inverse heat conduction problem

Science.gov (United States)

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.

A comparative study of surface waves inversion techniques at strong motion recording sites in Greece

Science.gov (United States)

Panagiotis C. Pelekis,; Savvaidis, Alexandros; Kayen, Robert E.; Vlachakis, Vasileios S.; Athanasopoulos, George A.

2015-01-01

Surface wave method was used for the estimation of Vs vs depth profile at 10 strong motion stations in Greece. The dispersion data were obtained by SASW method, utilizing a pair of electromechanical harmonic-wave source (shakers) or a random source (drop weight). In this study, three inversion techniques were used a) a recently proposed Simplified Inversion Method (SIM), b) an inversion technique based on a neighborhood algorithm (NA) which allows the incorporation of a priori information regarding the subsurface structure parameters, and c) Occam's inversion algorithm. For each site constant value of Poisson's ratio was assumed (ν=0.4) since the objective of the current study is the comparison of the three inversion schemes regardless the uncertainties resulting due to the lack of geotechnical data. A penalty function was introduced to quantify the deviations of the derived Vs profiles. The Vs models are compared as of Vs(z), Vs30 and EC8 soil category, in order to show the insignificance of the existing variations. The comparison results showed that the average variation of SIM profiles is 9% and 4.9% comparing with NA and Occam's profiles respectively whilst the average difference of Vs30 values obtained from SIM is 7.4% and 5.0% compared with NA and Occam's.

The inverse problem of sensing the mass and force induced by an adsorbate on a beam nanomechanical resonator

Energy Technology Data Exchange (ETDEWEB)

Liu, Yun [Faculty of Information and Automation, Kunming University of Science and Technology, Kunming, Yunnan Province 65005 (China); Zhang, Yin [State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190 (China)

2016-06-08

The mass sensing superiority of a micro/nanomechanical resonator sensor over conventional mass spectrometry has been, or at least, is being firmly established. Because the sensing mechanism of a mechanical resonator sensor is the shifts of resonant frequencies, how to link the shifts of resonant frequencies with the material properties of an analyte formulates an inverse problem. Besides the analyte/adsorbate mass, many other factors such as position and axial force can also cause the shifts of resonant frequencies. The in-situ measurement of the adsorbate position and axial force is extremely difficult if not impossible, especially when an adsorbate is as small as a molecule or an atom. Extra instruments are also required. In this study, an inverse problem of using three resonant frequencies to determine the mass, position and axial force is formulated and solved. The accuracy of the inverse problem solving method is demonstrated and how the method can be used in the real application of a nanomechanical resonator is also discussed. Solving the inverse problem is helpful to the development and application of mechanical resonator sensor on two things: reducing extra experimental equipments and achieving better mass sensing by considering more factors.

Evaluation of inverse modeling techniques for pinpointing water leakages at building constructions

NARCIS (Netherlands)

Schijndel, van A.W.M.

2015-01-01

The location and nature of the moisture leakages are sometimes difficult to detect. Moreover, the relation between observed inside surface moisture patterns and where the moisture enters the construction is often not clear. The objective of this paper is to investigate inverse modeling techniques as

Magnetic Resonance Elastography: Measurement of Hepatic Stiffness Using Different Direct Inverse Problem Reconstruction Methods in Healthy Volunteers and Patients with Liver Disease.

Science.gov (United States)

Saito, Shigeyoshi; Tanaka, Keiko; Hashido, Takashi

2016-02-01

The purpose of this study was to compare the mean hepatic stiffness values obtained by the application of two different direct inverse problem reconstruction methods to magnetic resonance elastography (MRE). Thirteen healthy men (23.2±2.1 years) and 16 patients with liver diseases (78.9±4.3 years; 12 men and 4 women) were examined for this study using a 3.0 T-MRI. The healthy volunteers underwent three consecutive scans, two 70-Hz waveform and a 50-Hz waveform scans. On the other hand, the patients with liver disease underwent scanning using the 70-Hz waveform only. The MRE data for each subject was processed twice for calculation of the mean hepatic stiffness (Pa), once using the multiscale direct inversion (MSDI) and once using the multimodel direct inversion (MMDI). There were no significant differences in the mean stiffness values among the scans obtained with two 70-Hz and different waveforms. However, the mean stiffness values obtained with the MSDI technique (with mask: 2895.3±255.8 Pa, without mask: 2940.6±265.4 Pa) were larger than those obtained with the MMDI technique (with mask: 2614.0±242.1 Pa, without mask: 2699.2±273.5 Pa). The reproducibility of measurements obtained using the two techniques was high for both the healthy volunteers [intraclass correlation coefficients (ICCs): 0.840-0.953] and the patients (ICC: 0.830-0.995). These results suggest that knowledge of the characteristics of different direct inversion algorithms is important for longitudinal liver stiffness assessments such as the comparison of different scanners and evaluation of the response to fibrosis therapy.

Shrinkage-thresholding enhanced born iterative method for solving 2D inverse electromagnetic scattering problem

KAUST Repository

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

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

The inverse problem of the calculus of variations for discrete systems

Science.gov (United States)

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.

Anomaly detection in random heterogeneous media Feynman-Kac formulae, stochastic homogenization and statistical inversion

CERN Document Server

Simon, Martin

2015-01-01

This monograph is concerned with the analysis and numerical solution of a stochastic inverse anomaly detection problem in electrical impedance tomography (EIT). Martin Simon studies the problem of detecting a parameterized anomaly in an isotropic, stationary and ergodic conductivity random field whose realizations are rapidly oscillating. For this purpose, he derives Feynman-Kac formulae to rigorously justify stochastic homogenization in the case of the underlying stochastic boundary value problem. The author combines techniques from the theory of partial differential equations and functional analysis with probabilistic ideas, paving the way to new mathematical theorems which may be fruitfully used in the treatment of the problem at hand. Moreover, the author proposes an efficient numerical method in the framework of Bayesian inversion for the practical solution of the stochastic inverse anomaly detection problem.   Contents Feynman-Kac formulae Stochastic homogenization Statistical inverse problems  Targe...

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)

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.

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.

PREFACE: International Conference on Inverse Problems 2010

Science.gov (United States)

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

Solution of the nonlinear inverse scattering problem by T-matrix completion. I. Theory.

Science.gov (United States)

Levinson, Howard W; Markel, Vadim A

2016-10-01

We propose a conceptually different method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology, and other applications. The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant formalism. We formulate the ISP as a problem whose goal is to determine an unknown interaction potential V from external scattering data. Although we seek a local (diagonally dominated) V as the solution to the posed problem, we allow V to be nonlocal at the intermediate stages of iterations. This allows us to utilize the one-to-one correspondence between V and the T matrix of the problem. Here it is important to realize that not every T corresponds to a diagonal V and we, therefore, relax the usual condition of strict diagonality (locality) of V. An iterative algorithm is proposed in which we seek T that is (i) compatible with the measured scattering data and (ii) corresponds to an interaction potential V that is as diagonally dominated as possible. We refer to this algorithm as to the data-compatible T-matrix completion. This paper is Part I in a two-part series and contains theory only. Numerical examples of image reconstruction in a strongly nonlinear regime are given in Part II [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043318 (2016)10.1103/PhysRevE.94.043318]. The method described in this paper is particularly well suited for very large data sets that become increasingly available with the use of modern measurement techniques and instrumentation.

Optimisation in radiotherapy II: Programmed and inversion optimisation algorithms

International Nuclear Information System (INIS)

Ebert, M.

1997-01-01

This is the second article in a three part examination of optimisation in radiotherapy. The previous article established the bases of optimisation in radiotherapy, and the formulation of the optimisation problem. This paper outlines several algorithms that have been used in radiotherapy, for searching for the best irradiation strategy within the full set of possible strategies. Two principle classes of algorithm are considered - those associated with mathematical programming which employ specific search techniques, linear programming type searches or artificial intelligence - and those which seek to perform a numerical inversion of the optimisation problem, finishing with deterministic iterative inversion. (author)

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

A Hybrid Optimization Method for Solving Bayesian Inverse Problems under Uncertainty.

Directory of Open Access Journals (Sweden)

Kai Zhang

Full Text Available In this paper, we investigate the application of a new method, the Finite Difference and Stochastic Gradient (Hybrid method, for history matching in reservoir models. History matching is one of the processes of solving an inverse problem by calibrating reservoir models to dynamic behaviour of the reservoir in which an objective function is formulated based on a Bayesian approach for optimization. The goal of history matching is to identify the minimum value of an objective function that expresses the misfit between the predicted and measured data of a reservoir. To address the optimization problem, we present a novel application using a combination of the stochastic gradient and finite difference methods for solving inverse problems. The optimization is constrained by a linear equation that contains the reservoir parameters. We reformulate the reservoir model's parameters and dynamic data by operating the objective function, the approximate gradient of which can guarantee convergence. At each iteration step, we obtain the relatively 'important' elements of the gradient, which are subsequently substituted by the values from the Finite Difference method through comparing the magnitude of the components of the stochastic gradient, which forms a new gradient, and we subsequently iterate with the new gradient. Through the application of the Hybrid method, we efficiently and accurately optimize the objective function. We present a number numerical simulations in this paper that show that the method is accurate and computationally efficient.

An Inverse Eigenvalue Problem for a Vibrating String with Two Dirichlet Spectra

KAUST Repository

Rundell, William

2013-04-23

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: the Dirichlet spectrum from the clamped end-point conditions is insufficient. There are many known ways to add additional information to gain a positive answer, and these include changing one of the boundary conditions and recomputing the spectrum or giving the energy in each eigenmode-the so-called norming constants. We make the assumption that neither of these changes are possible. Instead we will add known mass-densities to the string in a way we can prescribe and remeasure the Dirichlet spectrum. We will not be able to answer the uniqueness question in its most general form, but will give some insight to what "added masses" should be chosen and how this can lead to a reconstruction of the original string density. © 2013 Society for Industrial and Applied Mathematics.

Numerical method in reproducing kernel space for an inverse source problem for the fractional diffusion equation

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)

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

Solution to Two-Dimensional Steady Inverse Heat Transfer Problems with Interior Heat Source Based on the Conjugate Gradient Method

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.

Recovery of material parameters of soft hyperelastic tissue by an inverse spectral technique

KAUST Repository

Gou, Kun; Joshi, Sunnie; Walton, Jay R.

2012-01-01

An inverse spectral method is developed for recovering a spatially inhomogeneous shear modulus for soft tissue. The study is motivated by a novel use of the intravascular ultrasound technique to image arteries. The arterial wall is idealized as a

The Inverse Problem of Identification of Hydrogen Permeability Model

Directory of Open Access Journals (Sweden)

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.

Comparative evaluation of entero-anastomosis by inversion techniques with different suturing materials in bovine [Water buffalo

Energy Technology Data Exchange (ETDEWEB)

Gupta, S. C.P.; Khan, A. A.; Dass, L. L.; Sahay, P. N.; Jha, G. J.

1985-07-01

Single layer end-to-end inverted and everted techniques of entero-anastomosis were evaluated in sixteen male buffalo calves using silk and catgut sutures. All the animals of everting group showed areas of adhesion grossly, whereas it was only in three animals of inverting group. Histological evidences revealed a more uniform healing pattern in inversion group and radiography suggested comparatively greater degree of stenosis, but without functional impairment of intestinal lumen, than everting anastomosis. Connective tissue proliferation and mononuclear cell infiltrations were very minimal with silk suture whereas these were pronounced with catgut, irrespective of anastomotic technique. Thus inversion technique of anastomosis accomplished by single layer suturing with silk thread was ideal for enteroanastomosis in cattle.

Electromagnetic modelling, inversion and data-processing techniques for GPR: ongoing activities in Working Group 3 of COST Action TU1208

Science.gov (United States)

Pajewski, Lara; Giannopoulos, Antonis; van der Kruk, Jan

2015-04-01

This work aims at presenting the ongoing research activities carried out in Working Group 3 (WG3) 'EM methods for near-field scattering problems by buried structures; data processing techniques' of the COST (European COoperation in Science and Technology) Action TU1208 'Civil Engineering Applications of Ground Penetrating Radar' (www.GPRadar.eu). The principal goal of the COST Action TU1208 is to exchange and increase scientific-technical knowledge and experience of GPR techniques in civil engineering, simultaneously promoting throughout Europe the effective use of this safe and non-destructive technique in the monitoring of infrastructures and structures. WG3 is structured in four Projects. Project 3.1 deals with 'Electromagnetic modelling for GPR applications.' Project 3.2 is concerned with 'Inversion and imaging techniques for GPR applications.' The topic of Project 3.3 is the 'Development of intrinsic models for describing near-field antenna effects, including antenna-medium coupling, for improved radar data processing using full-wave inversion.' Project 3.4 focuses on 'Advanced GPR data-processing algorithms.' Electromagnetic modeling tools that are being developed and improved include the Finite-Difference Time-Domain (FDTD) technique and the spectral domain Cylindrical-Wave Approach (CWA). One of the well-known freeware and versatile FDTD simulators is GprMax that enables an improved realistic representation of the soil/material hosting the sought structures and of the GPR antennas. Here, input/output tools are being developed to ease the definition of scenarios and the visualisation of numerical results. The CWA expresses the field scattered by subsurface two-dimensional targets with arbitrary cross-section as a sum of cylindrical waves. In this way, the interaction is taken into account of multiple scattered fields within the medium hosting the sought targets. Recently, the method has been extended to deal with through-the-wall scenarios. One of the

Inverse kinetics technique for reactor shutdown measurement: an experimental assessment. [AGR

Energy Technology Data Exchange (ETDEWEB)

Lewis, T. A.; McDonald, D.

1975-09-15

It is proposed to use the Inverse Kinetics Technique to measure the subcritical reactivity as a function of time during the testing of the nitrogen injection systems on AGRs. A description is given of an experimental assessment of the technique by investigating known transients created by control rod movements on a small experimental reactor, (2m high, 1m radius). Spatial effects were observed close to the moving rods but otherwise derived reactivities were independent of detector position and agreed well with the existing calibrations. This prompted the suggestion that data from installed reactor instrumentation could be used to calibrate CAGR control rods.

Large scale inverse problems computational methods and applications in the earth sciences

CERN Document Server

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.

Hermite Polynomials and the Inverse Problem for Collisionless Equilibria

Science.gov (United States)

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

On Lambda and Time Operators: the Inverse Intertwining Problem Revisited

Science.gov (United States)

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.

Inverse problems for ODEs using contraction maps and suboptimality of the 'collage method'

Science.gov (United States)

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.

Standard Error Computations for Uncertainty Quantification in Inverse Problems: Asymptotic Theory vs. Bootstrapping.

Science.gov (United States)

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.

On the solution of the inverse scattering problem for the quadratic bundle of the one-dimensional Schroedinger operators of the whole axis

International Nuclear Information System (INIS)

Maksudov, F.G.; Gusejnov, G.Sh.

1986-01-01

Inverse scattering problem for the quadratic bundle of the Schroedinger one-dimensional operators in the whole axis is solved. The problem solution is given on the assumption of the discrete spectrum absence. In the discrete spectrum presence the inverse scattering problem solution is known for the Shroedinger differential equation considered

Utility of natural generalised inverse technique in the interpretation of dyke structures

Digital Repository Service at National Institute of Oceanography (India)

Rao, M.M.M.; Murty, T.V.R.; Rao, P.R.; Lakshminarayana, S.; Subrahmanyam, A.S.; Murthy, K.S.R.

environs along the central west coast of India: analysis using EOF, J. Geophys.Res.,91(1986) 8523 -8526. 9 Marquardt D W, An algorithm for least-squares estimation of non-linear parameters, J. Soc. Indust. Appl. Math, 11 (1963) 431-441. INDIAN J. MAR... technique in reconstruction of gravity anomalies due to a fault, Indian J. Pure. Appl. Math., 34 (2003) 31-47. 16 Ramana Murty T V, Somayajulu Y K & Murty C S, Reconstruction of sound speed profile through natural generalised inverse technique, Indian J...

Operational exposition and analysis of the inverse problem electroencephalographic; Planteamiento operacional y analisis del problema inverso electroencefalografico

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.

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

Generalized Uncertainty Quantification for Linear Inverse Problems in X-ray Imaging

Energy Technology Data Exchange (ETDEWEB)

Fowler, Michael James [Clarkson Univ., Potsdam, NY (United States)

2014-04-25

In industrial and engineering applications, X-ray radiography has attained wide use as a data collection protocol for the assessment of material properties in cases where direct observation is not possible. The direct measurement of nuclear materials, particularly when they are under explosive or implosive loading, is not feasible, and radiography can serve as a useful tool for obtaining indirect measurements. In such experiments, high energy X-rays are pulsed through a scene containing material of interest, and a detector records a radiograph by measuring the radiation that is not attenuated in the scene. One approach to the analysis of these radiographs is to model the imaging system as an operator that acts upon the object being imaged to produce a radiograph. In this model, the goal is to solve an inverse problem to reconstruct the values of interest in the object, which are typically material properties such as density or areal density. The primary objective in this work is to provide quantitative solutions with uncertainty estimates for three separate applications in X-ray radiography: deconvolution, Abel inversion, and radiation spot shape reconstruction. For each problem, we introduce a new hierarchical Bayesian model for determining a posterior distribution on the unknowns and develop efficient Markov chain Monte Carlo (MCMC) methods for sampling from the posterior. A Poisson likelihood, based on a noise model for photon counts at the detector, is combined with a prior tailored to each application: an edge-localizing prior for deconvolution; a smoothing prior with non-negativity constraints for spot reconstruction; and a full covariance sampling prior based on a Wishart hyperprior for Abel inversion. After developing our methods in a general setting, we demonstrate each model on both synthetically generated datasets, including those from a well known radiation transport code, and real high energy radiographs taken at two U. S. Department of Energy

The Adjoint Method for the Inverse Problem of Option Pricing

Directory of Open Access Journals (Sweden)

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.

Inverse boundary element calculations based on structural modes