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...

Inverse problems of geophysics

International Nuclear Information System (INIS)

Yanovskaya, T.B.

2003-07-01

This report gives an overview and the mathematical formulation of geophysical inverse problems. General principles of statistical estimation are explained. The maximum likelihood and least square fit methods, the Backus-Gilbert method and general approaches for solving inverse problems are discussed. General formulations of linearized inverse problems, singular value decomposition and properties of pseudo-inverse solutions are given

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...

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

The philosophical aspect of learning inverse problems of mathematical physics

Directory of Open Access Journals (Sweden)

Виктор Семенович Корнилов

2018-12-01

Full Text Available The article describes specific questions student learning inverse problems of mathematical physics. When teaching inverse problems of mathematical physics to the understanding of the students brought the information that the inverse problems of mathematical physics with a philosophical point of view are the problems of determining the unknown causes of known consequences, and the search for their solutions have great scientific and educational potential. The reasons are specified in the form of unknown coefficients, right side, initial conditions of the mathematical model of inverse problems, and as a consequence are functionals of the solution of this mathematical model. In the process of learning the inverse problems of mathematical physics focuses on the philosophical aspects of the phenomenon of information and identify cause-effect relations. It is emphasized that in the process of logical analysis applied and humanitarian character, students realize that information is always related to the fundamental philosophical questions that the analysis applied and the humanitarian aspects of the obtained results the inverse problem of mathematical physics allows students to make appropriate inferences about the studied process and to, ultimately, new information, to study its properties and understand its value. Philosophical understanding of the notion of information opens up to students a new methodological opportunities to comprehend the world and helps us to reinterpret existing science and philosophy of the theory related to the disclosure of the interrelationship of all phenomena of reality.

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 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.

Statistical perspectives on inverse problems

DEFF Research Database (Denmark)

Andersen, Kim Emil

of the interior of an object from electrical boundary measurements. One part of this thesis concerns statistical approaches for solving, possibly non-linear, inverse problems. Thus inverse problems are recasted in a form suitable for statistical inference. In particular, a Bayesian approach for regularisation...... problem is given in terms of probability distributions. Posterior inference is obtained by Markov chain Monte Carlo methods and new, powerful simulation techniques based on e.g. coupled Markov chains and simulated tempering is developed to improve the computational efficiency of the overall simulation......Inverse problems arise in many scientific disciplines and pertain to situations where inference is to be made about a particular phenomenon from indirect measurements. A typical example, arising in diffusion tomography, is the inverse boundary value problem for non-invasive reconstruction...

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.

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.

Inverse problems in the Bayesian framework

International Nuclear Information System (INIS)

Calvetti, Daniela; Somersalo, Erkki; Kaipio, Jari P

2014-01-01

The history of Bayesian methods dates back to the original works of Reverend Thomas Bayes and Pierre-Simon Laplace: the former laid down some of the basic principles on inverse probability in his classic article ‘An essay towards solving a problem in the doctrine of chances’ that was read posthumously in the Royal Society in 1763. Laplace, on the other hand, in his ‘Memoirs on inverse probability’ of 1774 developed the idea of updating beliefs and wrote down the celebrated Bayes’ formula in the form we know today. Although not identified yet as a framework for investigating inverse problems, Laplace used the formalism very much in the spirit it is used today in the context of inverse problems, e.g., in his study of the distribution of comets. With the evolution of computational tools, Bayesian methods have become increasingly popular in all fields of human knowledge in which conclusions need to be drawn based on incomplete and noisy data. Needless to say, inverse problems, almost by definition, fall into this category. Systematic work for developing a Bayesian inverse problem framework can arguably be traced back to the 1980s, (the original first edition being published by Elsevier in 1987), although articles on Bayesian methodology applied to inverse problems, in particular in geophysics, had appeared much earlier. Today, as testified by the articles in this special issue, the Bayesian methodology as a framework for considering inverse problems has gained a lot of popularity, and it has integrated very successfully with many traditional inverse problems ideas and techniques, providing novel ways to interpret and implement traditional procedures in numerical analysis, computational statistics, signal analysis and data assimilation. The range of applications where the Bayesian framework has been fundamental goes from geophysics, engineering and imaging to astronomy, life sciences and economy, and continues to grow. There is no question that Bayesian

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)

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...

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.

Parameter estimation and inverse problems

CERN Document Server

Aster, Richard C; Thurber, Clifford H

2005-01-01

Parameter Estimation and Inverse Problems primarily serves as a textbook for advanced undergraduate and introductory graduate courses. Class notes have been developed and reside on the World Wide Web for faciliting use and feedback by teaching colleagues. The authors'' treatment promotes an understanding of fundamental and practical issus associated with parameter fitting and inverse problems including basic theory of inverse problems, statistical issues, computational issues, and an understanding of how to analyze the success and limitations of solutions to these probles. The text is also a practical resource for general students and professional researchers, where techniques and concepts can be readily picked up on a chapter-by-chapter basis.Parameter Estimation and Inverse Problems is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who may not have an extensive mathematical background. It is accompanied by a Web site that...

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...

Application of numerical inverse method in calculation of composition-dependent interdiffusion coefficients in finite diffusion couples

DEFF Research Database (Denmark)

Liu, Yuanrong; Chen, Weimin; Zhong, Jing

2017-01-01

The previously developed numerical inverse method was applied to determine the composition-dependent interdiffusion coefficients in single-phase finite diffusion couples. The numerical inverse method was first validated in a fictitious binary finite diffusion couple by pre-assuming four standard...... sets of interdiffusion coefficients. After that, the numerical inverse method was then adopted in a ternary Al-Cu-Ni finite diffusion couple. Based on the measured composition profiles, the ternary interdiffusion coefficients along the entire diffusion path of the target ternary diffusion couple were...... obtained by using the numerical inverse approach. The comprehensive comparisons between the computations and the experiments indicate that the numerical inverse method is also applicable to high-throughput determination of the composition-dependent interdiffusion coefficients in finite diffusion couples....

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.

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)

EDITORIAL: Inverse Problems in Engineering

Science.gov (United States)

West, Robert M.; Lesnic, Daniel

2007-01-01

Presented here are 11 noteworthy papers selected from the Fifth International Conference on Inverse Problems in Engineering: Theory and Practice held in Cambridge, UK during 11-15 July 2005. The papers have been peer-reviewed to the usual high standards of this journal and the contributions of reviewers are much appreciated. The conference featured a good balance of the fundamental mathematical concepts of inverse problems with a diverse range of important and interesting applications, which are represented here by the selected papers. Aspects of finite-element modelling and the performance of inverse algorithms are investigated by Autrique et al and Leduc et al. Statistical aspects are considered by Emery et al and Watzenig et al with regard to Bayesian parameter estimation and inversion using particle filters. Electrostatic applications are demonstrated by van Berkel and Lionheart and also Nakatani et al. Contributions to the applications of electrical techniques and specifically electrical tomographies are provided by Wakatsuki and Kagawa, Kim et al and Kortschak et al. Aspects of inversion in optical tomography are investigated by Wright et al and Douiri et al. The authors are representative of the worldwide interest in inverse problems relating to engineering applications and their efforts in producing these excellent papers will be appreciated by many readers of this journal.

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)

BOOK REVIEW: Inverse Problems. Activities for Undergraduates

Science.gov (United States)

Yamamoto, Masahiro

2003-06-01

This book is a valuable introduction to inverse problems. In particular, from the educational point of view, the author addresses the questions of what constitutes an inverse problem and how and why we should study them. Such an approach has been eagerly awaited for a long time. Professor Groetsch, of the University of Cincinnati, is a world-renowned specialist in inverse problems, in particular the theory of regularization. Moreover, he has made a remarkable contribution to educational activities in the field of inverse problems, which was the subject of his previous book (Groetsch C W 1993 Inverse Problems in the Mathematical Sciences (Braunschweig: Vieweg)). For this reason, he is one of the most qualified to write an introductory book on inverse problems. Without question, inverse problems are important, necessary and appear in various aspects. So it is crucial to introduce students to exercises in inverse problems. However, there are not many introductory books which are directly accessible by students in the first two undergraduate years. As a consequence, students often encounter diverse concrete inverse problems before becoming aware of their general principles. The main purpose of this book is to present activities to allow first-year undergraduates to learn inverse theory. To my knowledge, this book is a rare attempt to do this and, in my opinion, a great success. The author emphasizes that it is very important to teach inverse theory in the early years. He writes; `If students consider only the direct problem, they are not looking at the problem from all sides .... The habit of always looking at problems from the direct point of view is intellectually limiting ...' (page 21). The book is very carefully organized so that teachers will be able to use it as a textbook. After an introduction in chapter 1, sucessive chapters deal with inverse problems in precalculus, calculus, differential equations and linear algebra. In order to let one gain some insight

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.)

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

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)

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.

A Numerical Approach to Solving an Inverse Heat Conduction Problem Using the Levenberg-Marquardt Algorithm

Directory of Open Access Journals (Sweden)

Tao Min

2014-01-01

Full Text Available This paper is intended to provide a numerical algorithm involving the combined use of the Levenberg-Marquardt algorithm and the Galerkin finite element method for estimating the diffusion coefficient in an inverse heat conduction problem (IHCP. In the present study, the functional form of the diffusion coefficient is unknown a priori. The unknown diffusion coefficient is approximated by the polynomial form and the present numerical algorithm is employed to find the solution. Numerical experiments are presented to show the efficiency of the proposed method.

Initial-boundary value problems for multi-term time-fractional diffusion equations with x-dependent coefficients

OpenAIRE

Li, Zhiyuan; Huang, Xinchi; Yamamoto, Masahiro

2018-01-01

In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffler functions and the eigenfunction expansion, we reduce the IBVP to an equivalent integral equation to show the unique existence and the analyticity of the solution for the equation. Especially, in the case where all the coefficients of the time-fractional derivatives are non-negative, by the Laplace and inversion L...

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

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 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.

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...

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.

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.

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.

3rd Annual Workshop on Inverse Problem

CERN Document Server

2015-01-01

This proceeding volume is based on papers presented on the Third Annual Workshop on Inverse Problems which was organized by the Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, and took place in May 2013 in Stockholm. The purpose of this workshop was to present new analytical developments and numerical techniques for solution of inverse problems for a wide range of applications in acoustics, electromagnetics, optical fibers, medical imaging, geophysics, etc. The contributions in this volume reflect these themes and will be beneficial to researchers who are working in the area of applied inverse problems.

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

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

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

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...

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

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.

A Survey on Inverse Problems for Applied Sciences

Directory of Open Access Journals (Sweden)

Fatih Yaman

2013-01-01

Full Text Available The aim of this paper is to introduce inversion-based engineering applications and to investigate some of the important ones from mathematical point of view. To do this we employ acoustic, electromagnetic, and elastic waves for presenting different types of inverse problems. More specifically, we first study location, shape, and boundary parameter reconstruction algorithms for the inaccessible targets in acoustics. The inverse problems for the time-dependent differential equations of isotropic and anisotropic elasticity are reviewed in the following section of the paper. These problems were the objects of the study by many authors in the last several decades. The physical interpretations for almost all of these problems are given, and the geophysical applications for some of them are described. In our last section, an introduction with many links into the literature is given for modern algorithms which combine techniques from classical inverse problems with stochastic tools into ensemble methods both for data assimilation as well as for forecasting.

Recovering a coefficient in a parabolic equation using an iterative approach

Science.gov (United States)

Azhibekova, Aliya S.

2016-06-01

In this paper we are concerned with the problem of determining a coefficient in a parabolic equation using an iterative approach. We investigate an inverse coefficient problem in the difference form. To recover the coefficient, we minimize a residual functional between the observed and calculated values. This is done in a constructive way by fitting a finite-difference approximation to the inverse problem. We obtain some theoretical estimates for a direct and adjoint problem. Using these estimates we prove monotonicity of the objective functional and the convergence of iteration sequences.

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...

Radiation measurement and inverse analysis techniques applied on the determination of the apparent mass diffusion coefficient for diverse contaminants and soil samples

International Nuclear Information System (INIS)

Rey Silva, D.V.F.M.; Oliveira, A.P.; Macacini, J.F.; Da Silva, N.C.; Cipriani, M.; Quinelato, A.L.

2005-01-01

Full text of publication follows: The study of the dispersion of radioactive materials in soils and in engineering barriers plays an important role in the safety analysis of nuclear waste repositories. In order to proceed with such kind of study the involved physical properties must be determined with precision, including the apparent mass diffusion coefficient, which is defined as the ratio between the effective mass diffusion coefficient and the retardation factor. Many different experimental and estimation techniques are available on the literature for the identification of the diffusion coefficient and this work describes the implementation of that developed by Pereira et al [1]. This technique is based on non-intrusive radiation measurements and the experimental setup consists of a cylindrical column filled with compacted media saturated with water. A radioactive contaminant is mixed with a portion of the media and then placed in the bottom of the column. Therefore, the contaminant will diffuse through the uncontaminated media due to the concentration gradient. A radiation detector is used to measure the number of counts, which is associated to the contaminant concentration, at several positions along the column during the experiment. Such measurements are then used to estimate the apparent diffusion coefficient of the contaminant in the porous media by inverse analysis. The inverse problem of parameter estimation is solved with the Levenberg-Marquart Method of minimization of the least-square norm. The experiment was optimized with respect to the number of measurement locations, frequency of measurements and duration of the experiment through the analysis of the sensitivity coefficients and by using a D-optimum approach. This setup is suitable for studying a great number of combinations of diverse contaminants and porous media varying in composition and compacting, with considerable easiness and reliable results, and it was chosen because that is the

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.

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

Introduction to Schroedinger inverse scattering

International Nuclear Information System (INIS)

Roberts, T.M.

1991-01-01

Schroedinger inverse scattering uses scattering coefficients and bound state data to compute underlying potentials. Inverse scattering has been studied extensively for isolated potentials q(x), which tend to zero as vertical strokexvertical stroke→∞. Inverse scattering for isolated impurities in backgrounds p(x) that are periodic, are Heaviside steps, are constant for x>0 and periodic for x<0, or that tend to zero as x→∞ and tend to ∞ as x→-∞, have also been studied. This paper identifies literature for the five inverse problems just mentioned, and for four other inverse problems. Heaviside-step backgrounds are discussed at length. (orig.)

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.

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.

Seismic inverse scattering in the downward continuation approach

NARCIS (Netherlands)

Stolk, C.C.; de Hoop, M.V.

Seismic data are commonly modeled by a linearization around a smooth background medium in combination with a high frequency approximation. The perturbation of the medium coefficient is assumed to contain the discontinuities. This leads to two inverse problems, first the linearized inverse problem

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

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

Problems on Divisibility of Binomial Coefficients

Science.gov (United States)

Osler, Thomas J.; Smoak, James

2004-01-01

Twelve unusual problems involving divisibility of the binomial coefficients are represented in this article. The problems are listed in "The Problems" section. All twelve problems have short solutions which are listed in "The Solutions" section. These problems could be assigned to students in any course in which the binomial theorem and Pascal's…

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...

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.

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.

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.

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.

Inverse planning for x-ray rotation therapy: a general solution of the inverse problem

International Nuclear Information System (INIS)

Oelfke, U.; Bortfeld, T.

1999-01-01

Rotation therapy with photons is currently under investigation for the delivery of intensity modulated radiotherapy (IMRT). An analytical approach for inverse treatment planning of this radiotherapy technique is described. The inverse problem for the delivery of arbitrary 2D dose profiles is first formulated and then solved analytically. In contrast to previously applied strategies for solving the inverse problem, it is shown that the most general solution for the fluence profiles consists of two independent solutions of different parity. A first analytical expression for both fluence profiles is derived. The mathematical derivation includes two different strategies, an elementary expansion of fluence and dose into polynomials and a more practical approach in terms of Fourier transforms. The obtained results are discussed in the context of previous work on this problem. (author)

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)

Inverse method for determining radon diffusion coefficient and free radon production rate of fragmented uranium ore

International Nuclear Information System (INIS)

Ye, Yong-jun; Wang, Li-heng; Ding, De-xin; Zhao, Ya-li; Fan, Nan-bin

2014-01-01

The radon diffusion coefficient and the free radon production rate are important parameters for describing radon migration in the fragmented uranium ore. In order to determine the two parameters, the pure diffusion migration equation for radon was firstly established and its analytic solution with the two parameters to be determined was derived. Then, a self manufactured experimental column was used to simulate the pure diffusion of the radon, the improved scintillation cell method was used to measure the pore radon concentrations at different depths of the column loaded with the fragmented uranium ore, and the nonlinear least square algorithm was used to inversely determine the radon diffusion coefficient and the free radon production rate. Finally, the solution with the two inversely determined parameters was used to predict the pore radon concentrations at some depths of the column, and the predicted results were compared with the measured results. The results show that the predicted results are in good agreement with the measured results and the numerical inverse method is applicable to the determination of the radon diffusion coefficient and the free radon production rate for the fragmented uranium ore. - Highlights: • Inverse method for determining two transport parameters of radon is proposed. • A self-made experimental apparatus is used to simulate radon diffusion process. • Sampling volume and position for measuring radon concentration are optimized. • The inverse results of an experimental sample are verified

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

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)

Problems with Discontinuous Diffusion/Dispersion Coefficients

Directory of Open Access Journals (Sweden)

Stefano Ferraris

2012-01-01

accurate on smooth solutions and based on a special numerical treatment of the diffusion/dispersion coefficients that makes its application possible also when such coefficients are discontinuous. Numerical experiments confirm the convergence of the numerical approximation and show a good behavior on a set of benchmark problems in two space dimensions.

On stability of the solutions of inverse problem for determining the right-hand side of a degenerate parabolic equation with two independent variables

Science.gov (United States)

Kamynin, V. L.; Bukharova, T. I.

2017-01-01

We prove the estimates of stability with respect to perturbations of input data for the solutions of inverse problems for degenerate parabolic equations with unbounded coefficients. An important feature of these estimates is that the constants in these estimates are written out explicitly by the input data of the problem.

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.

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

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.

The determination of solubility and diffusion coefficient for solids in liquids by an inverse measurement technique using cylinders of amorphous glucose as a model compound

International Nuclear Information System (INIS)

Hu, Chengyao; Huang, Pei

2011-01-01

The importance of sugar and sugar-containing materials is well recognized nowadays, owing to their application in industrial processes, particularly in the food, pharmaceutical and cosmetic industries. Because of the large numbers of those compounds involved and the relatively small number of solubility and/or diffusion coefficient data for each compound available, it is highly desirable to measure the solubility and/or diffusion coefficient as efficiently as possible and to be able to improve the accuracy of the methods used. In this work, a new technique was developed for the measurement of the diffusion coefficient of a stationary solid solute in a stagnant solvent which simultaneously measures solubility based on an inverse measurement problem algorithm with the real-time dissolved amount profile as a function of time. This study differs from established techniques in both the experimental method and the data analysis. The experimental method was developed in which the dissolved amount of solid solute in quiescent solvent was investigated using a continuous weighing technique. In the data analysis, the hybrid genetic algorithm is used to minimize an objective function containing a calculated and a measured dissolved amount with time. This is measured on a cylindrical sample of amorphous glucose in methanol or ethanol. The calculated dissolved amount, that is a function of the unknown physical properties of the solid solute in the solvent, is calculated by the solution of the two-dimensional nonlinear inverse natural convection problem. The estimated values of the solubility of amorphous glucose in methanol and ethanol at 293 K were respectively 32.1 g/100 g methanol and 1.48 g/100 g ethanol, in agreement with the literature values, and support the validity of the simultaneously measured diffusion coefficient. These results show the efficiency and the stability of the developed technique to simultaneously estimate the solubility and diffusion coefficient. Also

Physics-based Inverse Problem to Deduce Marine Atmospheric Boundary Layer Parameters

Science.gov (United States)

2017-03-07

knowledge and capabilities in the use and development of inverse problem techniques to deduce atmospheric parameters. WORK COMPLETED The research completed...please find the Final Technical Report with SF 298 for Dr. Erin E. Hackett’s ONR grant entitled Physics -based Inverse Problem to Deduce Marine...From- To) 07/03/2017 Final Technica l Dec 2012- Dec 2016 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Physics -based Inverse Problem to Deduce Marine

The Mathematical Basis of the Inverse Scattering Problem for Cracks from Near-Field Data

Directory of Open Access Journals (Sweden)

Yao Mao

2015-01-01

Full Text Available We consider the acoustic scattering problem from a crack which has Dirichlet boundary condition on one side and impedance boundary condition on the other side. The inverse scattering problem in this paper tries to determine the shape of the crack and the surface impedance coefficient from the near-field measurements of the scattered waves, while the source point is placed on a closed curve. We firstly establish a near-field operator and focus on the operator’s mathematical analysis. Secondly, we obtain a uniqueness theorem for the shape and surface impedance. Finally, by using the operator’s properties and modified linear sampling method, we reconstruct the shape and surface impedance.

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.

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)

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

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.

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

Science.gov (United States)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

monotone and stable discrete-analytical numerical schemes [1]-[3] conserving the positivity of the chemical substance concentrations and possessing the properties of energy and mass balance that are postulated in the general variational principle for integrated models. All algorithms for solution of transport, diffusion and transformation problems are direct (without iterations). The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS, by RFBR project 11-01-00187 and Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004. References Penenko V., Tsvetova E. Discrete-analytical methods for the implementation of variational principles in environmental applications// Journal of computational and applied mathematics, 2009, v. 226, 319-330. Penenko A.V. Discrete-analytic schemes for solving an inverse coefficient heat conduction problem in a layered medium with gradient methods// Numerical Analysis and Applications, 2012, V. 5, pp 326-341. V. Penenko, E. Tsvetova. Variational methods for constructing the monotone approximations for atmospheric chemistry models //Numerical Analysis and Applications, 2013 (in press).

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

Proximal methods for the resolution of inverse problems: application to positron emission tomography

International Nuclear Information System (INIS)

Pustelnik, N.

2010-12-01

The objective of this work is to propose reliable, efficient and fast methods for minimizing convex criteria, that are found in inverse problems for imagery. We focus on restoration/reconstruction problems when data is degraded with both a linear operator and noise, where the latter is not assumed to be necessarily additive.The reliability of the method is ensured through the use of proximal algorithms, the convergence of which is guaranteed when a convex criterion is considered. Efficiency is sought through the choice of criteria adapted to the noise characteristics, the linear operators and the image specificities. Of particular interest are regularization terms based on total variation and/or sparsity of signal frame coefficients. As a consequence of the use of frames, two approaches are investigated, depending on whether the analysis or the synthesis formulation is chosen. Fast processing requirements lead us to consider proximal algorithms with a parallel structure. Theoretical results are illustrated on several large size inverse problems arising in image restoration, stereoscopy, multi-spectral imagery and decomposition into texture and geometry components. We focus on a particular application, namely Positron Emission Tomography (PET), which is particularly difficult because of the presence of a projection operator combined with Poisson noise, leading to highly corrupted data. To optimize the quality of the reconstruction, we make use of the spatio-temporal characteristics of brain tissue activity. (author)

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.

Some results on inverse scattering

International Nuclear Information System (INIS)

Ramm, A.G.

2008-01-01

A review of some of the author's results in the area of inverse scattering is given. The following topics are discussed: (1) Property C and applications, (2) Stable inversion of fixed-energy 3D scattering data and its error estimate, (3) Inverse scattering with 'incomplete' data, (4) Inverse scattering for inhomogeneous Schroedinger equation, (5) Krein's inverse scattering method, (6) Invertibility of the steps in Gel'fand-Levitan, Marchenko, and Krein inversion methods, (7) The Newton-Sabatier and Cox-Thompson procedures are not inversion methods, (8) Resonances: existence, location, perturbation theory, (9) Born inversion as an ill-posed problem, (10) Inverse obstacle scattering with fixed-frequency data, (11) Inverse scattering with data at a fixed energy and a fixed incident direction, (12) Creating materials with a desired refraction coefficient and wave-focusing properties. (author)

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)

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.

Study on Material Parameters Identification of Brain Tissue Considering Uncertainty of Friction Coefficient

Science.gov (United States)

Guan, Fengjiao; Zhang, Guanjun; Liu, Jie; Wang, Shujing; Luo, Xu; Zhu, Feng

2017-10-01

Accurate material parameters are critical to construct the high biofidelity finite element (FE) models. However, it is hard to obtain the brain tissue parameters accurately because of the effects of irregular geometry and uncertain boundary conditions. Considering the complexity of material test and the uncertainty of friction coefficient, a computational inverse method for viscoelastic material parameters identification of brain tissue is presented based on the interval analysis method. Firstly, the intervals are used to quantify the friction coefficient in the boundary condition. And then the inverse problem of material parameters identification under uncertain friction coefficient is transformed into two types of deterministic inverse problem. Finally the intelligent optimization algorithm is used to solve the two types of deterministic inverse problems quickly and accurately, and the range of material parameters can be easily acquired with no need of a variety of samples. The efficiency and convergence of this method are demonstrated by the material parameters identification of thalamus. The proposed method provides a potential effective tool for building high biofidelity human finite element model in the study of traffic accident injury.

Analog fault diagnosis by inverse problem technique

KAUST Repository

Ahmed, Rania F.

2011-12-01

A novel algorithm for detecting soft faults in linear analog circuits based on the inverse problem concept is proposed. The proposed approach utilizes optimization techniques with the aid of sensitivity analysis. The main contribution of this work is to apply the inverse problem technique to estimate the actual parameter values of the tested circuit and so, to detect and diagnose single fault in analog circuits. The validation of the algorithm is illustrated through applying it to Sallen-Key second order band pass filter and the results show that the detecting percentage efficiency was 100% and also, the maximum error percentage of estimating the parameter values is 0.7%. This technique can be applied to any other linear circuit and it also can be extended to be applied to non-linear circuits. © 2011 IEEE.

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.

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

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

Science.gov (United States)

Kalenichenko, V. V.

1992-08-01

A method of the absolute calibration of the mass scale is proposed for solving the inverse problem of the physical theory of fireballs. The method is based on data on the masses of fallen meteorites whose fireballs have been photographed in flight. The method can be applied to fireballs whose bodies have not experienced significant fragmentation during their flight in the atmosphere and have kept their shape relatively well. Data on the Lost City and Innisfree meteorites are used to calculate the calibration coefficients.

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)

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

A numerical solution to an inverse unsteady-state heat transfer problem involving the Trefftz functions

Directory of Open Access Journals (Sweden)

Maciejewska Beata

2017-01-01

Full Text Available This paper shows the results concerning flow boiling heat transfer in an asymmetrically heated vertical minichannel. The heated element for FC-72 Fluorinert flowing in that minichannel was a thin foil. The foil surface temperature was monitored continuously at 18 points by K-type thermocouples from the outer foil surface. Fluid temperature and pressure in the minichannel inlet and outlet, current supplied to the foil and voltage drop were also monitored. Measurements were carried out at 1 s intervals. The objective was to determine the heat transfer coefficient on the heated foil–fluid contact surface in the minichannel. It was obtained from the Robin boundary condition. The foil temperature was the result of solving the nonstationary two-dimensional inverse boundary problem in the heated foil. Using the FEM combined with Trefftz functions as basis functions solved the problem. The unknown temperature values at nodes were calculated by minimising the adequate functional. The values of local heat transfer coefficients were consistent with the results obtained by the authors in their previous studies when steady-state conditions were analysed. This time, however, these values were analysed as time dependent, which facilitated observation of coefficient changes that were impossible to observe under the steady-state conditions.

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

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

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

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.

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

Non-linear Bayesian update of PCE coefficients

KAUST Repository

Litvinenko, Alexander

2014-01-06

Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(!) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).

Non-linear Bayesian update of PCE coefficients

KAUST Repository

Litvinenko, Alexander; Matthies, Hermann G.; Pojonk, Oliver; Rosic, Bojana V.; Zander, Elmar

2014-01-01

Given: a physical system modeled by a PDE or ODE with uncertain coefficient q(?), a measurement operator Y (u(q), q), where u(q, ?) uncertain solution. Aim: to identify q(?). The mapping from parameters to observations is usually not invertible, hence this inverse identification problem is generally ill-posed. To identify q(!) we derived non-linear Bayesian update from the variational problem associated with conditional expectation. To reduce cost of the Bayesian update we offer a unctional approximation, e.g. polynomial chaos expansion (PCE). New: We apply Bayesian update to the PCE coefficients of the random coefficient q(?) (not to the probability density function of q).

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.

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.

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.

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.

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

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.

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

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

The measurement problem on classical diffusion process: inverse method on stochastic processes

International Nuclear Information System (INIS)

Bigerelle, M.; Iost, A.

2004-01-01

In a high number of diffusive systems, measures are processed to calculate material parameters such as diffusion coefficients, or to verify the accuracy of mathematical models. However, the precision of the parameter determination or of the model relevance depends on the location of the measure itself. The aim of this paper is first to analyse, for a mono-dimensional system, the precision of the measure in relation with its location by an inverse problem algorithm and secondly to examine the physical meaning of the results. Statistical mechanic considerations show that, passing over a time-distance criterion, measurement becomes uncertain whatever the initial conditions. The criterion proves that this chaotic mode is related to the production of anti-entropy at a mesoscopique scale that is in violation to quantum theory about measurement

Reconstruction of absorption and scattering coefficients in two dimensional heterogeneous participating media

International Nuclear Information System (INIS)

Montero, Raul F. Carita; Roberty, Nilson C.; Silva Neto, Antonio J.; Universidade Federal, Rio de Janeiro, RJ

2002-01-01

In the present work it is presented the solution of the two dimensional inverse radiative transfer problem of scattering and absorption coefficients estimation, in heterogeneous media, using the source-detector methodology and a discrete ordinates method consistent with the source-detector system. The mathematical formulation of the direct and inverse problems is presented as well as test case results. (author)

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.

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

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.

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...

Joint Model and Parameter Dimension Reduction for Bayesian Inversion Applied to an Ice Sheet Flow Problem

Science.gov (United States)

Ghattas, O.; Petra, N.; Cui, T.; Marzouk, Y.; Benjamin, P.; Willcox, K.

2016-12-01

Model-based projections of the dynamics of the polar ice sheets play a central role in anticipating future sea level rise. However, a number of mathematical and computational challenges place significant barriers on improving predictability of these models. One such challenge is caused by the unknown model parameters (e.g., in the basal boundary conditions) that must be inferred from heterogeneous observational data, leading to an ill-posed inverse problem and the need to quantify uncertainties in its solution. In this talk we discuss the problem of estimating the uncertainty in the solution of (large-scale) ice sheet inverse problems within the framework of Bayesian inference. Computing the general solution of the inverse problem--i.e., the posterior probability density--is intractable with current methods on today's computers, due to the expense of solving the forward model (3D full Stokes flow with nonlinear rheology) and the high dimensionality of the uncertain parameters (which are discretizations of the basal sliding coefficient field). To overcome these twin computational challenges, it is essential to exploit problem structure (e.g., sensitivity of the data to parameters, the smoothing property of the forward model, and correlations in the prior). To this end, we present a data-informed approach that identifies low-dimensional structure in both parameter space and the forward model state space. This approach exploits the fact that the observations inform only a low-dimensional parameter space and allows us to construct a parameter-reduced posterior. Sampling this parameter-reduced posterior still requires multiple evaluations of the forward problem, therefore we also aim to identify a low dimensional state space to reduce the computational cost. To this end, we apply a proper orthogonal decomposition (POD) approach to approximate the state using a low-dimensional manifold constructed using ``snapshots'' from the parameter reduced posterior, and the discrete

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

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

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.

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.

On multiple level-set regularization methods for inverse problems

International Nuclear Information System (INIS)

DeCezaro, A; Leitão, A; Tai, X-C

2009-01-01

We analyze a multiple level-set method for solving inverse problems with piecewise constant solutions. This method corresponds to an iterated Tikhonov method for a particular Tikhonov functional G α based on TV–H 1 penalization. We define generalized minimizers for our Tikhonov functional and establish an existence result. Moreover, we prove convergence and stability results of the proposed Tikhonov method. A multiple level-set algorithm is derived from the first-order optimality conditions for the Tikhonov functional G α , similarly as the iterated Tikhonov method. The proposed multiple level-set method is tested on an inverse potential problem. Numerical experiments show that the method is able to recover multiple objects as well as multiple contrast levels

A Parameterized Inversion Model for Soil Moisture and Biomass from Polarimetric Backscattering Coefficients

Science.gov (United States)

Truong-Loi, My-Linh; Saatchi, Sassan; Jaruwatanadilok, Sermsak

2012-01-01

A semi-empirical algorithm for the retrieval of soil moisture, root mean square (RMS) height and biomass from polarimetric SAR data is explained and analyzed in this paper. The algorithm is a simplification of the distorted Born model. It takes into account the physical scattering phenomenon and has three major components: volume, double-bounce and surface. This simplified model uses the three backscattering coefficients ( sigma HH, sigma HV and sigma vv) at low-frequency (P-band). The inversion process uses the Levenberg-Marquardt non-linear least-squares method to estimate the structural parameters. The estimation process is entirely explained in this paper, from initialization of the unknowns to retrievals. A sensitivity analysis is also done where the initial values in the inversion process are varying randomly. The results show that the inversion process is not really sensitive to initial values and a major part of the retrievals has a root-mean-square error lower than 5% for soil moisture, 24 Mg/ha for biomass and 0.49 cm for roughness, considering a soil moisture of 40%, roughness equal to 3cm and biomass varying from 0 to 500 Mg/ha with a mean of 161 Mg/ha

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.

The inverse problem for the one-dimensional Schroedinger equation with an energy-dependent potential. II

International Nuclear Information System (INIS)

Jaulent, M.; Jean, C.

1976-01-01

The one-dimensional Schroedinger equation y + ''+ ) 7k 2 -V + (k,x){y + =0, x belonging to R, was previously considered when the potential V + (k,x) depends on the energy k 2 in the following way: V + (k,x)=U(x)+2kQ(x), (U(x), Q(x)) belonging to a large class of pairs of real potentials admitting no bound state). The two systems of differential and integral equations then introduced are solved. Then, investigating the inverse scattering problem it is found that a necessary and sufficient condition for one of the functions S + (k) and Ssub(-1)sup(+)(k) to be the scattering matrix associated with a pair (U(x), Q(x)) is that S + (k) (or equivalently Ssub(-1)sup(+)(k) belongs to the class S introduced. This pair is the only one admitting this function as its scattering matrix. Investigating the inverse reflection problem, it is found that a necessary and sufficient condition for a function S 21 + (k) to be the reflection coefficient to the right associated with a pair (U(x), Q(x)) is that S 21 + (k) belongs to the class R introduced. This pair is the only one admitting this function as

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.

Inverse Tasks In The Tsunami Problem: Nonlinear Regression With Inaccurate Input Data

Science.gov (United States)

Lavrentiev, M.; Shchemel, A.; Simonov, K.

A variant of modified training functional that allows considering inaccurate input data is suggested. A limiting case when a part of input data is completely undefined, and, therefore, a problem of reconstruction of hidden parameters should be solved, is also considered. Some numerical experiments are presented. It is assumed that a dependence of known output variables on known input ones should be found is the classic problem definition, which is widely used in the majority of neural nets algorithms. The quality of approximation is evaluated as a performance function. Often the error of the task is evaluated as squared distance between known input data and predicted data multiplied by weighed coefficients. These coefficients may be named "precision coefficients". When inputs are not known exactly, natural generalization of performance function is adding member that responsible for distance between known inputs and shifted inputs, which lessen model's error. It is desirable that the set of variable parameters is compact for training to be con- verging. In the above problem it is possible to choose variants of demands of a priori compactness, which allow meaningful interpretation in the smoothness of the model dependence. Two kinds of regularization was used, first limited squares of coefficients responsible for nonlinearity and second limited multiplication of the above coeffi- cients and linear coefficients. Asymptotic universality of neural net ability to approxi- mate various smooth functions with any accuracy by increase of the number of tunable parameters is often the base for selecting a type of neural net approximation. It is pos- sible to show that used neural net will approach to Fourier integral transform, which approximate abilities are known, with increasing of the number of tunable parameters. In the limiting case, when input data is set with zero precision, the problem of recon- struction of hidden parameters with observed output data appears. The

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

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.

Relevance vector machine technique for the inverse scattering problem

International Nuclear Information System (INIS)

Wang Fang-Fang; Zhang Ye-Rong

2012-01-01

A novel method based on the relevance vector machine (RVM) for the inverse scattering problem is presented in this paper. The nonlinearity and the ill-posedness inherent in this problem are simultaneously considered. The nonlinearity is embodied in the relation between the scattered field and the target property, which can be obtained through the RVM training process. Besides, rather than utilizing regularization, the ill-posed nature of the inversion is naturally accounted for because the RVM can produce a probabilistic output. Simulation results reveal that the proposed RVM-based approach can provide comparative performances in terms of accuracy, convergence, robustness, generalization, and improved performance in terms of sparse property in comparison with the support vector machine (SVM) based approach. (general)

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....

Parameterization of light scattering for solving the inverse problem of determining the concentrations of the principal light scattering and absorbing admixtures in shelf waters

Directory of Open Access Journals (Sweden)

Vadim N. Pelevin

2001-12-01

Full Text Available A method for estimating the water backscattering coefficient was put forward on the basis of experimental data of diffuse attenuation coefficient for downwelling irradiance and irradiance reflectance. Calculations were carried out for open sea waters of different types and the spectral dependencies were found ("anomalous" spectra and explained. On this basis, a new model of light backscattering on particles in the sea is proposed. This model may be useful for modelling remote sensing reflectance spectra in order to solve the inverse problems of estimating the concentration of natural admixtures in shelf waters.

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.

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

SU-E-J-161: Inverse Problems for Optical Parameters in Laser Induced Thermal Therapy

International Nuclear Information System (INIS)

Fahrenholtz, SJ; Stafford, RJ; Fuentes, DT

2014-01-01

Purpose: Magnetic resonance-guided laser-induced thermal therapy (MRgLITT) is investigated as a neurosurgical intervention for oncological applications throughout the body by active post market studies. Real-time MR temperature imaging is used to monitor ablative thermal delivery in the clinic. Additionally, brain MRgLITT could improve through effective planning for laser fiber's placement. Mathematical bioheat models have been extensively investigated but require reliable patient specific physical parameter data, e.g. optical parameters. This abstract applies an inverse problem algorithm to characterize optical parameter data obtained from previous MRgLITT interventions. Methods: The implemented inverse problem has three primary components: a parameter-space search algorithm, a physics model, and training data. First, the parameter-space search algorithm uses a gradient-based quasi-Newton method to optimize the effective optical attenuation coefficient, μ-eff. A parameter reduction reduces the amount of optical parameter-space the algorithm must search. Second, the physics model is a simplified bioheat model for homogeneous tissue where closed-form Green's functions represent the exact solution. Third, the training data was temperature imaging data from 23 MRgLITT oncological brain ablations (980 nm wavelength) from seven different patients. Results: To three significant figures, the descriptive statistics for μ-eff were 1470 m −1 mean, 1360 m −1 median, 369 m −1 standard deviation, 933 m −1 minimum and 2260 m −1 maximum. The standard deviation normalized by the mean was 25.0%. The inverse problem took <30 minutes to optimize all 23 datasets. Conclusion: As expected, the inferred average is biased by underlying physics model. However, the standard deviation normalized by the mean is smaller than literature values and indicates an increased precision in the characterization of the optical parameters needed to plan MRgLITT procedures. This investigation

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.

Retrieval of LAI and leaf chlorophyll content from remote sensing data by agronomy mechanism knowledge to solve the ill-posed inverse problem

Science.gov (United States)

Li, Zhenhai; Nie, Chenwei; Yang, Guijun; Xu, Xingang; Jin, Xiuliang; Gu, Xiaohe

2014-10-01

Leaf area index (LAI) and LCC, as the two most important crop growth variables, are major considerations in management decisions, agricultural planning and policy making. Estimation of canopy biophysical variables from remote sensing data was investigated using a radiative transfer model. However, the ill-posed problem is unavoidable for the unique solution of the inverse problem and the uncertainty of measurements and model assumptions. This study focused on the use of agronomy mechanism knowledge to restrict and remove the ill-posed inversion results. For this purpose, the inversion results obtained using the PROSAIL model alone (NAMK) and linked with agronomic mechanism knowledge (AMK) were compared. The results showed that AMK did not significantly improve the accuracy of LAI inversion. LAI was estimated with high accuracy, and there was no significant improvement after considering AMK. The validation results of the determination coefficient (R2) and the corresponding root mean square error (RMSE) between measured LAI and estimated LAI were 0.635 and 1.022 for NAMK, and 0.637 and 0.999 for AMK, respectively. LCC estimation was significantly improved with agronomy mechanism knowledge; the R2 and RMSE values were 0.377 and 14.495 μg cm-2 for NAMK, and 0.503 and 10.661 μg cm-2 for AMK, respectively. Results of the comparison demonstrated the need for agronomy mechanism knowledge in radiative transfer model inversion.

A nodal method applied to a diffusion problem with generalized coefficients

International Nuclear Information System (INIS)

Laazizi, A.; Guessous, N.

1999-01-01

In this paper, we consider second order neutrons diffusion problem with coefficients in L ∞ (Ω). Nodal method of the lowest order is applied to approximate the problem's solution. The approximation uses special basis functions in which the coefficients appear. The rate of convergence obtained is O(h 2 ) in L 2 (Ω), with a free rectangular triangulation. (authors)

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

Application of inverse models and XRD analysis to the determination of Ti-17 {beta}-phase coefficients of thermal expansion

Energy Technology Data Exchange (ETDEWEB)

Freour, S. [GeM, Institut de Recherche en Genie Civil et Mecanique (UMR CNRS 6183), Universite de Nantes, Ecole Centrale de Nantes, 37 Boulevard de l' Universite, BP 406, 44 602 Saint-Nazaire cedex (France)]. E-mail: freour@crttsn.univ-nantes.fr; Gloaguen, D. [GeM, Institut de Recherche en Genie Civil et Mecanique (UMR CNRS 6183), Universite de Nantes, Ecole Centrale de Nantes, 37 Boulevard de l' Universite, BP 406, 44 602 Saint-Nazaire cedex (France); Francois, M. [Laboratoire des Systemes Mecaniques et d' Ingenierie Simultanee (LASMIS FRE CNRS 2719), Universite de Technologie de Troyes, 12 Rue Marie Curie, BP 2060, 10010 Troyes (France); Guillen, R. [GeM, Institut de Recherche en Genie Civil et Mecanique (UMR CNRS 6183), Universite de Nantes, Ecole Centrale de Nantes, 37 Boulevard de l' Universite, BP 406, 44 602 Saint-Nazaire cedex (France)

2006-04-15

scope of this work is the determination of the coefficients of thermal expansion of the Ti-17 {beta}-phase. A rigorous inverse thermo-elastic self-consistent scale transition micro-mechanical model extended to multi-phase materials was used. The experimental data required for the application of the inverse method were obtained from both the available literature and especially dedicated X-ray diffraction lattice strain measurements performed on the studied ({alpha} + {beta}) two-phase titanium alloy.

Application of inverse models and XRD analysis to the determination of Ti-17 beta-phase Coefficients of Thermal Expansion

OpenAIRE

Fréour , Sylvain; Gloaguen , David; François , Marc; Guillén , Ronald

2006-01-01

International audience; The scope of this work is the determination of the coefficients of thermal expansion of the Ti-17 beta-phase. A rigorous inverse thermo-elastic self-consistent scale transition inicro-mechanical model extended to multi-phase materials was used. The experimental data required for the application of the inverse method were obtained from both the available literature and especially dedicated X-ray diffraction lattice strain measurements performed on the studied (alpha + b...

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

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.

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.

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.

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...

Identifying the principal coefficient of parabolic equations with non-divergent form

International Nuclear Information System (INIS)

Jiang, L S; Bian, B J

2005-01-01

We deal with an inverse problem of determining a coefficient a(x, t) of principal part for second order parabolic equations with non-divergent form when the solution is known. Such a problem has important applications in a large fields of applied science. We propose a well-posed approximate algorithm to identify the coefficient. The existence, uniqueness and stability of such solutions a(x, t) are proved. A necessary condition which is a couple system of a parabolic equation and a parabolic variational inequality is deduced. Our numerical simulations show that the coefficient is recovered very well

Identifying the principal coefficient of parabolic equations with non-divergent form

Science.gov (United States)

Jiang, L. S.; Bian, B. J.

2005-01-01

We deal with an inverse problem of determining a coefficient a(x, t) of principal part for second order parabolic equations with non-divergent form when the solution is known. Such a problem has important applications in a large fields of applied science. We propose a well-posed approximate algorithm to identify the coefficient. The existence, uniqueness and stability of such solutions a(x, t) are proved. A necessary condition which is a couple system of a parabolic equation and a parabolic variational inequality is deduced. Our numerical simulations show that the coefficient is recovered very well.

Riesz Frames and Approximation of the Frame Coefficients

DEFF Research Database (Denmark)

Christensen, Ole

1996-01-01

A frame is a familyof elements in a Hilbert space with the propertythat every element in the Hilbert space can be written as a (infinite)linear combination of the frame elements. Frame theory describes howone can choose the corresponding coefficients, which are calledframe coefficients. From...... the mathematical point of view this isgratifying, but for applications it is a problem that the calculationrequires inversion of an operator on the Hilbert space.The projection method is introduced in order to avoid this problem.The basic idea is to consider finite subfamiliesof the frame and the orthogonal...... projection onto its span. Forfin QTR H,P_nf has a representation as a linear combinationof f_i,i=1,2,..,n, and the corresponding coefficients can be calculatedusing finite dimensional methods. We find conditions implying that thosecoefficients converge to the correct frame coefficients as n goes...

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

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.

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.

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)

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.

Riesz frames and approximation of the frame coefficients

DEFF Research Database (Denmark)

Casazza, P.; Christensen, Ole

1998-01-01

A frame is a fmaily {f i } i=1 ∞ of elements in a Hilbert space with the property that every element in can be written as a (infinite) linear combination of the frame elements. Frame theory describes how one can choose the corresponding coefficients, which are called frame coefficients. From...... the mathematical point of view this is gratifying, but for applications it is a problem that the calculation requires inversion of an operator on . The projection method is introduced in order to avoid this problem. The basic idea is to consider finite subfamilies {f i } i=1 n of the frame and the orthogonal...... projection Pn onto its span. For has a representation as a linear combination of fi, i=1,2,..., n and the corresponding coefficients can be calculated using finite dimensional methods. We find conditions implying that those coefficients converge to the correct frame coefficients as n→∞, in which case we have...

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

Variable-coefficient nonisospectral Toda lattice hierarchy and its

Indian Academy of Sciences (India)

In this paper, a hierarchy of nonisospectral equations with variable coefficients is derived from the compatibility condition of Toda spectral problem and its time evolution. In order to solve the derived Toda lattice hierarchy, the inverse scattering transformation is utilized. As a result, new and more general exact solutions are ...

Hyperbolic systems with analytic coefficients well-posedness of the Cauchy problem

CERN Document Server

Nishitani, Tatsuo

2014-01-01

This monograph focuses on the well-posedness of the Cauchy problem for linear hyperbolic systems with matrix coefficients. Mainly two questions are discussed: (A) Under which conditions on lower order terms is the Cauchy problem well posed? (B) When is the Cauchy problem well posed for any lower order term? For first order two by two systems with two independent variables with real analytic coefficients, we present complete answers for both (A) and (B). For first order systems with real analytic coefficients we prove general necessary conditions for question (B) in terms of minors of the principal symbols. With regard to sufficient conditions for (B), we introduce hyperbolic systems with nondegenerate characteristics, which contains strictly hyperbolic systems, and prove that the Cauchy problem for hyperbolic systems with nondegenerate characteristics is well posed for any lower order term. We also prove that any hyperbolic system which is close to a hyperbolic system with a nondegenerate characteristic of mu...

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.

Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients

KAUST Repository

Bonito, Andrea; DeVore, Ronald A.; Nochetto, Ricardo H.

2013-01-01

Elliptic PDEs with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electromagnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the L∞ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an Lq norm with q < ∞ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis. © 2013 Societ y for Industrial and Applied Mathematics.

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.

Space-dependent perfusion coefficient estimation in a 2D bioheat transfer problem

Science.gov (United States)

Bazán, Fermín S. V.; Bedin, Luciano; Borges, Leonardo S.

2017-05-01

In this work, a method for estimating the space-dependent perfusion coefficient parameter in a 2D bioheat transfer model is presented. In the method, the bioheat transfer model is transformed into a time-dependent semidiscrete system of ordinary differential equations involving perfusion coefficient values as parameters, and the estimation problem is solved through a nonlinear least squares technique. In particular, the bioheat problem is solved by the method of lines based on a highly accurate pseudospectral approach, and perfusion coefficient values are estimated by the regularized Gauss-Newton method coupled with a proper regularization parameter. The performance of the method on several test problems is illustrated numerically.

Software tool for resolution of inverse problems using artificial intelligence techniques: an application in neutron spectrometry

International Nuclear Information System (INIS)

Castaneda M, V. H.; Martinez B, M. R.; Solis S, L. O.; Castaneda M, R.; Leon P, A. A.; Hernandez P, C. F.; Espinoza G, J. G.; Ortiz R, J. M.; Vega C, H. R.; Mendez, R.; Gallego, E.; Sousa L, M. A.

2016-10-01

The Taguchi methodology has proved to be highly efficient to solve inverse problems, in which the values of some parameters of the model must be obtained from the observed data. There are intrinsic mathematical characteristics that make a problem known as inverse. Inverse problems appear in many branches of science, engineering and mathematics. To solve this type of problem, researches have used different techniques. Recently, the use of techniques based on Artificial Intelligence technology is being explored by researches. This paper presents the use of a software tool based on artificial neural networks of generalized regression in the solution of inverse problems with application in high energy physics, specifically in the solution of the problem of neutron spectrometry. To solve this problem we use a software tool developed in the Mat Lab programming environment, which employs a friendly user interface, intuitive and easy to use for the user. This computational tool solves the inverse problem involved in the reconstruction of the neutron spectrum based on measurements made with a Bonner spheres spectrometric system. Introducing this information, the neural network is able to reconstruct the neutron spectrum with high performance and generalization capability. The tool allows that the end user does not require great training or technical knowledge in development and/or use of software, so it facilitates the use of the program for the resolution of inverse problems that are in several areas of knowledge. The techniques of Artificial Intelligence present singular veracity to solve inverse problems, given the characteristics of artificial neural networks and their network topology, therefore, the tool developed has been very useful, since the results generated by the Artificial Neural Network require few time in comparison to other techniques and are correct results comparing them with the actual data of the experiment. (Author)

Conditional stability and uniqueness for determining two coefficients in a hyperbolic–parabolic system

International Nuclear Information System (INIS)

Wu, Bin; Liu, Jijun

2011-01-01

We study the inverse problem of determining two spatially varying coefficients in a thermoelastic model with the following observation data: displacement in a subdomain ω satisfying ∂ω superset of ∂Ω along a sufficiently large time interval, both displacement and temperature at a suitable time over the whole spatial domain. Based on a Carleman estimate on the hyperbolic–parabolic system, we prove the Lipschitz stability and the uniqueness for this inverse problem under some a priori information

Inverse source problem and null controllability for multidimensional parabolic operators of Grushin type

International Nuclear Information System (INIS)

Beauchard, K; Cannarsa, P; Yamamoto, M

2014-01-01

The approach to Lipschitz stability for uniformly parabolic equations introduced by Imanuvilov and Yamamoto in 1998 based on Carleman estimates, seems hard to apply to the case of Grushin-type operators of interest to this paper. Indeed, such estimates are still missing for parabolic operators degenerating in the interior of the space domain. Nevertheless, we are able to prove Lipschitz stability results for inverse source problems for such operators, with locally distributed measurements in an arbitrary space dimension. For this purpose, we follow a mixed strategy which combines the approach due to Lebeau and Robbiano, relying on Fourier decomposition and Carleman inequalities for heat equations with non-smooth coefficients (solved by the Fourier modes). As a corollary, we obtain a direct proof of the observability of multidimensional Grushin-type parabolic equations, with locally distributed observations—which is equivalent to null controllability with locally distributed controls. (paper)

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.

Approximate Global Convergence and Quasi-Reversibility for a Coefficient Inverse Problem with Backscattering Data

Science.gov (United States)

2011-04-01

L1u. Assume that geodesic lines, generated by the eikonal equation corresponding to the function c (x) are regular, i.e. any two points in R3 can be...source x0 is located far from Ω, then similarly with (107) ∆l (x, x0) ≈ 0 in Ω. The function l (x, x0) satisfies the eikonal equation [38] |∇xl (x, x0...called “inverse kinematic problem” which aims to recover the function c (x) from the eikonal equation assuming that the function l (x, x0) is known for

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

KAUST Repository

Aldoghaither, Abeer

2015-11-12

Fractional calculus has been introduced as an e cient tool for modeling physical phenomena, thanks to its memory and hereditary properties. For example, fractional models have been successfully used to describe anomalous di↵usion processes such as contaminant transport in soil, oil flow in porous media, and groundwater flow. These models capture important features of particle transport such as particles with velocity variations and long-rest periods. Mathematical modeling of physical phenomena requires the identification of pa- rameters and variables from available measurements. This is referred to as an inverse problem. In this work, we are interested in studying theoretically and numerically inverse problems for space Fractional Advection-Dispersion Equation (FADE), which is used to model solute transport in porous media. Identifying parameters for such an equa- tion is important to understand how chemical or biological contaminants are trans- ported throughout surface aquifer systems. For instance, an estimate of the di↵eren- tiation order in groundwater contaminant transport model can provide information about soil properties, such as the heterogeneity of the medium. Our main contribution is to propose a novel e cient algorithm based on modulat-ing functions to estimate the coe cients and the di↵erentiation order for space FADE, which can be extended to general fractional Partial Di↵erential Equation (PDE). We also show how the method can be applied to the source inverse problem. This work is divided into two parts: In part I, the proposed method is described and studied through an extensive numerical analysis. The local convergence of the proposed two-stage algorithm is proven for 1D space FADE. The properties of this method are studied along with its limitations. Then, the algorithm is generalized to the 2D FADE. In part II, we analyze direct and inverse source problems for a space FADE. The problem consists of recovering the source term using final

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.

Microwave photonic filters with negative coefficients based on phase inversion in an electro-optic modulator.

Science.gov (United States)

Capmany, José; Pastor, Daniel; Martinez, Alfonso; Ortega, Beatriz; Sales, Salvador

2003-08-15

We report on a novel technical approach to the implementation of photonic rf filters that is based on the pi phase inversion that a rf modulating signal suffers in an electro-optic Mach-Zehnder modulator, which depends on whether the positive or the negative linear slope of the signal's modulation transfer function is employed. Experimental evidence is provided of the implementation of filters with negative coefficients that shows excellent agreement with results predicted by the theory.

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

Estimation of interfacial heat transfer coefficient in inverse heat conduction problems based on artificial fish swarm algorithm

Science.gov (United States)

Wang, Xiaowei; Li, Huiping; Li, Zhichao

2018-04-01

The interfacial heat transfer coefficient (IHTC) is one of the most important thermal physical parameters which have significant effects on the calculation accuracy of physical fields in the numerical simulation. In this study, the artificial fish swarm algorithm (AFSA) was used to evaluate the IHTC between the heated sample and the quenchant in a one-dimensional heat conduction problem. AFSA is a global optimization method. In order to speed up the convergence speed, a hybrid method which is the combination of AFSA and normal distribution method (ZAFSA) was presented. The IHTC evaluated by ZAFSA were compared with those attained by AFSA and the advanced-retreat method and golden section method. The results show that the reasonable IHTC is obtained by using ZAFSA, the convergence of hybrid method is well. The algorithm based on ZAFSA can not only accelerate the convergence speed, but also reduce the numerical oscillation in the evaluation of IHTC.

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.

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...

Problems is applying new internal dose coefficients to radiation control

Energy Technology Data Exchange (ETDEWEB)

Sato, Yuichi [Oarai Laboratory, Chiyoda Technol Corporation, Ibaraki (Japan)

1998-06-01

The author discussed problems concerning the conceivable influence in the radiation control and those newly developing when the new internal dose coefficients are applied in the law in the future. For the conceivable influence, the occupational and public exposure was discussed: In the former, the effective dose equivalent limit (at present, 50 mSv/y) was thought to be reduced and in the latter, the limit to be obscure although it might be more greatly influenced by the new coefficients. For newly developing problems, since the new biological model which is more realistic was introduced for calculation of the internal dose and made the calculation more complicated, use of computer is requisite. The effective dose of the internal exposure in the individual monitoring should be conveniently calculated as done at present even after application of the new coefficients. For calculation of the effective dose of the internal exposure, there are such problems as correction of the inhaled particle size and of the individual personal parameter. A model calculation of residual rate in the chest where the respiratory tract alone participated was presented as an example but for the whole body, more complicated functions were pointed out necessary. The concept was concluded to be incorporated in the law in a convenient and easy manner and a software for calculation of internal dose using the new coefficients was wanted. (K.H.)

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

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

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.

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.

Materials analysis using x-ray linear attenuation coefficient measurements at four photon energies

International Nuclear Information System (INIS)

Midgley, S M

2005-01-01

The analytical properties of an accurate parameterization scheme for the x-ray linear attenuation coefficient are examined. The parameterization utilizes an additive combination of N compositional- and energy-dependent coefficients. The former were derived from a parameterization of elemental cross-sections using a polynomial in atomic number. The compositional-dependent coefficients are referred to as the mixture parameters, representing the electron density and higher order statistical moments describing elemental distribution. Additivity is an important property of the parameterization, allowing measured x-ray linear attenuation coefficients to be written as linear simultaneous equations, and then solved for the unknown coefficients. The energy-dependent coefficients can be determined by calibration from measurements with materials of known composition. The inverse problem may be utilized for materials analysis, whereby the simultaneous equations represent multi-energy linear attenuation coefficient measurements, and are solved for the mixture parameters. For in vivo studies, the choice of measurement energies is restricted to the diagnostic region (approximately 20 keV to 150 keV), where the parameterization requires N ≥ 4 energies. We identify a mathematical pathology that must be overcome in order to solve the inverse problem in this energy regime. An iterative inversion strategy is presented for materials analysis using four or more measurements, and then tested against real data obtained at energies 32 keV to 66 keV. The results demonstrate that it is possible to recover the electron density to within ±4% and fourth mixture parameter. It is also a key finding that the second and third mixture parameters cannot be recovered, as they are of minor importance in the parameterization at diagnostic x-ray energies

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.

Three-dimensional inverse transient heat transfer analysis of thick functionally graded plates

Energy Technology Data Exchange (ETDEWEB)

Haghighi, M.R. Golbahar; Malekzadeh, P. [Department of Mechanical Engineering, School of Engineering, Persian Gulf University, Bushehr 75168 (Iran); Eghtesad, M. [Department of Mechanical Engineering, School of Engineering, Shiraz University, Shiraz 71348-51154 (Iran); Necsulescu, D.S. [Department of Mechanical Engineering, Faculty of Engineering, University of Ottawa, Ottawa, Ontario (Canada)

2009-03-15

In this paper, a three-dimensional transient inverse heat conduction (IHC) procedure is presented to estimate the unknown boundary heat flux of thick functionally graded (FG) plates. For this purpose, the conjugate gradient method (CGM) in conjunction with adjoint problem is used. A recently developed three-dimensional efficient hybrid method is employed to solve variable-coefficient initial-boundary-value differential equations of direct problem as a part of the inverse solution. The accuracy of the inverse analysis is examined by simulating the exact and noisy data for problems with different types of boundary conditions and material properties. In addition to rectangular domain, skew plates are considered. The results obtained show good accuracy for the estimation of boundary heat fluxes. (author)

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)

Propagation of Singularities and Some Inverse Problems in Wave Propagation

National Research Council Canada - National Science Library

Symes, William W

1989-01-01

... in various useful coefficient classes, separation of scales,...We explain the essential role of travel time in the study of these problems, and show how its function may be generalized to multidimensional (i.e. non-layered) problems.

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.

Fuzzy solution of the linear programming problem with interval coefficients in the constraints

OpenAIRE

Dorota Kuchta

2005-01-01

A fuzzy concept of solving the linear programming problem with interval coefficients is proposed. For each optimism level of the decision maker (where the optimism concerns the certainty that no errors have been committed in the estimation of the interval coefficients and the belief that optimistic realisations of the interval coefficients will occur) another interval solution of the problem will be generated and the decision maker will be able to choose the final solution having a complete v...

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)

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.

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.

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.

Theoretical stability in coefficient inverse problems for general hyperbolic equations with numerical reconstruction

Science.gov (United States)

Yu, Jie; Liu, Yikan; Yamamoto, Masahiro

2018-04-01

In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic operators and an auxiliary Carleman estimate, we establish local Hölder stability with either partial boundary or interior measurements under certain geometrical conditions. For numerical reconstruction, we minimize a Tikhonov functional which penalizes the gradient of the unknown function. Based on the resulting variational equation, we design an iteration method which is updated by solving a Poisson equation at each step. One-dimensional prototype examples illustrate the numerical performance of the proposed iteration.

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.

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 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.

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

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).

A Compensatory Approach to Multiobjective Linear Transportation Problem with Fuzzy Cost Coefficients

Directory of Open Access Journals (Sweden)

Hale Gonce Kocken

2011-01-01

Full Text Available This paper deals with the Multiobjective Linear Transportation Problem that has fuzzy cost coefficients. In the solution procedure, many objectives may conflict with each other; therefore decision-making process becomes complicated. And also due to the fuzziness in the costs, this problem has a nonlinear structure. In this paper, fuzziness in the objective functions is handled with a fuzzy programming technique in the sense of multiobjective approach. And then we present a compensatory approach to solve Multiobjective Linear Transportation Problem with fuzzy cost coefficients by using Werner's and operator. Our approach generates compromise solutions which are both compensatory and Pareto optimal. A numerical example has been provided to illustrate the problem.

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)

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.

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)

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

Accounting for Antenna in Half-Space Fresnel Coefficient Estimation

Directory of Open Access Journals (Sweden)

A. D'Alterio

2012-01-01

Full Text Available The problem of retrieving the Fresnel reflection coefficients of a half-space medium starting from measurements collected under a reflection mode multistatic configuration is dealt with. According to our previous results, reflection coefficient estimation is cast as the inversion of linear operator. However, here, we take a step ahead towards more realistic scenarios as the role of antennas (both transmitting and receiving is embodied in the estimation procedure. Numerical results are presented to show the effectiveness of the method for different types of half-space media.

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.

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.

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.

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.

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

An inverse method for non linear ablative thermics with experimentation of automatic differentiation

Energy Technology Data Exchange (ETDEWEB)

Alestra, S [Simulation Information Technology and Systems Engineering, EADS IW Toulouse (France); Collinet, J [Re-entry Systems and Technologies, EADS ASTRIUM ST, Les Mureaux (France); Dubois, F [Professor of Applied Mathematics, Conservatoire National des Arts et Metiers Paris (France)], E-mail: stephane.alestra@eads.net, E-mail: jean.collinet@astrium.eads.net, E-mail: fdubois@cnam.fr

2008-11-01

Thermal Protection System is a key element for atmospheric re-entry missions of aerospace vehicles. The high level of heat fluxes encountered in such missions has a direct effect on mass balance of the heat shield. Consequently, the identification of heat fluxes is of great industrial interest but is in flight only available by indirect methods based on temperature measurements. This paper is concerned with inverse analyses of highly evolutive heat fluxes. An inverse problem is used to estimate transient surface heat fluxes (convection coefficient), for degradable thermal material (ablation and pyrolysis), by using time domain temperature measurements on thermal protection. The inverse problem is formulated as a minimization problem involving an objective functional, through an optimization loop. An optimal control formulation (Lagrangian, adjoint and gradient steepest descent method combined with quasi-Newton method computations) is then developed and applied, using Monopyro, a transient one-dimensional thermal model with one moving boundary (ablative surface) that has been developed since many years by ASTRIUM-ST. To compute numerically the adjoint and gradient quantities, for the inverse problem in heat convection coefficient, we have used both an analytical manual differentiation and an Automatic Differentiation (AD) engine tool, Tapenade, developed at INRIA Sophia-Antipolis by the TROPICS team. Several validation test cases, using synthetic temperature measurements are carried out, by applying the results of the inverse method with minimization algorithm. Accurate results of identification on high fluxes test cases, and good agreement for temperatures restitutions, are obtained, without and with ablation and pyrolysis, using bad fluxes initial guesses. First encouraging results with an automatic differentiation procedure are also presented in this paper.

Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients

KAUST Repository

Ayuso Dios, Blanca

2013-10-30

We introduce and analyze two-level and multilevel preconditioners for a family of Interior Penalty (IP) discontinuous Galerkin (DG) discretizations of second order elliptic problems with large jumps in the diffusion coefficient. Our approach to IPDG-type methods is based on a splitting of the DG space into two components that are orthogonal in the energy inner product naturally induced by the methods. As a result, the methods and their analysis depend in a crucial way on the diffusion coefficient of the problem. The analysis of the proposed preconditioners is presented for both symmetric and non-symmetric IP schemes; dealing simultaneously with the jump in the diffusion coefficient and the non-nested character of the relevant discrete spaces presents additional difficulties in the analysis, which precludes a simple extension of existing results. However, we are able to establish robustness (with respect to the diffusion coefficient) and near-optimality (up to a logarithmic term depending on the mesh size) for both two-level and BPX-type preconditioners, by using a more refined Conjugate Gradient theory. Useful by-products of the analysis are the supporting results on the construction and analysis of simple, efficient and robust two-level and multilevel preconditioners for non-conforming Crouzeix-Raviart discretizations of elliptic problems with jump coefficients. Following the analysis, we present a sequence of detailed numerical results which verify the theory and illustrate the performance of the methods. © 2013 American Mathematical Society.

Multilevel preconditioners for discontinuous, Galerkin approximations of elliptic problems, with jump coefficients

KAUST Repository

Ayuso Dios, Blanca; Holst, Michael; Zhu, Yunrong; Zikatanov, Ludmil

2013-01-01

We introduce and analyze two-level and multilevel preconditioners for a family of Interior Penalty (IP) discontinuous Galerkin (DG) discretizations of second order elliptic problems with large jumps in the diffusion coefficient. Our approach to IPDG-type methods is based on a splitting of the DG space into two components that are orthogonal in the energy inner product naturally induced by the methods. As a result, the methods and their analysis depend in a crucial way on the diffusion coefficient of the problem. The analysis of the proposed preconditioners is presented for both symmetric and non-symmetric IP schemes; dealing simultaneously with the jump in the diffusion coefficient and the non-nested character of the relevant discrete spaces presents additional difficulties in the analysis, which precludes a simple extension of existing results. However, we are able to establish robustness (with respect to the diffusion coefficient) and near-optimality (up to a logarithmic term depending on the mesh size) for both two-level and BPX-type preconditioners, by using a more refined Conjugate Gradient theory. Useful by-products of the analysis are the supporting results on the construction and analysis of simple, efficient and robust two-level and multilevel preconditioners for non-conforming Crouzeix-Raviart discretizations of elliptic problems with jump coefficients. Following the analysis, we present a sequence of detailed numerical results which verify the theory and illustrate the performance of the methods. © 2013 American Mathematical Society.

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

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

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

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

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

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.)

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.

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...

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

Complexity analysis of accelerated MCMC methods for Bayesian inversion

International Nuclear Information System (INIS)

Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M

2013-01-01

The Bayesian approach to inverse problems, in which the posterior probability distribution on an unknown field is sampled for the purposes of computing posterior expectations of quantities of interest, is starting to become computationally feasible for partial differential equation (PDE) inverse problems. Balancing the sources of error arising from finite-dimensional approximation of the unknown field, the PDE forward solution map and the sampling of the probability space under the posterior distribution are essential for the design of efficient computational Bayesian methods for PDE inverse problems. We study Bayesian inversion for a model elliptic PDE with an unknown diffusion coefficient. We provide complexity analyses of several Markov chain Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the Bayesian posterior distribution, given data δ. Particular attention is given to bounds on the overall work required to achieve a prescribed error level ε. Specifically, we first bound the computational complexity of ‘plain’ MCMC, based on combining MCMC sampling with linear complexity multi-level solvers for elliptic PDE. Our (new) work versus accuracy bounds show that the complexity of this approach can be quite prohibitive. Two strategies for reducing the computational complexity are then proposed and analyzed: first, a sparse, parametric and deterministic generalized polynomial chaos (gpc) ‘surrogate’ representation of the forward response map of the PDE over the entire parameter space, and, second, a novel multi-level Markov chain Monte Carlo strategy which utilizes sampling from a multi-level discretization of the posterior and the forward PDE. For both of these strategies, we derive asymptotic bounds on work versus accuracy, and hence asymptotic bounds on the computational complexity of the algorithms. In particular, we provide sufficient conditions on the regularity of the unknown coefficients of the PDE and on the

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)

Multilevel Methods for Elliptic Problems with Highly Varying Coefficients on Nonaligned Coarse Grids

Energy Technology Data Exchange (ETDEWEB)

Scheichl, Robert [Univ. of Bath (United Kingdom). Dept. of Mathematical Sciences; Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Zikatanov, Ludmil T. [Pennsylvania State Univ., University Park, PA (United States). Dept. of Mathematics

2012-06-21

We generalize the analysis of classical multigrid and two-level overlapping Schwarz methods for 2nd order elliptic boundary value problems to problems with large discontinuities in the coefficients that are not resolved by the coarse grids or the subdomain partition. The theoretical results provide a recipe for designing hierarchies of standard piecewise linear coarse spaces such that the multigrid convergence rate and the condition number of the Schwarz preconditioned system do not depend on the coefficient variation or on any mesh parameters. One assumption we have to make is that the coarse grids are sufficiently fine in the vicinity of cross points or where regions with large diffusion coefficients are separated by a narrow region where the coefficient is small. We do not need to align them with possible discontinuities in the coefficients. The proofs make use of novel stable splittings based on weighted quasi-interpolants and weighted Poincaré-type inequalities. Finally, numerical experiments are included that illustrate the sharpness of the theoretical bounds and the necessity of the technical assumptions.

Estimating surface acoustic impedance with the inverse method.

Science.gov (United States)

Piechowicz, Janusz

2011-01-01

Sound field parameters are predicted with numerical methods in sound control systems, in acoustic designs of building and in sound field simulations. Those methods define the acoustic properties of surfaces, such as sound absorption coefficients or acoustic impedance, to determine boundary conditions. Several in situ measurement techniques were developed; one of them uses 2 microphones to measure direct and reflected sound over a planar test surface. Another approach is used in the inverse boundary elements method, in which estimating acoustic impedance of a surface is expressed as an inverse boundary problem. The boundary values can be found from multipoint sound pressure measurements in the interior of a room. This method can be applied to arbitrarily-shaped surfaces. This investigation is part of a research programme on using inverse methods in industrial room acoustics.

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

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

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

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...

Geopotential coefficient determination and the gravimetric boundary value problem: A new approach

Science.gov (United States)

Sjoeberg, Lars E.

1989-01-01

New integral formulas to determine geopotential coefficients from terrestrial gravity and satellite altimetry data are given. The formulas are based on the integration of data over the non-spherical surface of the Earth. The effect of the topography to low degrees and orders of coefficients is estimated numerically. Formulas for the solution of the gravimetric boundary value problem are derived.

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

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 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)

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)

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.

A Novel Inversion Method of Manufacturing Flaws in the Packaging of Conformal Load-Bearing Antenna Structure

Directory of Open Access Journals (Sweden)

P. Li

2015-01-01

Full Text Available Composite material is widely used in the conformal load-bearing antenna structure (CLAS, and the manufacturing flaws in the packaging process of the CLAS will lead to the degradation of its wave-transparent property. For this problem, a novel inverse method of the flaw’s dimension by antenna-radome system’s far field data has been proposed. Two steps are included in the inversion: the first one is the inversion from the far filed data to the transmission coefficient of the CLAS’s radome; the second one is the inversion from the transmission coefficient to the flaw’s dimension. The inversion also has a good potential for the separable multilayer composite material radome. A 12.5 GHz CLAS with microstrip antenna array is used in the simulation, which indicates the effectiveness of the novel inversion method. Finally, the error analysis of the inversion method is presented by numerical simulation; the results is that the inversed error could be less than 10%, if the measurement error of far field data is less than 0.45 dB in amplitude and ±5° in phase.

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

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

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 novel inverse numerical modeling method for the estimation of water and salt mass transfer coefficients during ultrasonic assisted-osmotic dehydration of cucumber cubes.

Science.gov (United States)

Kiani, Hosein; Karimi, Farzaneh; Labbafi, Mohsen; Fathi, Morteza

2018-06-01

The objective of this paper was to study the moisture and salt diffusivity during ultrasonic assisted-osmotic dehydration of cucumbers. Experimental measurements of moisture and salt concentration versus time were carried out and an inverse numerical method was performed by coupling a CFD package (OpenFOAM) with a parameter estimation software (DAKOTA) to determine mass transfer coefficients. A good agreement between experimental and numerical results was observed. Mass transfer coefficients were from 3.5 × 10 -9 to 7 × 10 -9  m/s for water and from 4.8 × 10 -9  m/s to 7.4 × 10 -9  m/s for salt at different conditions (diffusion coefficients of around 3.5 × 10 -12 -11.5 × 10 -12  m 2 /s for water and 5 × 10 -12  m/s-12 × 10 -12  m 2 /s for salt). Ultrasound irradiation could increase the mass transfer coefficient. The values obtained by this method were closer to the actual data. The inverse simulation method can be an accurate technique to study the mass transfer phenomena during food processing. Copyright © 2018 Elsevier B.V. All rights reserved.

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.

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

Nonlinear perturbations of systems of partial differential equations with constant coefficients

Directory of Open Access Journals (Sweden)

Carmen J. Vanegas

2000-01-01

Full Text Available In this article, we show the existence of solutions to boundary-value problems, consisting of nonlinear systems of partial differential equations with constant coefficients. For this purpose, we use the right inverse of an associated operator and a fix point argument. As illustrations, we apply this method to Helmholtz equations and to second order systems of elliptic equations.

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...

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

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.

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)

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.

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.

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 \

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

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.

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

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

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.)

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.

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

Direct inversion of circulation and mixing from tracer measurements – Part 1: Method

Directory of Open Access Journals (Sweden)

T. von Clarmann

2016-11-01

Full Text Available From a series of zonal mean global stratospheric tracer measurements sampled in altitude vs. latitude, circulation and mixing patterns are inferred by the inverse solution of the continuity equation. As a first step, the continuity equation is written as a tendency equation, which is numerically integrated over time to predict a later atmospheric state, i.e., mixing ratio and air density. The integration is formally performed by the multiplication of the initially measured atmospheric state vector by a linear prediction operator. Further, the derivative of the predicted atmospheric state with respect to the wind vector components and mixing coefficients is used to find the most likely wind vector components and mixing coefficients which minimize the residual between the predicted atmospheric state and the later measurement of the atmospheric state. Unless multiple tracers are used, this inversion problem is under-determined, and dispersive behavior of the prediction further destabilizes the inversion. Both these problems are addressed by regularization. For this purpose, a first-order smoothness constraint has been chosen. The usefulness of this method is demonstrated by application to various tracer measurements recorded with the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS. This method aims at a diagnosis of the Brewer–Dobson circulation without involving the concept of the mean age of stratospheric air, and related problems like the stratospheric tape recorder, or intrusions of mesospheric air into the stratosphere.

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.

Estimation of internal heat transfer coefficients and detection of rib positions in gas turbine blades from transient surface temperature measurements

International Nuclear Information System (INIS)

Heidrich, P; Wolfersdorf, J v; Schmidt, S; Schnieder, M

2008-01-01

This paper describes a non-invasive, non-destructive, transient inverse measurement technique that allows one to determine internal heat transfer coefficients and rib positions of real gas turbine blades from outer surface temperature measurements after a sudden flow heating. The determination of internal heat transfer coefficients is important during the design process to adjust local heat transfer to spatial thermal load. The detection of rib positions is important during production to fulfill design and quality requirements. For the analysis the one-dimensional transient heat transfer problem inside of the turbine blade's wall was solved. This solution was combined with the Levenberg-Marquardt method to estimate the unknown boundary condition by an inverse technique. The method was tested with artificial data to determine uncertainties with positive results. Then experimental testing with a reference model was carried out. Based on the results, it is concluded that the presented inverse technique could be used to determine internal heat transfer coefficients and to detect rib positions of real turbine blades.

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 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.

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

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.

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

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.

Cybernetic group method of data handling (GMDH) statistical learning for hyperspectral remote sensing inverse problems in coastal ocean optics

Science.gov (United States)

Filippi, Anthony Matthew

For complex systems, sufficient a priori knowledge is often lacking about the mathematical or empirical relationship between cause and effect or between inputs and outputs of a given system. Automated machine learning may offer a useful solution in such cases. Coastal marine optical environments represent such a case, as the optical remote sensing inverse problem remains largely unsolved. A self-organizing, cybernetic mathematical modeling approach known as the group method of data handling (GMDH), a type of statistical learning network (SLN), was used to generate explicit spectral inversion models for optically shallow coastal waters. Optically shallow water light fields represent a particularly difficult challenge in oceanographic remote sensing. Several algorithm-input data treatment combinations were utilized in multiple experiments to automatically generate inverse solutions for various inherent optical property (IOP), bottom optical property (BOP), constituent concentration, and bottom depth estimations. The objective was to identify the optimal remote-sensing reflectance Rrs(lambda) inversion algorithm. The GMDH also has the potential of inductive discovery of physical hydro-optical laws. Simulated data were used to develop generalized, quasi-universal relationships. The Hydrolight numerical forward model, based on radiative transfer theory, was used to compute simulated above-water remote-sensing reflectance Rrs(lambda) psuedodata, matching the spectral channels and resolution of the experimental Naval Research Laboratory Ocean PHILLS (Portable Hyperspectral Imager for Low-Light Spectroscopy) sensor. The input-output pairs were for GMDH and artificial neural network (ANN) model development, the latter of which was used as a baseline, or control, algorithm. Both types of models were applied to in situ and aircraft data. Also, in situ spectroradiometer-derived Rrs(lambda) were used as input to an optimization-based inversion procedure. Target variables

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

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.

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.

A model reduction approach to numerical inversion for a parabolic partial differential equation

International Nuclear Information System (INIS)

Borcea, Liliana; Druskin, Vladimir; Zaslavsky, Mikhail; Mamonov, Alexander V

2014-01-01

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss–Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments. (paper)

A model reduction approach to numerical inversion for a parabolic partial differential equation

Science.gov (United States)

Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail

2014-12-01

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.

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

Convergence of Cell Based Finite Volume Discretizations for Problems of Control in the Conduction Coefficients

DEFF Research Database (Denmark)

Evgrafov, Anton; Gregersen, Misha Marie; Sørensen, Mads Peter

2011-01-01

We present a convergence analysis of a cell-based finite volume (FV) discretization scheme applied to a problem of control in the coefficients of a generalized Laplace equation modelling, for example, a steady state heat conduction. Such problems arise in applications dealing with geometric optimal......, whereas the convergence of the coefficients happens only with respect to the "volumetric" Lebesgue measure. Additionally, depending on whether the stationarity conditions are stated for the discretized or the original continuous problem, two distinct concepts of stationarity at a discrete level arise. We...... provide characterizations of limit points, with respect to FV mesh size, of globally optimal solutions and two types of stationary points to the discretized problems. We illustrate the practical behaviour of our cell-based FV discretization algorithm on a numerical example....

Calculation of total number of disintegrations after intake of radioactive nuclides using the pseudo inverse matrix

International Nuclear Information System (INIS)

Noh, Si Wan; Sol, Jeong; Lee, Jai Ki; Lee, Jong Il; Kim, Jang Lyul

2012-01-01

Calculation of total number of disintegrations after intake of radioactive nuclides is indispensable to calculate a dose coefficient which means committed effective dose per unit activity (Sv/Bq). In order to calculate the total number of disintegrations analytically, Birch all's algorithm has been commonly used. As described below, an inverse matrix should be calculated in the algorithm. As biokinetic models have been complicated, however, the inverse matrix does not exist sometime and the total number of disintegrations cannot be calculated. Thus, a numerical method has been applied to DCAL code used to calculate dose coefficients in ICRP publication and IMBA code. In this study, however, we applied the pseudo inverse matrix to solve the problem that the inverse matrix does not exist for. In order to validate our method, the method was applied to two examples and the results were compared to the tabulated data in ICRP publication. MATLAB 2012a was used to calculate the total number of disintegrations and exp m and p inv MATLAB built in functions were employed

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.

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.

On the Quantum Inverse problem for the continuous Heisenberg spin chain with axial anisotropy

International Nuclear Information System (INIS)

Roy Chowdhury, A.; Chanda, P.K.

1986-06-01

We have considered the Quantum Inverse problem for the continuous form of Heisenberg spin chain with anisotropy. The form of quantum R-matrix, the commutation rules for the scattering data, and the explicit structure of the excitation spectrum are obtained. (author)

On the method of inverse scattering problem and Baecklund transformations for supersymmetric equations

International Nuclear Information System (INIS)

Chaichian, M.; Kulish, P. P.

1978-04-01

Supersymmetric Liouville and sine-Gordon equations are studied. We write down for these models the system of linear equations for which the method of inverse scattering problem should be applicable. Expressions for an infinite set of conserved currents are explicitly given. Supersymmetric Baecklund transformations and generalized conservation laws are constructed. (author)

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

KAUST Repository

Karve, Pranav M.

2014-12-28

© 2014, Springer International Publishing Switzerland. We discuss an optimization methodology for focusing wave energy to subterranean formations using strong motion actuators placed on the ground surface. The motivation stems from the desire to increase the mobility of otherwise entrapped oil. The goal is to arrive at the spatial and temporal description of surface sources that are capable of maximizing mobility in the target reservoir. The focusing problem is posed as an inverse source problem. The underlying wave propagation problems are abstracted in two spatial dimensions, and the semi-infinite extent of the physical domain is negotiated by a buffer of perfectly-matched-layers (PMLs) placed at the domain’s truncation boundary. We discuss two possible numerical implementations: Their utility for deciding the tempo-spatial characteristics of optimal wave sources is shown via numerical experiments. Overall, the simulations demonstrate the inverse source method’s ability to simultaneously optimize load locations and time signals leading to the maximization of energy delivery to a target formation.

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.

Self-diffusion coefficients and shear viscosity of inverse power fluids: from hard- to soft-spheres.

Science.gov (United States)

Heyes, D M; Brańka, A C

2008-07-21

Molecular dynamics computer simulation has been used to compute the self-diffusion coefficient, D, and shear viscosity, eta(s), of soft-sphere fluids, in which the particles interact through the soft-sphere or inverse power pair potential, phi(r) = epsilon(sigma/r)(n), where n measures the steepness or stiffness of the potential, and epsilon and sigma are a characteristic energy and distance, respectively. The simulations were carried out on monodisperse systems for a range of n values from the hard-sphere (n --> infinity) limit down to n = 4, and up to densities in excess of the fluid-solid co-existence value. A new analytical procedure is proposed which reproduces the transport coefficients at high densities, and can be used to extrapolate the data to densities higher than accurately accessible by simulation or experiment, and tending to the glass transition. This formula, DX(c-1) proportional, variant A/X + B, where c is an adjustable parameter, and X is either the packing fraction or the pressure, is a development of one proposed by Dymond. In the expression, -A/B is the value of X at the ideal glass transition (i.e., where D and eta(s)(-1) --> 0). Estimated values are presented for the packing fraction and the pressure at the glass transition for n values between the hard and soft particle limits. The above expression is also shown to reproduce the high density viscosity data of supercritical argon, krypton and nitrogen. Fits to the soft-sphere simulation transport coefficients close to solid-fluid co-existence are also made using the analytic form, ln(D) = alpha(X)X, and n-dependence of the alpha(X) is presented (X is either the packing fraction or the pressure).

Electrostatic point charge fitting as an inverse problem: Revealing the underlying ill-conditioning

International Nuclear Information System (INIS)

Ivanov, Maxim V.; Talipov, Marat R.; Timerghazin, Qadir K.

2015-01-01

Atom-centered point charge (PC) model of the molecular electrostatics—a major workhorse of the atomistic biomolecular simulations—is usually parameterized by least-squares (LS) fitting of the point charge values to a reference electrostatic potential, a procedure that suffers from numerical instabilities due to the ill-conditioned nature of the LS problem. To reveal the origins of this ill-conditioning, we start with a general treatment of the point charge fitting problem as an inverse problem and construct an analytical model with the point charges spherically arranged according to Lebedev quadrature which is naturally suited for the inverse electrostatic problem. This analytical model is contrasted to the atom-centered point-charge model that can be viewed as an irregular quadrature poorly suited for the problem. This analysis shows that the numerical problems of the point charge fitting are due to the decay of the curvatures corresponding to the eigenvectors of LS sum Hessian matrix. In part, this ill-conditioning is intrinsic to the problem and is related to decreasing electrostatic contribution of the higher multipole moments, that are, in the case of Lebedev grid model, directly associated with the Hessian eigenvectors. For the atom-centered model, this association breaks down beyond the first few eigenvectors related to the high-curvature monopole and dipole terms; this leads to even wider spread-out of the Hessian curvature values. Using these insights, it is possible to alleviate the ill-conditioning of the LS point-charge fitting without introducing external restraints and/or constraints. Also, as the analytical Lebedev grid PC model proposed here can reproduce multipole moments up to a given rank, it may provide a promising alternative to including explicit multipole terms in a force field

NUMERICAL ANALYSIS OF AN INVERSE PROBLEM ORIGINATED IN PHENOMENON OF POLLUTION AIR URBAN

Directory of Open Access Journals (Sweden)

Aníbal Coronel

2016-12-01

Full Text Available This paper presents the calibration study of a two - dimensional mathematical model for the problem of urban air pollution. It is mainly assumed that air pollution is afected by wind convection, diffusion and chemical reactions of pollutants. Consequently, a convection-diffusion-reaction equation is obtained as a direct problem. In the inverse problem, the determination of the diffusion is analyzed, assuming that one has an observation of the pollutants in a nite time. To solve it numerically the nite volume method is used, the least squares function is considered as cost function and the gradient is calculated with the sensitivity method.

Impact of External Pressure on the Heat Transfer Coefficient during Solidification of Al-A356 Alloy

DEFF Research Database (Denmark)

Jabbari, Masoud; Ilkhchy, A.Fardi; Moumani, E.

In this paper the interfacial heat transfer coefficient (IHTC) is correlated to applied external pressure, in which IHTC at the interface between A356 aluminum alloy and metallic mold during the solidification of the casting under different pressures were obtained using the Inverse Heat Conduction...... Problem (IHCP) method. The method covers the expedient of comparing theoretical and experimental thermal histories. Temperature profiles obtained from thermocouples were used in a finite difference heat flow program to estimate the transient heat transfer coefficients. The new simple formula was presented...

Cerebellum-inspired neural network solution of the inverse kinematics problem.

Science.gov (United States)

Asadi-Eydivand, Mitra; Ebadzadeh, Mohammad Mehdi; Solati-Hashjin, Mehran; Darlot, Christian; Abu Osman, Noor Azuan

2015-12-01

The demand today for more complex robots that have manipulators with higher degrees of freedom is increasing because of technological advances. Obtaining the precise movement for a desired trajectory or a sequence of arm and positions requires the computation of the inverse kinematic (IK) function, which is a major problem in robotics. The solution of the IK problem leads robots to the precise position and orientation of their end-effector. We developed a bioinspired solution comparable with the cerebellar anatomy and function to solve the said problem. The proposed model is stable under all conditions merely by parameter determination, in contrast to recursive model-based solutions, which remain stable only under certain conditions. We modified the proposed model for the simple two-segmented arm to prove the feasibility of the model under a basic condition. A fuzzy neural network through its learning method was used to compute the parameters of the system. Simulation results show the practical feasibility and efficiency of the proposed model in robotics. The main advantage of the proposed model is its generalizability and potential use in any robot.

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

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

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.

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.

Algebraic properties of generalized inverses

CERN Document Server

Cvetković‐Ilić, Dragana S

2017-01-01

This book addresses selected topics in the theory of generalized inverses. Following a discussion of the “reverse order law” problem and certain problems involving completions of operator matrices, it subsequently presents a specific approach to solving the problem of the reverse order law for {1} -generalized inverses. Particular emphasis is placed on the existence of Drazin invertible completions of an upper triangular operator matrix; on the invertibility and different types of generalized invertibility of a linear combination of operators on Hilbert spaces and Banach algebra elements; on the problem of finding representations of the Drazin inverse of a 2x2 block matrix; and on selected additive results and algebraic properties for the Drazin inverse. In addition to the clarity of its content, the book discusses the relevant open problems for each topic discussed. Comments on the latest references on generalized inverses are also included. Accordingly, the book will be useful for graduate students, Ph...

A direct sampling method to an inverse medium scattering problem

KAUST Repository

Ito, Kazufumi

2012-01-10

In this work we present a novel sampling method for time harmonic inverse medium scattering problems. It provides a simple tool to directly estimate the shape of the unknown scatterers (inhomogeneous media), and it is applicable even when the measured data are only available for one or two incident directions. A mathematical derivation is provided for its validation. Two- and three-dimensional numerical simulations are presented, which show that the method is accurate even with a few sets of scattered field data, computationally efficient, and very robust with respect to noises in the data. © 2012 IOP Publishing Ltd.

Limits to Nonlinear Inversion

DEFF Research Database (Denmark)

Mosegaard, Klaus

2012-01-01

For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...... pure meta-heuristics. We study problem-adapted inversion algorithms that exploit the knowledge of the smoothness of the misfit function of the problem. Optimal sampling strategies exist for such problems, but many of these problems remain hard. © 2012 Springer-Verlag....

The Prediction Properties of Inverse and Reverse Regression for the Simple Linear Calibration Problem

Science.gov (United States)

Parker, Peter A.; Geoffrey, Vining G.; Wilson, Sara R.; Szarka, John L., III; Johnson, Nels G.

2010-01-01

The calibration of measurement systems is a fundamental but under-studied problem within industrial statistics. The origins of this problem go back to basic chemical analysis based on NIST standards. In today's world these issues extend to mechanical, electrical, and materials engineering. Often, these new scenarios do not provide "gold standards" such as the standard weights provided by NIST. This paper considers the classic "forward regression followed by inverse regression" approach. In this approach the initial experiment treats the "standards" as the regressor and the observed values as the response to calibrate the instrument. The analyst then must invert the resulting regression model in order to use the instrument to make actual measurements in practice. This paper compares this classical approach to "reverse regression," which treats the standards as the response and the observed measurements as the regressor in the calibration experiment. Such an approach is intuitively appealing because it avoids the need for the inverse regression. However, it also violates some of the basic regression assumptions.

Inverse problems in machine learning: An application to brain activity interpretation

International Nuclear Information System (INIS)

Prato, M; Zanni, L

2008-01-01

In a typical machine learning problem one has to build a model from a finite training set which is able to generalize the properties characterizing the examples of the training set to new examples. The model has to reflect as much as possible the set of training examples but, especially in real-world problems in which the data are often corrupted by different sources of noise, it has to avoid a too strict dependence on the training examples themselves. Recent studies on the relationship between this kind of learning problem and the regularization theory for ill-posed inverse problems have given rise to new regularized learning algorithms. In this paper we recall some of these learning methods and we propose an accelerated version of the classical Landweber iterative scheme which results particularly efficient from the computational viewpoint. Finally, we compare the performances of these methods with the classical Support Vector Machines learning algorithm on a real-world experiment concerning brain activity interpretation through the analysis of functional magnetic resonance imaging data.

Efficient evaluation of influence coefficients in three-dimensional extended boundary-node method for potential problems

International Nuclear Information System (INIS)

Itoh, Taku; Saitoh, Ayumu; Kamitani, Atsushi; Nakamura, Hiroaki

2011-01-01

For the purpose of speed-up of the three-dimensional eXtended Boundary-Node Method (X-BNM), an efficient algorithm for evaluating influence coefficients has been developed. The algorithm can be easily implemented into the X-BNM without using any integration cells. By applying the resulting X-BNM to the Laplace problem, the performance of the algorithm is numerically investigated. The numerical experiments show that, by using the algorithm, computational costs for evaluating influence coefficients in the X-BNM are reduced considerably. Especially for a large-sized problem, the algorithm is efficiently performed, and the computational costs of the X-BNM are close to those of the Boundary-Element Method (BEM). In addition, for the problem, the X-BNM shows almost the same accuracy as that of the BEM. (author)

Inverse Problems in Geodynamics Using Machine Learning Algorithms

Science.gov (United States)

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.