Particle Swarm Optimization and Uncertainty Assessment in Inverse Problems

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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.

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.

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)

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

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

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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.

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...

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

The philosophical aspect of learning inverse problems of mathematical physics

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Виктор Семенович Корнилов

2018-12-01

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

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.

Inverse Problems in Systems Biology: A Critical Review.

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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.

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...

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

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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.

An Entropic Estimator for Linear Inverse Problems

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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.

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

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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

Optimization and inverse problems in electromagnetism

CERN Document Server

Wiak, Sławomir

2003-01-01

From 12 to 14 September 2002, the Academy of Humanities and Economics (AHE) hosted the workshop "Optimization and Inverse Problems in Electromagnetism". After this bi-annual event, a large number of papers were assembled and combined in this book. During the workshop recent developments and applications in optimization and inverse methodologies for electromagnetic fields were discussed. The contributions selected for the present volume cover a wide spectrum of inverse and optimal electromagnetic methodologies, ranging from theoretical to practical applications. A number of new optimal and inverse methodologies were proposed. There are contributions related to dedicated software. Optimization and Inverse Problems in Electromagnetism consists of three thematic chapters, covering: -General papers (survey of specific aspects of optimization and inverse problems in electromagnetism), -Methodologies, -Industrial Applications. The book can be useful to students of electrical and electronics engineering, computer sci...

Inverse kinematics problem in robotics using neural networks

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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.

Inverse and Ill-posed Problems Theory and Applications

CERN Document Server

Kabanikhin, S I

2011-01-01

The text demonstrates the methods for proving the existence (if et all) and finding of inverse and ill-posed problems solutions in linear algebra, integral and operator equations, integral geometry, spectral inverse problems, and inverse scattering problems. It is given comprehensive background material for linear ill-posed problems and for coefficient inverse problems for hyperbolic, parabolic, and elliptic equations. A lot of examples for inverse problems from physics, geophysics, biology, medicine, and other areas of application of mathematics are included.

The Inverse Problem of Identification of Hydrogen Permeability Model

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Yury V. Zaika

2018-01-01

Full Text Available One of the technological challenges for hydrogen materials science is the currently active search for structural materials with important applications (including the ITER project and gas-separation plants. One had to estimate the parameters of diffusion and sorption to numerically model the different scenarios and experimental conditions of the material usage (including extreme ones. The article presents boundary value problems of hydrogen permeability and thermal desorption with dynamical boundary conditions. A numerical method is developed for TDS spectrum simulation, where only integration of a nonlinear system of low order ordinary differential equations is required. The main final output of the article is a noise-resistant algorithm for solving the inverse problem of parametric identification for the aggregated experiment where desorption and diffusion are dynamically interrelated (without the artificial division of studies into the diffusion limited regime (DLR and the surface limited regime (SLR.

Inverse problems for Maxwell's equations

CERN Document Server

Romanov, V G

1994-01-01

The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.

Inverse scattering problems with multi-frequencies

International Nuclear Information System (INIS)

Bao, Gang; Li, Peijun; Lin, Junshan; Triki, Faouzi

2015-01-01

This paper is concerned with computational approaches and mathematical analysis for solving inverse scattering problems in the frequency domain. The problems arise in a diverse set of scientific areas with significant industrial, medical, and military applications. In addition to nonlinearity, there are two common difficulties associated with the inverse problems: ill-posedness and limited resolution (diffraction limit). Due to the diffraction limit, for a given frequency, only a low spatial frequency part of the desired parameter can be observed from measurements in the far field. The main idea developed here is that if the reconstruction is restricted to only the observable part, then the inversion will become stable. The challenging task is how to design stable numerical methods for solving these inverse scattering problems inspired by the diffraction limit. Recently, novel recursive linearization based algorithms have been presented in an attempt to answer the above question. These methods require multi-frequency scattering data and proceed via a continuation procedure with respect to the frequency from low to high. The objective of this paper is to give a brief review of these methods, their error estimates, and the related mathematical analysis. More attention is paid to the inverse medium and inverse source problems. Numerical experiments are included to illustrate the effectiveness of these methods. (topical review)

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.

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

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

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.

Alloy design as an inverse problem of cluster expansion models

DEFF Research Database (Denmark)

Larsen, Peter Mahler; Kalidindi, Arvind R.; Schmidt, Søren

2017-01-01

Central to a lattice model of an alloy system is the description of the energy of a given atomic configuration, which can be conveniently developed through a cluster expansion. Given a specific cluster expansion, the ground state of the lattice model at 0 K can be solved by finding the configurat......Central to a lattice model of an alloy system is the description of the energy of a given atomic configuration, which can be conveniently developed through a cluster expansion. Given a specific cluster expansion, the ground state of the lattice model at 0 K can be solved by finding...... the inverse problem in terms of energetically distinct configurations, using a constraint satisfaction model to identify constructible configurations, and show that a convex hull can be used to identify ground states. To demonstrate the approach, we solve for all ground states for a binary alloy in a 2D...

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

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.

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

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....

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

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

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...

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

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

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

Solving inverse problem for Markov chain model of customer lifetime value using flower pollination algorithm

Science.gov (United States)

Al-Ma'shumah, Fathimah; Permana, Dony; Sidarto, Kuntjoro Adji

2015-12-01

Customer Lifetime Value is an important and useful concept in marketing. One of its benefits is to help a company for budgeting marketing expenditure for customer acquisition and customer retention. Many mathematical models have been introduced to calculate CLV considering the customer retention/migration classification scheme. A fairly new class of these models which will be described in this paper uses Markov Chain Models (MCM). This class of models has the major advantage for its flexibility to be modified to several different cases/classification schemes. In this model, the probabilities of customer retention and acquisition play an important role. From Pfeifer and Carraway, 2000, the final formula of CLV obtained from MCM usually contains nonlinear form of the transition probability matrix. This nonlinearity makes the inverse problem of CLV difficult to solve. This paper aims to solve this inverse problem, yielding the approximate transition probabilities for the customers, by applying metaheuristic optimization algorithm developed by Yang, 2013, Flower Pollination Algorithm. The major interpretation of obtaining the transition probabilities are to set goals for marketing teams in keeping the relative frequencies of customer acquisition and customer retention.

An inverse problem for a mathematical model of aquaponic agriculture

Science.gov (United States)

Bobak, Carly; Kunze, Herb

2017-01-01

Aquaponic agriculture is a sustainable ecosystem that relies on a symbiotic relationship between fish and macrophytes. While the practice has been growing in popularity, relatively little mathematical models exist which aim to study the system processes. In this paper, we present a system of ODEs which aims to mathematically model the population and concetrations dynamics present in an aquaponic environment. Values of the parameters in the system are estimated from the literature so that simulated results can be presented to illustrate the nature of the solutions to the system. As well, a brief sensitivity analysis is performed in order to identify redundant parameters and highlight those which may need more reliable estimates. Specifically, an inverse problem with manufactured data for fish and plants is presented to demonstrate the ability of the collage theorem to recover parameter estimates.

Forward modeling. Route to electromagnetic inversion

Energy Technology Data Exchange (ETDEWEB)

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

1996-05-01

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

Obtaining sparse distributions in 2D inverse problems

OpenAIRE

Reci, A; Sederman, Andrew John; Gladden, Lynn Faith

2017-01-01

The mathematics of inverse problems has relevance across numerous estimation problems in science and engineering. L1 regularization has attracted recent attention in reconstructing the system properties in the case of sparse inverse problems; i.e., when the true property sought is not adequately described by a continuous distribution, in particular in Compressed Sensing image reconstruction. In this work, we focus on the application of L1 regularization to a class of inverse problems; relaxat...

The seismic reflection inverse problem

International Nuclear Information System (INIS)

Symes, W W

2009-01-01

The seismic reflection method seeks to extract maps of the Earth's sedimentary crust from transient near-surface recording of echoes, stimulated by explosions or other controlled sound sources positioned near the surface. Reasonably accurate models of seismic energy propagation take the form of hyperbolic systems of partial differential equations, in which the coefficients represent the spatial distribution of various mechanical characteristics of rock (density, stiffness, etc). Thus the fundamental problem of reflection seismology is an inverse problem in partial differential equations: to find the coefficients (or at least some of their properties) of a linear hyperbolic system, given the values of a family of solutions in some part of their domains. The exploration geophysics community has developed various methods for estimating the Earth's structure from seismic data and is also well aware of the inverse point of view. This article reviews mathematical developments in this subject over the last 25 years, to show how the mathematics has both illuminated innovations of practitioners and led to new directions in practice. Two themes naturally emerge: the importance of single scattering dominance and compensation for spectral incompleteness by spatial redundancy. (topical review)

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.

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.

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.

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.

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)

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.

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

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.

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

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.

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 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

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....

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

The inverse conductivity problem with limited data and applications

International Nuclear Information System (INIS)

Isakov, Victor

2007-01-01

This paper describes recent uniqueness results in inverse problems for semiconductor devices and in the inverse conductivity problem. We remind basic inverse probelsm in semiconductor theory and outline use of an adjoint equation and a proof of uniqueness of piecewise constant doping profile. For the inverse conductivity problem we give a first uniqueness proof when the Dirichlet-to-Neumann map is given at an arbitrarily small part of the boundary of a three-dimensional domain

Approximation of Bayesian Inverse Problems for PDEs

OpenAIRE

Cotter, S. L.; Dashti, M.; Stuart, A. M.

2010-01-01

Inverse problems are often ill posed, with solutions that depend sensitively on data.n any numerical approach to the solution of such problems, regularization of some form is needed to counteract the resulting instability. This paper is based on an approach to regularization, employing a Bayesian formulation of the problem, which leads to a notion of well posedness for inverse problems, at the level of probability measures. The stability which results from this well posedness may be used as t...

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

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.

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)

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.

Atmospheric inverse modeling via sparse reconstruction

Science.gov (United States)

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

2017-10-01

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

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...

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)

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.

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.

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 Methods for Inverse Problems with Partial Data

DEFF Research Database (Denmark)

Hoffmann, Kristoffer

This thesis presents a theoretical and numerical analysis of a general mathematical formulation of hybrid inverse problems in impedance tomography. This includes problems from several existing hybrid imaging modalities such as Current Density Impedance Imaging, Magnetic Resonance Electrical...... Impedance Tomography, and Ultrasound Modulated Electrical Impedance Tomography. After giving an introduction to hybrid inverse problems in impedance tomography and the mathematical tools that facilitate the related analysis, we explain in detail the stability properties associated with the classification...... of a linearised hybrid inverse problem. This is done using pseudo-differential calculus and theory for overdetermined boundary value problem. Using microlocal analysis we then present novel results on the propagation of singularities, which give a precise description of the distinct features of solutions...

Gradient-type methods in inverse parabolic problems

International Nuclear Information System (INIS)

Kabanikhin, Sergey; Penenko, Aleksey

2008-01-01

This article is devoted to gradient-based methods for inverse parabolic problems. In the first part, we present a priori convergence theorems based on the conditional stability estimates for linear inverse problems. These theorems are applied to backwards parabolic problem and sideways parabolic problem. The convergence conditions obtained coincide with sourcewise representability in the self-adjoint backwards parabolic case but they differ in the sideways case. In the second part, a variational approach is formulated for a coefficient identification problem. Using adjoint equations, a formal gradient of an objective functional is constructed. A numerical test illustrates the performance of conjugate gradient algorithm with the formal gradient.

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.

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

Inverse modeling for seawater intrusion in coastal aquifers: Insights about parameter sensitivities, variances, correlations and estimation procedures derived from the Henry problem

Science.gov (United States)

Sanz, E.; Voss, C.I.

2006-01-01

Inverse modeling studies employing data collected from the classic Henry seawater intrusion problem give insight into several important aspects of inverse modeling of seawater intrusion problems and effective measurement strategies for estimation of parameters for seawater intrusion. Despite the simplicity of the Henry problem, it embodies the behavior of a typical seawater intrusion situation in a single aquifer. Data collected from the numerical problem solution are employed without added noise in order to focus on the aspects of inverse modeling strategies dictated by the physics of variable-density flow and solute transport during seawater intrusion. Covariances of model parameters that can be estimated are strongly dependent on the physics. The insights gained from this type of analysis may be directly applied to field problems in the presence of data errors, using standard inverse modeling approaches to deal with uncertainty in data. Covariance analysis of the Henry problem indicates that in order to generally reduce variance of parameter estimates, the ideal places to measure pressure are as far away from the coast as possible, at any depth, and the ideal places to measure concentration are near the bottom of the aquifer between the center of the transition zone and its inland fringe. These observations are located in and near high-sensitivity regions of system parameters, which may be identified in a sensitivity analysis with respect to several parameters. However, both the form of error distribution in the observations and the observation weights impact the spatial sensitivity distributions, and different choices for error distributions or weights can result in significantly different regions of high sensitivity. Thus, in order to design effective sampling networks, the error form and weights must be carefully considered. For the Henry problem, permeability and freshwater inflow can be estimated with low estimation variance from only pressure or only

Inverse modelling for flow and transport in porous media

International Nuclear Information System (INIS)

Giudici, M.

2004-01-01

The problem of parameter identification for flow and transport model in porous media is discussed in this communication. First, a general framework for the development and application of environmental models is discussed. Then the forward and inverse problems for discrete models are described in detail, introducing fundamental concepts (uniqueness, identifiability, stability, conditioning). The importance of model scales is reviewed and is shown its link with the stability and conditioning issues. Finally some remarks are given to the use of several independent sets of data in inverse modelling

Inverse radiative transfer problems in two-dimensional heterogeneous media

International Nuclear Information System (INIS)

Tito, Mariella Janette Berrocal

2001-01-01

The analysis of inverse problems in participating media where emission, absorption and scattering take place has several relevant applications in engineering and medicine. Some of the techniques developed for the solution of inverse problems have as a first step the solution of the direct problem. In this work the discrete ordinates method has been used for the solution of the linearized Boltzmann equation in two dimensional cartesian geometry. The Levenberg - Marquardt method has been used for the solution of the inverse problem of internal source and absorption and scattering coefficient estimation. (author)

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

NARCIS (Netherlands)

Knapik, B.T.; Szabó, B.T.; van der Vaart, A.W.; van Zanten, J.H.

2016-01-01

We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies regularity. We prove that both methods we consider succeed

Inverse 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.

One-dimensional inverse problems of mathematical physics

CERN Document Server

Lavrent'ev, M M; Yakhno, V G; Schulenberger, J R

1986-01-01

This monograph deals with the inverse problems of determining a variable coefficient and right side for hyperbolic and parabolic equations on the basis of known solutions at fixed points of space for all times. The problems are one-dimensional in nature since the desired coefficient of the equation is a function of only one coordinate, while the desired right side is a function only of time. The authors use methods based on the spectral theory of ordinary differential operators of second order and also methods which make it possible to reduce the investigation of the inverse problems to the in

Sparse optimization for inverse problems in atmospheric modelling

Czech Academy of Sciences Publication Activity Database

Adam, Lukáš; Branda, Martin

2016-01-01

Roč. 79, č. 3 (2016), s. 256-266 ISSN 1364-8152 R&D Projects: GA MŠk(CZ) 7F14287 Institutional support: RVO:67985556 Keywords : Inverse modelling * Sparse optimization * Integer optimization * Least squares * European tracer experiment * Free Matlab codes Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.404, year: 2016 http://library.utia.cas.cz/separaty/2016/MTR/adam-0457037.pdf

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

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

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

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.

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

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).

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)

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.

Direct and inverse problems of studying the properties of multilayer nanostructures based on a two-dimensional model of X-ray reflection and scattering

Science.gov (United States)

Khachaturov, R. V.

2014-06-01

A mathematical model of X-ray reflection and scattering by multilayered nanostructures in the quasi-optical approximation is proposed. X-ray propagation and the electric field distribution inside the multilayered structure are considered with allowance for refraction, which is taken into account via the second derivative with respect to the depth of the structure. This model is used to demonstrate the possibility of solving inverse problems in order to determine the characteristics of irregularities not only over the depth (as in the one-dimensional problem) but also over the length of the structure. An approximate combinatorial method for system decomposition and composition is proposed for solving the inverse problems.

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

Inverse problems in ordinary differential equations and applications

CERN Document Server

Llibre, Jaume

2016-01-01

This book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties. The Nambu bracket is the central tool in developing this approach. The authors start characterizing the ordinary differential equations in R^N which have a given set of partial integrals or first integrals. The results obtained are applied first to planar polynomial differential systems with a given set of such integrals, second to solve the 16th Hilbert problem restricted to generic algebraic limit cycles, third for solving the inverse problem for constrained Lagrangian and Hamiltonian mechanical systems, fourth for studying the integrability of a constrained rigid body. Finally the authors conclude with an analysis on nonholonomic mechanics, a generalization of the Hamiltonian principle, and the statement an solution of the inverse problem in vakonomic mechanics.

A tutorial on inverse problems for anomalous diffusion processes

International Nuclear Information System (INIS)

Jin, Bangti; Rundell, William

2015-01-01

Over the last two decades, anomalous diffusion processes in which the mean squares variance grows slower or faster than that in a Gaussian process have found many applications. At a macroscopic level, these processes are adequately described by fractional differential equations, which involves fractional derivatives in time or/and space. The fractional derivatives describe either history mechanism or long range interactions of particle motions at a microscopic level. The new physics can change dramatically the behavior of the forward problems. For example, the solution operator of the time fractional diffusion diffusion equation has only limited smoothing property, whereas the solution for the space fractional diffusion equation may contain weak singularity. Naturally one expects that the new physics will impact related inverse problems in terms of uniqueness, stability, and degree of ill-posedness. The last aspect is especially important from a practical point of view, i.e., stably reconstructing the quantities of interest. In this paper, we employ a formal analytic and numerical way, especially the two-parameter Mittag-Leffler function and singular value decomposition, to examine the degree of ill-posedness of several ‘classical’ inverse problems for fractional differential equations involving a Djrbashian–Caputo fractional derivative in either time or space, which represent the fractional analogues of that for classical integral order differential equations. We discuss four inverse problems, i.e., backward fractional diffusion, sideways problem, inverse source problem and inverse potential problem for time fractional diffusion, and inverse Sturm–Liouville problem, Cauchy problem, backward fractional diffusion and sideways problem for space fractional diffusion. It is found that contrary to the wide belief, the influence of anomalous diffusion on the degree of ill-posedness is not definitive: it can either significantly improve or worsen the conditioning

The inverse spectral problem for pencils of differential operators

International Nuclear Information System (INIS)

Guseinov, I M; Nabiev, I M

2007-01-01

The inverse problem of spectral analysis for a quadratic pencil of Sturm-Liouville operators on a finite interval is considered. A uniqueness theorem is proved, a solution algorithm is presented, and sufficient conditions for the solubility of the inverse problem are obtained. Bibliography: 31 titles.

Applications of elliptic Carleman inequalities to Cauchy and inverse problems

CERN Document Server

Choulli, Mourad

2016-01-01

This book presents a unified approach to studying the stability of both elliptic Cauchy problems and selected inverse problems. Based on elementary Carleman inequalities, it establishes three-ball inequalities, which are the key to deriving logarithmic stability estimates for elliptic Cauchy problems and are also useful in proving stability estimates for certain elliptic inverse problems. The book presents three inverse problems, the first of which consists in determining the surface impedance of an obstacle from the far field pattern. The second problem investigates the detection of corrosion by electric measurement, while the third concerns the determination of an attenuation coefficient from internal data, which is motivated by a problem encountered in biomedical imaging.

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)

Inverse source problems in elastodynamics

Science.gov (United States)

Bao, Gang; Hu, Guanghui; Kian, Yavar; Yin, Tao

2018-04-01

We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain approaches to show uniqueness in determining the spatial function from wave fields on a large sphere over a finite time interval. The stability estimate of the temporal function from the data of one receiver and the uniqueness result using partial boundary data are proved. Our arguments rely heavily on the use of the Fourier transform, which motivates inversion schemes that can be easily implemented. A Landweber iterative algorithm for recovering the spatial function and a non-iterative inversion scheme based on the uniqueness proof for recovering the temporal function are proposed. Numerical examples are demonstrated in both two and three dimensions.

Integral 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

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)

A model for the inverse 1-median problem on trees under uncertain costs

Directory of Open Access Journals (Sweden)

Kien Trung Nguyen

2016-01-01

Full Text Available We consider the problem of justifying vertex weights of a tree under uncertain costs so that a prespecified vertex become optimal and the total cost should be optimal in the uncertainty scenario. We propose a model which delivers the information about the optimal cost which respect to each confidence level \\(\\alpha \\in [0,1]\\. To obtain this goal, we first define an uncertain variable with respect to the minimum cost in each confidence level. If all costs are independently linear distributed, we present the inverse distribution function of this uncertain variable in \\(O(n^{2}\\log n\\ time, where \\(n\\ is the number of vertices in the tree.

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)

Integral geometry and inverse problems for hyperbolic equations

CERN Document Server

Romanov, V G

1974-01-01

There are currently many practical situations in which one wishes to determine the coefficients in an ordinary or partial differential equation from known functionals of its solution. These are often called "inverse problems of mathematical physics" and may be contrasted with problems in which an equation is given and one looks for its solution under initial and boundary conditions. Although inverse problems are often ill-posed in the classical sense, their practical importance is such that they may be considered among the pressing problems of current mathematical re­ search. A. N. Tihonov showed [82], [83] that there is a broad class of inverse problems for which a particular non-classical definition of well-posed ness is appropriate. This new definition requires that a solution be unique in a class of solutions belonging to a given subset M of a function space. The existence of a solution in this set is assumed a priori for some set of data. The classical requirement of continuous dependence of the solutio...

The inverse problem of the magnetostatic nondestructive testing

International Nuclear Information System (INIS)

Pechenkov, A.N.; Shcherbinin, V.E.

2006-01-01

The inverse problem of magnetostatic nondestructive testing consists in the calculation of the shape and magnetic characteristics of a flaw in a uniform magnetized body with measurement of static magnetic field beyond the body. If the flaw does not contain any magnetic material, the inverse problem is reduced to identification of the shape and magnetic susceptibility of the substance. This case has been considered in the study [ru

Model Based Beamforming and Bayesian Inversion Signal Processing Methods for Seismic Localization of Underground Source

DEFF Research Database (Denmark)

Oh, Geok Lian

properties such as the elastic wave speeds and soil densities. One processing method is casting the estimation problem into an inverse problem to solve for the unknown material parameters. The forward model for the seismic signals used in the literatures include ray tracing methods that consider only...... density values of the discretized ground medium, which leads to time-consuming computations and instability behaviour of the inversion process. In addition, the geophysics inverse problem is generally ill-posed due to non-exact forward model that introduces errors. The Bayesian inversion method through...... the first arrivals of the reflected compressional P-waves from the subsurface structures, or 3D elastic wave models that model all the seismic wave components. The ray tracing forward model formulation is linear, whereas the full 3D elastic wave model leads to a nonlinear inversion problem. In this Ph...

An inverse problem for evolution inclusions

OpenAIRE

Ton, Bui An

2002-01-01

An inverse problem, the determination of the shape and a convective coefficient on a part of the boundary from partial measurements of the solution, is studied using 2-person optimal control techniques.

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.

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.

Two-dimensional probabilistic inversion of plane-wave electromagnetic data: Methodology, model constraints and joint inversion with electrical resistivity data

NARCIS (Netherlands)

Rosas-Carbajal, M.; Linde, N.; Kalscheuer, T.; Vrugt, J.A.

2014-01-01

Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space

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.

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.

Data inversion in coupled subsurface flow and geomechanics models

International Nuclear Information System (INIS)

Iglesias, Marco A; McLaughlin, Dennis

2012-01-01

We present an inverse modeling approach to estimate petrophysical and elastic properties of the subsurface. The aim is to use the fully coupled geomechanics-flow model of Girault et al (2011 Math. Models Methods Appl. Sci. 21 169–213) to jointly invert surface deformation and pressure data from wells. We use a functional-analytic framework to construct a forward operator (parameter-to-output map) that arises from the geomechanics-flow model of Girault et al. Then, we follow a deterministic approach to pose the inverse problem of finding parameter estimates from measurements of the output of the forward operator. We prove that this inverse problem is ill-posed in the sense of stability. The inverse problem is then regularized with the implementation of the Newton-conjugate gradient (CG) algorithm of Hanke (1997 Numer. Funct. Anal. Optim. 18 18–971). For a consistent application of the Newton-CG scheme, we establish the differentiability of the forward map and characterize the adjoint of its linearization. We provide assumptions under which the theory of Hanke ensures convergence and regularizing properties of the Newton-CG scheme. These properties are verified in our numerical experiments. In addition, our synthetic experiments display the capabilities of the proposed inverse approach to estimate parameters of the subsurface by means of data inversion. In particular, the added value of measurements of surface deformation in the estimation of absolute permeability is quantified with respect to the standard history matching approach of inverting production data with flow models. The proposed methodology can be potentially used to invert satellite geodetic data (e.g. InSAR and GPS) in combination with production data for optimal monitoring and characterization of the subsurface. (paper)

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

International Nuclear Information System (INIS)

Bertagna, Luca; Veneziani, Alessandro

2014-01-01

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

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

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.

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

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.

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.

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

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

Large-scale inverse model analyses employing fast randomized data reduction

Science.gov (United States)

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

2017-08-01

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

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

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.

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...

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

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

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

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.

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

Science.gov (United States)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

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

Collage-based approaches for elliptic partial differential equations inverse problems

Science.gov (United States)

Yodzis, Michael; Kunze, Herb

2017-01-01

The collage method for inverse problems has become well-established in the literature in recent years. Initial work developed a collage theorem, based upon Banach's fixed point theorem, for treating inverse problems for ordinary differential equations (ODEs). Amongst the subsequent work was a generalized collage theorem, based upon the Lax-Milgram representation theorem, useful for treating inverse problems for elliptic partial differential equations (PDEs). Each of these two different approaches can be applied to elliptic PDEs in one space dimension. In this paper, we explore and compare how the two different approaches perform for the estimation of the diffusivity for a steady-state heat equation.

General inverse problems for regular variation

DEFF Research Database (Denmark)

Damek, Ewa; Mikosch, Thomas Valentin; Rosinski, Jan

2014-01-01

Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed random object is caused by regular variation of components ...

Inverse problem of solar oscillations

International Nuclear Information System (INIS)

Sekii, T.; Shibahashi, H.

1987-01-01

The authors present some preliminary results of numerical simulation to infer the sound velocity distribution in the solar interior from the oscillation data of the Sun as the inverse problem. They analyze the acoustic potential itself by taking account of some factors other than the sound velocity, and infer the sound velocity distribution in the deep interior of the Sun

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.

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)

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

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.

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

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.

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.

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.

Metamodel-based inverse method for parameter identification: elastic-plastic damage model

Science.gov (United States)

Huang, Changwu; El Hami, Abdelkhalak; Radi, Bouchaïb

2017-04-01

This article proposed a metamodel-based inverse method for material parameter identification and applies it to elastic-plastic damage model parameter identification. An elastic-plastic damage model is presented and implemented in numerical simulation. The metamodel-based inverse method is proposed in order to overcome the disadvantage in computational cost of the inverse method. In the metamodel-based inverse method, a Kriging metamodel is constructed based on the experimental design in order to model the relationship between material parameters and the objective function values in the inverse problem, and then the optimization procedure is executed by the use of a metamodel. The applications of the presented material model and proposed parameter identification method in the standard A 2017-T4 tensile test prove that the presented elastic-plastic damage model is adequate to describe the material's mechanical behaviour and that the proposed metamodel-based inverse method not only enhances the efficiency of parameter identification but also gives reliable results.

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

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.

Reservoir Modeling Combining Geostatistics with Markov Chain Monte Carlo Inversion

DEFF Research Database (Denmark)

Zunino, Andrea; Lange, Katrine; Melnikova, Yulia

2014-01-01

We present a study on the inversion of seismic reflection data generated from a synthetic reservoir model. Our aim is to invert directly for rock facies and porosity of the target reservoir zone. We solve this inverse problem using a Markov chain Monte Carlo (McMC) method to handle the nonlinear...

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.

Developing a particle tracking surrogate model to improve inversion of ground water - Surface water models

Science.gov (United States)

Cousquer, Yohann; Pryet, Alexandre; Atteia, Olivier; Ferré, Ty P. A.; Delbart, Célestine; Valois, Rémi; Dupuy, Alain

2018-03-01

The inverse problem of groundwater models is often ill-posed and model parameters are likely to be poorly constrained. Identifiability is improved if diverse data types are used for parameter estimation. However, some models, including detailed solute transport models, are further limited by prohibitive computation times. This often precludes the use of concentration data for parameter estimation, even if those data are available. In the case of surface water-groundwater (SW-GW) models, concentration data can provide SW-GW mixing ratios, which efficiently constrain the estimate of exchange flow, but are rarely used. We propose to reduce computational limits by simulating SW-GW exchange at a sink (well or drain) based on particle tracking under steady state flow conditions. Particle tracking is used to simulate advective transport. A comparison between the particle tracking surrogate model and an advective-dispersive model shows that dispersion can often be neglected when the mixing ratio is computed for a sink, allowing for use of the particle tracking surrogate model. The surrogate model was implemented to solve the inverse problem for a real SW-GW transport problem with heads and concentrations combined in a weighted hybrid objective function. The resulting inversion showed markedly reduced uncertainty in the transmissivity field compared to calibration on head data alone.

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

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

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 \

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.

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

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

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)

Wake Vortex Inverse Model User's Guide

Science.gov (United States)

Lai, David; Delisi, Donald

2008-01-01

NorthWest Research Associates (NWRA) has developed an inverse model for inverting landing aircraft vortex data. The data used for the inversion are the time evolution of the lateral transport position and vertical position of both the port and starboard vortices. The inverse model performs iterative forward model runs using various estimates of vortex parameters, vertical crosswind profiles, and vortex circulation as a function of wake age. Forward model predictions of lateral transport and altitude are then compared with the observed data. Differences between the data and model predictions guide the choice of vortex parameter values, crosswind profile and circulation evolution in the next iteration. Iterations are performed until a user-defined criterion is satisfied. Currently, the inverse model is set to stop when the improvement in the rms deviation between the data and model predictions is less than 1 percent for two consecutive iterations. The forward model used in this inverse model is a modified version of the Shear-APA model. A detailed description of this forward model, the inverse model, and its validation are presented in a different report (Lai, Mellman, Robins, and Delisi, 2007). This document is a User's Guide for the Wake Vortex Inverse Model. Section 2 presents an overview of the inverse model program. Execution of the inverse model is described in Section 3. When executing the inverse model, a user is requested to provide the name of an input file which contains the inverse model parameters, the various datasets, and directories needed for the inversion. A detailed description of the list of parameters in the inversion input file is presented in Section 4. A user has an option to save the inversion results of each lidar track in a mat-file (a condensed data file in Matlab format). These saved mat-files can be used for post-inversion analysis. A description of the contents of the saved files is given in Section 5. An example of an inversion input

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.

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

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.

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-06-30

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

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...

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...

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.

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.

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 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...

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

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.

Estimation of biological parameters of marine organisms using linear and nonlinear acoustic scattering model-based inversion methods.

Science.gov (United States)

Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H

2016-05-01

The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.

Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem

Directory of Open Access Journals (Sweden)

Baiyu Wang

2014-01-01

Full Text Available This paper investigates the numerical solution of a class of one-dimensional inverse parabolic problems using the moving least squares approximation; the inverse problem is the determination of an unknown source term depending on time. The collocation method is used for solving the equation; some numerical experiments are presented and discussed to illustrate the stability and high efficiency of the method.

Coefficient Inverse Problem for Poisson's Equation in a Cylinder

NARCIS (Netherlands)

Solov'ev, V. V.

2011-01-01

The inverse problem of determining the coefficient on the right-hand side of Poisson's equation in a cylindrical domain is considered. The Dirichlet boundary value problem is studied. Two types of additional information (overdetermination) can be specified: (i) the trace of the solution to the

NUMERICAL SOLUTION OF SINGULAR INVERSE NODAL PROBLEM BY USING CHEBYSHEV POLYNOMIALS

OpenAIRE

NEAMATY, ABDOLALI; YILMAZ, EMRAH; AKBARPOOR, SHAHRBANOO; DABBAGHIAN, ABDOLHADI

2017-01-01

In this study, we consider Sturm-Liouville problem in two cases: the first case having no singularity and the second case having a singularity at zero. Then, we calculate the eigenvalues and the nodal points and present the uniqueness theorem for the solution of the inverse problem by using a dense subset of the nodal points in two given cases. Also, we use Chebyshev polynomials of the first kind for calculating the approximate solution of the inverse nodal problem in these cases. Finally, we...

An inverse heat transfer problem for optimization of the thermal ...

Indian Academy of Sciences (India)

This paper takes a different approach towards identification of the thermal process in machining, using inverse heat transfer problem. Inverse heat transfer method allows the closest possible experimental and analytical approximation of thermal state for a machining process. Based on a temperature measured at any point ...

Regularization method for solving the inverse scattering problem

International Nuclear Information System (INIS)

Denisov, A.M.; Krylov, A.S.

1985-01-01

The inverse scattering problem for the Schroedinger radial equation consisting in determining the potential according to the scattering phase is considered. The problem of potential restoration according to the phase specified with fixed error in a finite range is solved by the regularization method based on minimization of the Tikhonov's smoothing functional. The regularization method is used for solving the problem of neutron-proton potential restoration according to the scattering phases. The determined potentials are given in the table

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

Science.gov (United States)

Cheng, Jin; Hon, Yiu-Chung; Seo, Jin Keun; Yamamoto, Masahiro

2005-01-01

The Second International Conference on Inverse Problems: Recent Theoretical Developments and Numerical Approaches was held at Fudan University, Shanghai from 16-21 June 2004. The first conference in this series was held at the City University of Hong Kong in January 2002 and it was agreed to hold the conference once every two years in a Pan-Pacific Asian country. The next conference is scheduled to be held at Hokkaido University, Sapporo, Japan in July 2006. The purpose of this series of biennial conferences is to establish and develop constant international collaboration, especially among the Pan-Pacific Asian countries. In recent decades, interest in inverse problems has been flourishing all over the globe because of both the theoretical interest and practical requirements. In particular, in Asian countries, one is witnessing remarkable new trends of research in inverse problems as well as the participation of many young talents. Considering these trends, the second conference was organized with the chairperson Professor Li Tat-tsien (Fudan University), in order to provide forums for developing research cooperation and to promote activities in the field of inverse problems. Because solutions to inverse problems are needed in various applied fields, we entertained a total of 92 participants at the second conference and arranged various talks which ranged from mathematical analyses to solutions of concrete inverse problems in the real world. This volume contains 18 selected papers, all of which have undergone peer review. The 18 papers are classified as follows: Surveys: four papers give reviews of specific inverse problems. Theoretical aspects: six papers investigate the uniqueness, stability, and reconstruction schemes. Numerical methods: four papers devise new numerical methods and their applications to inverse problems. Solutions to applied inverse problems: four papers discuss concrete inverse problems such as scattering problems and inverse problems in

Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model

KAUST Repository

Mondal, Anirban

2014-07-03

We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a random field (spatial or temporal). The Bayesian approach contains a natural mechanism for regularization in the form of prior information, can incorporate information from heterogeneous sources and provide a quantitative assessment of uncertainty in the inverse solution. The Bayesian setting casts the inverse solution as a posterior probability distribution over the model parameters. The Karhunen-Loeve expansion is used for dimension reduction of the random field. Furthermore, we use a hierarchical Bayes model to inject multiscale data in the modeling framework. In this Bayesian framework, we show that this inverse problem is well-posed by proving that the posterior measure is Lipschitz continuous with respect to the data in total variation norm. Computational challenges in this construction arise from the need for repeated evaluations of the forward model (e.g., in the context of MCMC) and are compounded by high dimensionality of the posterior. We develop two-stage reversible jump MCMC that has the ability to screen the bad proposals in the first inexpensive stage. Numerical results are presented by analyzing simulated as well as real data from hydrocarbon reservoir. This article has supplementary material available online. © 2014 American Statistical Association and the American Society for Quality.

SIPPI: A Matlab toolbox for sampling the solution to inverse problems with complex prior information

DEFF Research Database (Denmark)

Hansen, Thomas Mejer; Cordua, Knud Skou; Looms, Majken Caroline

2013-01-01

We present an application of the SIPPI Matlab toolbox, to obtain a sample from the a posteriori probability density function for the classical tomographic inversion problem. We consider a number of different forward models, linear and non-linear, such as ray based forward models that rely...

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

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)

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.

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

Science.gov (United States)

Marinin, I. V.; Kabanikhin, S. I.; Krivorotko, O. I.; Karas, A.; Khidasheli, D. G.

2012-04-01

We consider new techniques and methods for earthquake and tsunami related problems, particularly - inverse problems for the determination of tsunami source parameters, numerical simulation of long wave propagation in soil and water and tsunami risk estimations. In addition, we will touch upon the issue of database management and destruction scenario visualization. New approaches and strategies, as well as mathematical tools and software are to be shown. The long joint investigations by researchers of the Institute of Mathematical Geophysics and Computational Mathematics SB RAS and specialists from WAPMERR and Informap have produced special theoretical approaches, numerical methods, and software tsunami and earthquake modeling (modeling of propagation and run-up of tsunami waves on coastal areas), visualization, risk estimation of tsunami, and earthquakes. Algorithms are developed for the operational definition of the origin and forms of the tsunami source. The system TSS numerically simulates the source of tsunami and/or earthquakes and includes the possibility to solve the direct and the inverse problem. It becomes possible to involve advanced mathematical results to improve models and to increase the resolution of inverse problems. Via TSS one can construct maps of risks, the online scenario of disasters, estimation of potential damage to buildings and roads. One of the main tools for the numerical modeling is the finite volume method (FVM), which allows us to achieve stability with respect to possible input errors, as well as to achieve optimum computing speed. Our approach to the inverse problem of tsunami and earthquake determination is based on recent theoretical results concerning the Dirichlet problem for the wave equation. This problem is intrinsically ill-posed. We use the optimization approach to solve this problem and SVD-analysis to estimate the degree of ill-posedness and to find the quasi-solution. The software system we developed is intended to

Machine Learning and Inverse Problem in Geodynamics

Science.gov (United States)

Shahnas, M. H.; Yuen, D. A.; Pysklywec, R.

2017-12-01

During the past few decades numerical modeling and traditional HPC have been widely deployed in many diverse fields for problem solutions. However, in recent years the rapid emergence of machine learning (ML), a subfield of the artificial intelligence (AI), in many fields of sciences, engineering, and finance seems to mark a turning point in the replacement of traditional modeling procedures with artificial intelligence-based techniques. The study of the circulation in the interior of Earth relies on the study of high pressure mineral physics, geochemistry, and petrology where the number of the mantle parameters is large and the thermoelastic parameters are highly pressure- and temperature-dependent. More complexity arises from the fact that many of these parameters that are incorporated in the numerical models as input parameters are not yet well established. In such complex systems the application of machine learning algorithms can play a valuable role. Our focus in this study is the application of supervised machine learning (SML) algorithms in predicting mantle properties with the emphasis on SML techniques in solving the inverse problem. As a sample problem we focus on the spin transition in ferropericlase and perovskite that may cause slab and plume stagnation at mid-mantle depths. The degree of the stagnation depends on the degree of negative density anomaly at the spin transition zone. The training and testing samples for the machine learning models are produced by the numerical convection models with known magnitudes of density anomaly (as the class labels of the samples). The volume fractions of the stagnated slabs and plumes which can be considered as measures for the degree of stagnation are assigned as sample features. The machine learning models can determine the magnitude of the spin transition-induced density anomalies that can cause flow stagnation at mid-mantle depths. Employing support vector machine (SVM) algorithms we show that SML techniques

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.

A Direct inverse model to determine permeability fields from pressure and flow rate measurements

NARCIS (Netherlands)

Brouwer, G.K.; Fokker, P.A.; Wilschut, F.; Zijl, W.

2008-01-01

The determination of the permeability field from pressure and flow rate measurements in wells is a key problem in reservoir engineering. This paper presents a Double Constraint method for inverse modeling that is an example of direct inverse modeling. The method is used with a standard

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

Calibrating corneal material model parameters using only inflation data: an ill-posed problem

CSIR Research Space (South Africa)

Kok, S

2014-08-01

Full Text Available is to perform numerical modelling using the finite element method, for which a calibrated material model is required. These material models are typically calibrated using experimental inflation data by solving an inverse problem. In the inverse problem...

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.

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

Science.gov (United States)

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

2017-09-01

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

Inverse Problem 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.

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.

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

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.

THE DIDACTIC ANALYSIS OF STUDIES ON THE INVERSE PROBLEMS FOR THE DIFFERENTIAL EQUATIONS

Directory of Open Access Journals (Sweden)

В С Корнилов

2017-12-01

Full Text Available In article results of the didactic analysis of the organization and carrying out seminar classes in the inverse problems for the differential equations for students of higher educational institutions of the physical and mathematical directions of preparation are discussed. Such analysis includes a general characteristic of mathematical content of seminar occupations, the analysis of structure of seminar occupation, the analysis of realization of the developing and educational purposes, allocation of didactic units and informative means which have to be acquired by students when training each section of content of training in the inverse problems and other important psychology and pedagogical aspects. The attention to establishment of compliance to those of seminar occupations to lecture material and identification of functions in teaching and educational process which are carried out at the solution of the inverse problems, and also is paid to need to show various mathematical receptions and methods of their decision. Such didactic analysis helps not only to reveal such inverse problems at which solution students can collectively join in creative process of search of their decision, but also effectively organize control of assimilation of knowledge and abilities of students on the inverse problems for the differential equations.

Solving probabilistic inverse problems rapidly with prior samples

NARCIS (Netherlands)

Käufl, Paul; Valentine, Andrew P.; de Wit, Ralph W.; Trampert, Jeannot

2016-01-01

Owing to the increasing availability of computational resources, in recent years the probabilistic solution of non-linear, geophysical inverse problems by means of sampling methods has become increasingly feasible. Nevertheless, we still face situations in which a Monte Carlo approach is not

SIAM conference on inverse problems: Geophysical applications. Final technical report

Energy Technology Data Exchange (ETDEWEB)

NONE

1995-12-31

This conference was the second in a series devoted to a particular area of inverse problems. The theme of this series is to discuss problems of major scientific importance in a specific area from a mathematical perspective. The theme of this symposium was geophysical applications. In putting together the program we tried to include a wide range of mathematical scientists and to interpret geophysics in as broad a sense as possible. Our speaker came from industry, government laboratories, and diverse departments in academia. We managed to attract a geographically diverse audience with participation from five continents. There were talks devoted to seismology, hydrology, determination of the earth`s interior on a global scale as well as oceanographic and atmospheric inverse problems.

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

OpenAIRE

Klibanov, Michael V.; Romanov, Vladimir G.

2014-01-01

The inverse scattering problem of the reconstruction of the unknown potential with compact support in the 3-d Schr\\"odinger equation is considered. Only the modulus of the scattering complex valued wave field is known, whereas the phase is unknown. It is shown that the unknown potential can be reconstructed via the inverse Radon transform. Therefore, a long standing problem posed in 1977 by K. Chadan and P.C. Sabatier in their book "Inverse Problems in Quantum Scattering Theory" is solved.

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)

The Adjoint Method for the Inverse Problem of Option Pricing

Directory of Open Access Journals (Sweden)

Shou-Lei Wang

2014-01-01

Full Text Available The estimation of implied volatility is a typical PDE inverse problem. In this paper, we propose the TV-L1 model for identifying the implied volatility. The optimal volatility function is found by minimizing the cost functional measuring the discrepancy. The gradient is computed via the adjoint method which provides us with an exact value of the gradient needed for the minimization procedure. We use the limited memory quasi-Newton algorithm (L-BFGS to find the optimal and numerical examples shows the effectiveness of the presented method.

Inverse 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.

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

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

Computational electromagnetics and model-based inversion a modern paradigm for eddy-current nondestructive evaluation

CERN Document Server

Sabbagh, Harold A; Sabbagh, Elias H; Aldrin, John C; Knopp, Jeremy S

2013-01-01

Computational Electromagnetics and Model-Based Inversion: A Modern Paradigm for Eddy Current Nondestructive Evaluation describes the natural marriage of the computer to eddy-current NDE. Three distinct topics are emphasized in the book: (a) fundamental mathematical principles of volume-integral equations as a subset of computational electromagnetics, (b) mathematical algorithms applied to signal-processing and inverse scattering problems, and (c) applications of these two topics to problems in which real and model data are used. By showing how mathematics and the computer can solve problems more effectively than current analog practices, this book defines the modern technology of eddy-current NDE. This book will be useful to advanced students and practitioners in the fields of computational electromagnetics, electromagnetic inverse-scattering theory, nondestructive evaluation, materials evaluation and biomedical imaging. Users of eddy-current NDE technology in industries as varied as nuclear power, aerospace,...

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 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

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

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

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)

Automatic Flight Controller With Model Inversion

Science.gov (United States)

Meyer, George; Smith, G. Allan

1992-01-01

Automatic digital electronic control system based on inverse-model-follower concept being developed for proposed vertical-attitude-takeoff-and-landing airplane. Inverse-model-follower control places inverse mathematical model of dynamics of controlled plant in series with control actuators of controlled plant so response of combination of model and plant to command is unity. System includes feedback to compensate for uncertainties in mathematical model and disturbances imposed from without.

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.

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.

Forward and Inverse Modeling of Self-potential. A Tomography of Groundwater Flow and Comparison Between Deterministic and Stochastic Inversion Methods

Science.gov (United States)

Quintero-Chavarria, E.; Ochoa Gutierrez, L. H.

2016-12-01

Applications of the Self-potential Method in the fields of Hydrogeology and Environmental Sciences have had significant developments during the last two decades with a strong use on groundwater flows identification. Although only few authors deal with the forward problem's solution -especially in geophysics literature- different inversion procedures are currently being developed but in most cases they are compared with unconventional groundwater velocity fields and restricted to structured meshes. This research solves the forward problem based on the finite element method using the St. Venant's Principle to transform a point dipole, which is the field generated by a single vector, into a distribution of electrical monopoles. Then, two simple aquifer models were generated with specific boundary conditions and head potentials, velocity fields and electric potentials in the medium were computed. With the model's surface electric potential, the inverse problem is solved to retrieve the source of electric potential (vector field associated to groundwater flow) using deterministic and stochastic approaches. The first approach was carried out by implementing a Tikhonov regularization with a stabilized operator adapted to the finite element mesh while for the second a hierarchical Bayesian model based on Markov chain Monte Carlo (McMC) and Markov Random Fields (MRF) was constructed. For all implemented methods, the result between the direct and inverse models was contrasted in two ways: 1) shape and distribution of the vector field, and 2) magnitude's histogram. Finally, it was concluded that inversion procedures are improved when the velocity field's behavior is considered, thus, the deterministic method is more suitable for unconfined aquifers than confined ones. McMC has restricted applications and requires a lot of information (particularly in potentials fields) while MRF has a remarkable response especially when dealing with confined aquifers.

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

Science.gov (United States)

Sabatier, P. C.

1972-01-01

Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.

A penalty method for PDE-constrained optimization in inverse problems

International Nuclear Information System (INIS)

Leeuwen, T van; Herrmann, F J

2016-01-01

Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for several right-hand sides. Such PDE-constrained problems can be solved by finding a stationary point of the Lagrangian, which entails simultaneously updating the parameters and the (adjoint) state variables. For large-scale problems, such an all-at-once approach is not feasible as it requires storing all the state variables. In this case one usually resorts to a reduced approach where the constraints are explicitly eliminated (at each iteration) by solving the PDEs. These two approaches, and variations thereof, are the main workhorses for solving PDE-constrained optimization problems arising from inverse problems. In this paper, we present an alternative method that aims to combine the advantages of both approaches. Our method is based on a quadratic penalty formulation of the constrained optimization problem. By eliminating the state variable, we develop an efficient algorithm that has roughly the same computational complexity as the conventional reduced approach while exploiting a larger search space. Numerical results show that this method indeed reduces some of the nonlinearity of the problem and is less sensitive to the initial iterate. (paper)

Application of Lead Field Theory and Computerized Thorax Modeling for the ECG Inverse Problem

National Research Council Canada - National Science Library

Puurtinen, H

2001-01-01

.... In this study, one anatomically detailed 3D FDM model of the human thorax as a volume conductor was employed for forward and inverse estimation of ECG potentials and cardiac sources, respectively...

On parameterization of the inverse problem for estimating aquifer properties using tracer data

International Nuclear Information System (INIS)

Kowalsky, M. B.; Finsterle, Stefan A.; Williams, Kenneth H.; Murray, Christopher J.; Commer, Michael; Newcomer, Darrell R.; Englert, Andreas L.; Steefel, Carl I.; Hubbard, Susan

2012-01-01

We consider a field-scale tracer experiment conducted in 2007 in a shallow uranium-contaminated aquifer at Rifle, Colorado. In developing a reliable approach for inferring hydrological properties at the site through inverse modeling of the tracer data, decisions made on how to parameterize heterogeneity (i.e., how to represent a heterogeneous distribution using a limited number of parameters that are amenable to estimation) are of paramount importance. We present an approach for hydrological inversion of the tracer data and explore, using a 2D synthetic example at first, how parameterization affects the solution, and how additional characterization data could be incorporated to reduce uncertainty. Specifically, we examine sensitivity of the results to the configuration of pilot points used in a geostatistical parameterization, and to the sampling frequency and measurement error of the concentration data. A reliable solution of the inverse problem is found when the pilot point configuration is carefully implemented. In addition, we examine the use of a zonation parameterization, in which the geometry of the geological facies is known (e.g., from geophysical data or core data), to reduce the non-uniqueness of the solution and the number of unknown parameters to be estimated. When zonation information is only available for a limited region, special treatment in the remainder of the model is necessary, such as using a geostatistical parameterization. Finally, inversion of the actual field data is performed using 2D and 3D models, and results are compared with slug test data.

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

KAUST Repository

Rundell, William

2013-04-23

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

NUMERICAL 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.

Uniqueness in the inverse boundary value problem for piecewise homogeneous anisotropic elasticity

OpenAIRE

Cârstea, Cătălin I.; Honda, Naofumi; Nakamura, Gen

2016-01-01

Consider a three dimensional piecewise homogeneous anisotropic elastic medium $\\Omega$ which is a bounded domain consisting of a finite number of bounded subdomains $D_\\alpha$, with each $D_\\alpha$ a homogeneous elastic medium. One typical example is a finite element model with elements with curvilinear interfaces for an ansiotropic elastic medium. Assuming the $D_\\alpha$ are known and Lipschitz, we are concerned with the uniqueness in the inverse boundary value problem of identifying the ani...

Eigenvalue based inverse model of beam for structural modification and diagnostics: theoretical formulation

Directory of Open Access Journals (Sweden)

Leszek Majkut

Full Text Available In the work, the problems of the beam structural modification through coupling the additional mass or elastic support, as well as the problem of diagnostics of the beam cracks, are discussed. The common feature for both problems is that the material parameters in each of the discussed cases change only in one point (additional mass, the support in one point, the crack described by the elastic joint. These systems, after determination of the value of additional element and its localization, should have a given natural vibration frequency. In order to solve the inverse problem, i.e. the problem of finding values of the additional quantities (mass, elasticity, the beam inverse model was proposed. Analysis of this model allows finding such a value of additional mass (elasticity as a function of its localization so that the system has the free vibration frequency, which is desired in the modification problem or measured on the object in the diagnostics.

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)

Joint inversion of seismic refraction and resistivity data using layered models - applications to hydrogeology

Science.gov (United States)

Juhojuntti, N. G.; Kamm, J.

2010-12-01

We present a layered-model approach to joint inversion of shallow seismic refraction and resistivity (DC) data, which we believe is a seldom tested method of addressing the problem. This method has been developed as we believe that for shallow sedimentary environments (roughly fairly simple 2D geometries, mainly for checking the validity of the calculations. The inversion generally converges towards the correct solution, although there could be stability problems if the starting model is too erroneous. We have also applied the code to field data from seismic refraction and multi-electrode resistivity measurements at typical sand-gravel groundwater reservoirs. The tests are promising, as the calculated depths agree fairly well with information from drilling and the velocity and resistivity values appear reasonable. Current work includes better regularization of the inversion as well as defining individual weight factors for the different datasets, as the present algorithm tends to constrain the depths mainly by using the seismic data. More complex synthetic examples will also be tested, including models addressing the seismic hidden-layer problem.

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)

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

Improving multiple-point-based a priori models for inverse problems by combining Sequential Simulation with the Frequency Matching Method

DEFF Research Database (Denmark)

Cordua, Knud Skou; Hansen, Thomas Mejer; Lange, Katrine

In order to move beyond simplified covariance based a priori models, which are typically used for inverse problems, more complex multiple-point-based a priori models have to be considered. By means of marginal probability distributions ‘learned’ from a training image, sequential simulation has...... proven to be an efficient way of obtaining multiple realizations that honor the same multiple-point statistics as the training image. The frequency matching method provides an alternative way of formulating multiple-point-based a priori models. In this strategy the pattern frequency distributions (i.......e. marginals) of the training image and a subsurface model are matched in order to obtain a solution with the same multiple-point statistics as the training image. Sequential Gibbs sampling is a simulation strategy that provides an efficient way of applying sequential simulation based algorithms as a priori...

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.

Information criteria to estimate hyperparameters in groundwater inverse problems

Science.gov (United States)

Zanini, A.; Tanda, M. G.; Woodbury, A. D.

2017-12-01

One of the main issues in groundwater modeling is the knowledge of the hydraulic parameters such as transmissivity and storativity. In literature there are several efficacious inverse methods that are able to estimate these unknown properties. Most methods assume, as a priori knowledge, the form of the variogram (or covariance function) of the unknown parameters. The hyperparameters of the variogram (or covariance function) can be inferred from observations, assumed known or estimated. Information criteria are widely used in inverse problems in several disciplines (such as geophysics, hydrology, ...) to estimate the hyperparameters. In this work, in order to estimate the hyperparameters, we consider the Akaike Information Criterion (AIC) and the Akaike Bayesian Information Criterion (ABIC). AIC is computed as -2 ln[fitted model]+2 number of unknown parameters. The iterative procedure allows to identify the hyperparameters that minimize the AIC. The ABIC is similar to the AIC in form and is computed in terms of the Bayesian likelihood; it is appropriate when prior information is considered in the form of prior probability. ABIC = -2 ln[predictive distribution]+2 (number of hyperparameters). The predictive distribution is the normalizing constant that is at the denominator of the Bayes theorem and represents the pdf of observing the data with the uncertainty in the model parameters marginalized out of consideration. The correct hyperparameters are evaluated at the minimum value of the ABIC. In this work we compare the results obtained from AIC to ABIC, using a literature example and we describe pros and cons of the two approaches.

High effective inverse dynamics modelling for dual-arm robot

Science.gov (United States)

Shen, Haoyu; Liu, Yanli; Wu, Hongtao

2018-05-01

To deal with the problem of inverse dynamics modelling for dual arm robot, a recursive inverse dynamics modelling method based on decoupled natural orthogonal complement is presented. In this model, the concepts and methods of Decoupled Natural Orthogonal Complement matrices are used to eliminate the constraint forces in the Newton-Euler kinematic equations, and the screws is used to express the kinematic and dynamics variables. On this basis, the paper has developed a special simulation program with symbol software of Mathematica and conducted a simulation research on the a dual-arm robot. Simulation results show that the proposed method based on decoupled natural orthogonal complement can save an enormous amount of CPU time that was spent in computing compared with the recursive Newton-Euler kinematic equations and the results is correct and reasonable, which can verify the reliability and efficiency of the method.

Inverse problems in 1D hemodynamics on systemic networks: a sequential approach.

Science.gov (United States)

Lombardi, D

2014-02-01

In this work, a sequential approach based on the unscented Kalman filter is applied to solve inverse problems in 1D hemodynamics, on a systemic network. For instance, the arterial stiffness is estimated by exploiting cross-sectional area and mean speed observations in several locations of the arteries. The results are compared with those ones obtained by estimating the pulse wave velocity and the Moens-Korteweg formula. In the last section, a perspective concerning the identification of the terminal models parameters and peripheral circulation (modeled by a Windkessel circuit) is presented. Copyright © 2013 John Wiley & Sons, Ltd.

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.

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)

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

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....

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...

Flow modelling in fractured aquifers, development of multi-continua model (direct and inverse problems) and application to the CEA/Cadarache site

International Nuclear Information System (INIS)

Cartalade, Alain

2002-01-01

This research thesis concerns the modelling of aquifer flows under the CEA/Cadarache site. The author reports the implementation of a numerical simulation tool adapted to large scale flows in fractured media, and its application to the Cadarache nuclear site. After a description of the site geological and hydrogeological characteristics, the author presents the conceptual model on which the modelling is based, presents the inverse model which allows a better definition of parameters, reports the validation of the inverse approach by means of synthetic and semi-synthetic cases. Then, he reports experiments and simulation of the Cadarache site

An Inverse Problem Formulation Methodology for Stochastic Models

Science.gov (United States)

2010-05-02

form the surveillance data Infection control measures were implemented in the form of health care worker hand - hygiene before and after patients contact...manuscript derives from our interest in understanding the spread of infectious diseases in particular, nosocomial infections , in order to prevent major...given by the inverse of the parameter of the exponential distribution. A hand - hygiene policy applied to health care workers on isolated VRE colonized

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...

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.

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

Multiscattering inversion for low-model wavenumbers

KAUST Repository

Alkhalifah, Tariq Ali

2016-09-21

A successful full-waveform inversion implementation updates the low-wavenumber model components first for a proper description of the wavefield propagation and slowly adds the high wavenumber potentially scattering parts of the model. The low-wavenumber components can be extracted from the transmission parts of the recorded wavefield emanating directly from the source or the transmission parts from the single- or double-scattered wavefield computed from a predicted scatter field acting as secondary sources.We use a combined inversion of data modeled from the source and those corresponding to single and double scattering to update the velocity model and the component of the velocity (perturbation) responsible for the single and double scattering. The combined inversion helps us access most of the potential model wavenumber information that may be embedded in the data. A scattering-angle filter is used to divide the gradient of the combined inversion, so initially the high-wavenumber (low-scattering-angle) components of the gradient are directed to the perturbation model and the low-wavenumber (highscattering- angle) components are directed to the velocity model. As our background velocity matures, the scatteringangle divide is slowly lowered to allow for more of the higher wavenumbers to contribute the velocity model. Synthetic examples including the Marmousi model are used to demonstrate the additional illumination and improved velocity inversion obtained when including multiscattered energy. © 2016 Society of Exploration Geophysicists.

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.

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.

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)

Solution of the inverse scattering problem at fixed energy with non-physical S matrix elements

International Nuclear Information System (INIS)

Eberspaecher, M.; Amos, K.; Apagyi, B.

1999-12-01

The quantum mechanical inverse elastic scattering problem is solved with the modified Newton-Sabatier method. A set of S matrix elements calculated from a realistic analytic optical model potential serves as input data. It is demonstrated that the quality of the inversion potential can be improved by including non-physical S matrix elements to half, quarter and eighth valued partial waves if the original set does not contain enough information to determine the interaction potential. We demonstrate that results can be very sensitive to the choice of those non-physical S matrix values both with the analytic potential model and in a real application in which the experimental cross section for the symmetrical scattering system of 12 C+ 12 C at E=7.998 MeV is analyzed

A mathematical framework for inverse wave problems in heterogeneous media

NARCIS (Netherlands)

Blazek, K.D.; Stolk, C.; Symes, W.W.

2013-01-01

This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The coefficients of these time-dependent partial differential equations

Mixed linear-nonlinear fault slip inversion: Bayesian inference of model, weighting, and smoothing parameters

Science.gov (United States)

Fukuda, J.; Johnson, K. M.

2009-12-01

Studies utilizing inversions of geodetic data for the spatial distribution of coseismic slip on faults typically present the result as a single fault plane and slip distribution. Commonly the geometry of the fault plane is assumed to be known a priori and the data are inverted for slip. However, sometimes there is not strong a priori information on the geometry of the fault that produced the earthquake and the data is not always strong enough to completely resolve the fault geometry. We develop a method to solve for the full posterior probability distribution of fault slip and fault geometry parameters in a Bayesian framework using Monte Carlo methods. The slip inversion problem is particularly challenging because it often involves multiple data sets with unknown relative weights (e.g. InSAR, GPS), model parameters that are related linearly (slip) and nonlinearly (fault geometry) through the theoretical model to surface observations, prior information on model parameters, and a regularization prior to stabilize the inversion. We present the theoretical framework and solution method for a Bayesian inversion that can handle all of these aspects of the problem. The method handles the mixed linear/nonlinear nature of the problem through combination of both analytical least-squares solutions and Monte Carlo methods. We first illustrate and validate the inversion scheme using synthetic data sets. We then apply the method to inversion of geodetic data from the 2003 M6.6 San Simeon, California earthquake. We show that the uncertainty in strike and dip of the fault plane is over 20 degrees. We characterize the uncertainty in the slip estimate with a volume around the mean fault solution in which the slip most likely occurred. Slip likely occurred somewhere in a volume that extends 5-10 km in either direction normal to the fault plane. We implement slip inversions with both traditional, kinematic smoothing constraints on slip and a simple physical condition of uniform stress

Core flow inversion tested with numerical dynamo models

Science.gov (United States)

Rau, Steffen; Christensen, Ulrich; Jackson, Andrew; Wicht, Johannes

2000-05-01

We test inversion methods of geomagnetic secular variation data for the pattern of fluid flow near the surface of the core with synthetic data. These are taken from self-consistent 3-D models of convection-driven magnetohydrodynamic dynamos in rotating spherical shells, which generate dipole-dominated magnetic fields with an Earth-like morphology. We find that the frozen-flux approximation, which is fundamental to all inversion schemes, is satisfied to a fair degree in the models. In order to alleviate the non-uniqueness of the inversion, usually a priori conditions are imposed on the flow; for example, it is required to be purely toroidal or geostrophic. Either condition is nearly satisfied by our model flows near the outer surface. However, most of the surface velocity field lies in the nullspace of the inversion problem. Nonetheless, the a priori constraints reduce the nullspace, and by inverting the magnetic data with either one of them we recover a significant part of the flow. With the geostrophic condition the correlation coefficient between the inverted and the true velocity field can reach values of up to 0.65, depending on the choice of the damping parameter. The correlation is significant at the 95 per cent level for most spherical harmonic degrees up to l=26. However, it degrades substantially, even at long wavelengths, when we truncate the magnetic data sets to l currents, similar to those seen in core-flow models derived from geomagnetic data, occur in the equatorial region. However, the true flow does not contain this flow component. The results suggest that some meaningful information on the core-flow pattern can be retrieved from secular variation data, but also that the limited resolution of the magnetic core field could produce serious artefacts.

Incorporating modelled subglacial hydrology into inversions for basal drag

Directory of Open Access Journals (Sweden)

C. P. Koziol

2017-12-01

Full Text Available A key challenge in modelling coupled ice-flow–subglacial hydrology is initializing the state and parameters of the system. We address this problem by presenting a workflow for initializing these values at the start of a summer melt season. The workflow depends on running a subglacial hydrology model for the winter season, when the system is not forced by meltwater inputs, and ice velocities can be assumed constant. Key parameters of the winter run of the subglacial hydrology model are determined from an initial inversion for basal drag using a linear sliding law. The state of the subglacial hydrology model at the end of winter is incorporated into an inversion of basal drag using a non-linear sliding law which is a function of water pressure. We demonstrate this procedure in the Russell Glacier area and compare the output of the linear sliding law with two non-linear sliding laws. Additionally, we compare the modelled winter hydrological state to radar observations and find that it is in line with summer rather than winter observations.

Application of a numerical Laplace transform inversion technique to a problem in reactor dynamics

International Nuclear Information System (INIS)

Ganapol, B.D.; Sumini, M.

1990-01-01

A newly developed numerical technique for the Laplace transform inversion is applied to a classical time-dependent problem of reactor physics. The dynamic behaviour of a multiplying system has been analyzed through a continuous slowing down model, taking into account a finite slowing down time, the presence of several groups of neutron precursors and simplifying the spatial analysis using the space asymptotic approximation. The results presented, show complete agreement with analytical ones previously obtained and allow a deeper understanding of the model features. (author)

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

Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems

International Nuclear Information System (INIS)

Haber, E; Horesh, L; Tenorio, L

2010-01-01

Design of experiments for discrete ill-posed problems is a relatively new area of research. While there has been some limited work concerning the linear case, little has been done to study design criteria and numerical methods for ill-posed nonlinear problems. We present an algorithmic framework for nonlinear experimental design with an efficient numerical implementation. The data are modeled as indirect, noisy observations of the model collected via a set of plausible experiments. An inversion estimate based on these data is obtained by a weighted Tikhonov regularization whose weights control the contribution of the different experiments to the data misfit term. These weights are selected by minimization of an empirical estimate of the Bayes risk that is penalized to promote sparsity. This formulation entails a bilevel optimization problem that is solved using a simple descent method. We demonstrate the viability of our design with a problem in electromagnetic imaging based on direct current resistivity and magnetotelluric data

On the feasibility of inversion methods based on models of urban sky glow

International Nuclear Information System (INIS)

Kolláth, Z.; Kránicz, B.

2014-01-01

Multi-wavelength imaging luminance photometry of sky glow provides a huge amount of information on light pollution. However, the understanding of the measured data involves the combination of different processes and data of radiation transfer, atmospheric physics and atmospheric constitution. State-of-the-art numerical radiation transfer models provide the possibility to define an inverse problem to obtain information on the emission intensity distribution of a city and perhaps the physical properties of the atmosphere. We provide numerical tests on the solvability and feasibility of such procedures. - Highlights: • A method of urban sky glow inversion is introduced based on Monte-Carlo calculations. • Imaging photometry can provide enough information for basic inversions. • The inversion technique can be used to construct maps of light pollution. • The inclusion of multiple scattering in the models plays an important role

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.

A nonlinear inversion for the velocity background and perturbation models

KAUST Repository

Wu, Zedong

2015-08-19

Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect diving waves, which is an important source of information for extracting the long wavelength components of the velocity model. Thus, we propose a new optimization problem through breaking the velocity model into the background and the perturbation in the wave equation directly. In this case, the perturbed model is no longer the single scattering model, but includes all scattering. We optimize both components simultaneously, and thus, the objective function is nonlinear with respect to both the background and perturbation. The new introduced w can absorb the non-smooth update of background naturally. Application to the Marmousi model with frequencies that start at 5 Hz shows that this method can converge to the accurate velocity starting from a linearly increasing initial velocity. Application to the SEG2014 demonstrates the versatility of the approach.

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.

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.

Inverse problem of Ocean Acoustic Tomography (OAT) - A numerical experiment

Digital Repository Service at National Institute of Oceanography (India)

Murty, T.V.R.; Somayajulu, Y.K.; Mahadevan, R.; Murty, C.S.

Acoustic model simulation experiments related to the forward and inverse aspects of ocean tomography have been taken up with a view to estimate the vertical sound speed field by inverting the travel time data. Two methods of inversion have been...

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.

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.

New prospects in direct, inverse and control problems for evolution equations

CERN Document Server

Fragnelli, Genni; Mininni, Rosa

2014-01-01

This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences. Applied sciences consider situations in which the evolution of a given system over time is observed, and the related models can be formulated in terms of evolution equations (EEs). These equations have been studied intensively in theoretical research and are the source of an enormous number of applications. In this volume, particular attention is given to direct, inverse and control problems for EEs. The book provides an updated overview of the field, revealing its richness and vitality.

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.

An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling

Science.gov (United States)

Li, Weixuan; Lin, Guang; Zhang, Dongxiao

2014-02-01

The probabilistic collocation-based Kalman filter (PCKF) is a recently developed approach for solving inverse problems. It resembles the ensemble Kalman filter (EnKF) in every aspect-except that it represents and propagates model uncertainty by polynomial chaos expansion (PCE) instead of an ensemble of model realizations. Previous studies have shown PCKF is a more efficient alternative to EnKF for many data assimilation problems. However, the accuracy and efficiency of PCKF depends on an appropriate truncation of the PCE series. Having more polynomial chaos basis functions in the expansion helps to capture uncertainty more accurately but increases computational cost. Selection of basis functions is particularly important for high-dimensional stochastic problems because the number of polynomial chaos basis functions required to represent model uncertainty grows dramatically as the number of input parameters (random dimensions) increases. In classic PCKF algorithms, the PCE basis functions are pre-set based on users' experience. Also, for sequential data assimilation problems, the basis functions kept in PCE expression remain unchanged in different Kalman filter loops, which could limit the accuracy and computational efficiency of classic PCKF algorithms. To address this issue, we present a new algorithm that adaptively selects PCE basis functions for different problems and automatically adjusts the number of basis functions in different Kalman filter loops. The algorithm is based on adaptive functional ANOVA (analysis of variance) decomposition, which approximates a high-dimensional function with the summation of a set of low-dimensional functions. Thus, instead of expanding the original model into PCE, we implement the PCE expansion on these low-dimensional functions, which is much less costly. We also propose a new adaptive criterion for ANOVA that is more suited for solving inverse problems. The new algorithm was tested with different examples and demonstrated

Spin model for nontrivial types of magnetic order in inverse-perovskite antiferromagnets

Science.gov (United States)

Mochizuki, Masahito; Kobayashi, Masaya; Okabe, Reoya; Yamamoto, Daisuke

2018-02-01

Nontrivial magnetic orders in the inverse-perovskite manganese nitrides are theoretically studied by constructing a classical spin model describing the magnetic anisotropy and frustrated exchange interactions inherent in specific crystal and electronic structures of these materials. With a replica-exchange Monte Carlo technique, a theoretical analysis of this model reproduces the experimentally observed triangular Γ5 g and Γ4 g spin-ordered patterns and the systematic evolution of magnetic orders. Our Rapid Communication solves a 40-year-old problem of nontrivial magnetism for the inverse-perovskite manganese nitrides and provides a firm basis for clarifying the magnetism-driven negative thermal expansion phenomenon discovered in this class of materials.

A boundary-value inverse model and its application to the calculation of tidal oscillation systems in the Western South Atlantic Ocean

International Nuclear Information System (INIS)

Miranda-Alonso, S.

1991-01-01

A Cauchy-Riemann problem is solved for the case of the linearized equations for long waves. The initial-values are amplitudes and phases measured at the coast. No boundary values are made use of. This inverse-problem is solved by starting the calculations at the coast and continuing outwards to the open ocean in a rectangular areas with one side at the coast and the other three at the open ocean. The initial values were expanded into the complex plane to get a platform to perform with the calculations. This non-well-posed problem was solved by means of two different mathematical techniques for comparison. The results produced with the inverse model were compared with those produced with a 'classical' model initialized at the three open boundaries with the results of the inverse model. The oscillating systems produced by both models were quite similar, giving validity to this invese modeling approach which should be a useful technique to solve problems when only initial values are known. (orig.)

Entropy, Information Theory, Information Geometry and Bayesian Inference in Data, Signal and Image Processing and Inverse Problems

Directory of Open Access Journals (Sweden)

Ali Mohammad-Djafari

2015-06-01

Full Text Available The main content of this review article is first to review the main inference tools using Bayes rule, the maximum entropy principle (MEP, information theory, relative entropy and the Kullback–Leibler (KL divergence, Fisher information and its corresponding geometries. For each of these tools, the precise context of their use is described. The second part of the paper is focused on the ways these tools have been used in data, signal and image processing and in the inverse problems, which arise in different physical sciences and engineering applications. A few examples of the applications are described: entropy in independent components analysis (ICA and in blind source separation, Fisher information in data model selection, different maximum entropy-based methods in time series spectral estimation and in linear inverse problems and, finally, the Bayesian inference for general inverse problems. Some original materials concerning the approximate Bayesian computation (ABC and, in particular, the variational Bayesian approximation (VBA methods are also presented. VBA is used for proposing an alternative Bayesian computational tool to the classical Markov chain Monte Carlo (MCMC methods. We will also see that VBA englobes joint maximum a posteriori (MAP, as well as the different expectation-maximization (EM algorithms as particular cases.

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

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)

Global Monthly CO2 Flux Inversion Based on Results of Terrestrial Ecosystem Modeling

Science.gov (United States)

Deng, F.; Chen, J.; Peters, W.; Krol, M.

2008-12-01

Most of our understanding of the sources and sinks of atmospheric CO2 has come from inverse studies of atmospheric CO2 concentration measurements. However, the number of currently available observation stations and our ability to simulate the diurnal planetary boundary layer evolution over continental regions essentially limit the number of regions that can be reliably inverted globally, especially over continental areas. In order to overcome these restrictions, a nested inverse modeling system was developed based on the Bayesian principle for estimating carbon fluxes of 30 regions in North America and 20 regions for the rest of the globe. Inverse modeling was conducted in monthly steps using CO2 concentration measurements of 5 years (2000 - 2005) with the following two models: (a) An atmospheric transport model (TM5) is used to generate the transport matrix where the diurnal variation n of atmospheric CO2 concentration is considered to enhance the use of the afternoon-hour average CO2 concentration measurements over the continental sites. (b) A process-based terrestrial ecosystem model (BEPS) is used to produce hourly step carbon fluxes, which could minimize the limitation due to our inability to solve the inverse problem in a high resolution, as the background of our inversion. We will present our recent results achieved through a combination of the bottom-up modeling with BEPS and the top-down modeling based on TM5 driven by offline meteorological fields generated by the European Centre for Medium Range Weather Forecast (ECMFW).

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.

Inverse problem studies of biochemical systems with structure identification of S-systems by embedding training functions in a genetic algorithm.

Science.gov (United States)

Sarode, Ketan Dinkar; Kumar, V Ravi; Kulkarni, B D

2016-05-01

An efficient inverse problem approach for parameter estimation, state and structure identification from dynamic data by embedding training functions in a genetic algorithm methodology (ETFGA) is proposed for nonlinear dynamical biosystems using S-system canonical models. Use of multiple shooting and decomposition approach as training functions has been shown for handling of noisy datasets and computational efficiency in studying the inverse problem. The advantages of the methodology are brought out systematically by studying it for three biochemical model systems of interest. By studying a small-scale gene regulatory system described by a S-system model, the first example demonstrates the use of ETFGA for the multifold aims of the inverse problem. The estimation of a large number of parameters with simultaneous state and network identification is shown by training a generalized S-system canonical model with noisy datasets. The results of this study bring out the superior performance of ETFGA on comparison with other metaheuristic approaches. The second example studies the regulation of cAMP oscillations in Dictyostelium cells now assuming limited availability of noisy data. Here, flexibility of the approach to incorporate partial system information in the identification process is shown and its effect on accuracy and predictive ability of the estimated model are studied. The third example studies the phenomenological toy model of the regulation of circadian oscillations in Drosophila that follows rate laws different from S-system power-law. For the limited noisy data, using a priori information about properties of the system, we could estimate an alternate S-system model that showed robust oscillatory behavior with predictive abilities. Copyright © 2016 Elsevier Inc. All rights reserved.

Effect of coupling asymmetry on mean-field solutions of the direct and inverse Sherrington-Kirkpatrick model

DEFF Research Database (Denmark)

Sakellariou, Jason; Roudi, Yasser; Mezard, Marc

2012-01-01

We study how the degree of symmetry in the couplings influences the performance of three mean field methods used for solving the direct and inverse problems for generalized Sherrington-Kirkpatrick models. In this context, the direct problem is predicting the potentially time-varying magnetizations...... than the other two approximations, TAP outperforms MF when the coupling matrix is nearly symmetric, while MF works better when it is strongly asymmetric. For the inverse problem, MF performs better than both TAP and nMF, although an ad hoc adjustment of TAP can make it comparable to MF. For high...

Effects of induced stress on seismic forward modelling and inversion

Science.gov (United States)

Tromp, Jeroen; Trampert, Jeannot

2018-05-01

We demonstrate how effects of induced stress may be incorporated in seismic modelling and inversion. Our approach is motivated by the accommodation of pre-stress in global seismology. Induced stress modifies both the equation of motion and the constitutive relationship. The theory predicts that induced pressure linearly affects the unstressed isotropic moduli with a slope determined by their adiabatic pressure derivatives. The induced deviatoric stress produces anisotropic compressional and shear wave speeds; the latter result in shear wave splitting. For forward modelling purposes, we determine the weak form of the equation of motion under induced stress. In the context of the inverse problem, we determine induced stress sensitivity kernels, which may be used for adjoint tomography. The theory is illustrated by considering 2-D propagation of SH waves and related Fréchet derivatives based on a spectral-element method.

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.

Time-reversal and Bayesian inversion

Science.gov (United States)

Debski, Wojciech

2017-04-01

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

pyGIMLi: An open-source library for modelling and inversion in geophysics

Science.gov (United States)

Rücker, Carsten; Günther, Thomas; Wagner, Florian M.

2017-12-01

Many tasks in applied geosciences cannot be solved by single measurements, but require the integration of geophysical, geotechnical and hydrological methods. Numerical simulation techniques are essential both for planning and interpretation, as well as for the process understanding of modern geophysical methods. These trends encourage open, simple, and modern software architectures aiming at a uniform interface for interdisciplinary and flexible modelling and inversion approaches. We present pyGIMLi (Python Library for Inversion and Modelling in Geophysics), an open-source framework that provides tools for modelling and inversion of various geophysical but also hydrological methods. The modelling component supplies discretization management and the numerical basis for finite-element and finite-volume solvers in 1D, 2D and 3D on arbitrarily structured meshes. The generalized inversion framework solves the minimization problem with a Gauss-Newton algorithm for any physical forward operator and provides opportunities for uncertainty and resolution analyses. More general requirements, such as flexible regularization strategies, time-lapse processing and different sorts of coupling individual methods are provided independently of the actual methods used. The usage of pyGIMLi is first demonstrated by solving the steady-state heat equation, followed by a demonstration of more complex capabilities for the combination of different geophysical data sets. A fully coupled hydrogeophysical inversion of electrical resistivity tomography (ERT) data of a simulated tracer experiment is presented that allows to directly reconstruct the underlying hydraulic conductivity distribution of the aquifer. Another example demonstrates the improvement of jointly inverting ERT and ultrasonic data with respect to saturation by a new approach that incorporates petrophysical relations in the inversion. Potential applications of the presented framework are manifold and include time

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

Sparse deconvolution for the large-scale ill-posed inverse problem of impact force reconstruction

Science.gov (United States)

Qiao, Baijie; Zhang, Xingwu; Gao, Jiawei; Liu, Ruonan; Chen, Xuefeng

2017-01-01

Most previous regularization methods for solving the inverse problem of force reconstruction are to minimize the l2-norm of the desired force. However, these traditional regularization methods such as Tikhonov regularization and truncated singular value decomposition, commonly fail to solve the large-scale ill-posed inverse problem in moderate computational cost. In this paper, taking into account the sparse characteristic of impact force, the idea of sparse deconvolution is first introduced to the field of impact force reconstruction and a general sparse deconvolution model of impact force is constructed. Second, a novel impact force reconstruction method based on the primal-dual interior point method (PDIPM) is proposed to solve such a large-scale sparse deconvolution model, where minimizing the l2-norm is replaced by minimizing the l1-norm. Meanwhile, the preconditioned conjugate gradient algorithm is used to compute the search direction of PDIPM with high computational efficiency. Finally, two experiments including the small-scale or medium-scale single impact force reconstruction and the relatively large-scale consecutive impact force reconstruction are conducted on a composite wind turbine blade and a shell structure to illustrate the advantage of PDIPM. Compared with Tikhonov regularization, PDIPM is more efficient, accurate and robust whether in the single impact force reconstruction or in the consecutive impact force reconstruction.

On the Inverse EEG Problem for a 1D Current Distribution

Directory of Open Access Journals (Sweden)

George Dassios

2014-01-01

Full Text Available Albanese and Monk (2006 have shown that, it is impossible to recover the support of a three-dimensional current distribution within a conducting medium from the knowledge of the electric potential outside the conductor. On the other hand, it is possible to obtain the support of a current which lives in a subspace of dimension lower than three. In the present work, we actually demonstrate this possibility by assuming a one-dimensional current distribution supported on a small line segment having arbitrary location and orientation within a uniform spherical conductor. The immediate representation of this problem refers to the inverse problem of electroencephalography (EEG with a linear current distribution and the spherical model of the brain-head system. It is shown that the support is identified through the solution of a nonlinear algebraic system which is investigated thoroughly. Numerical tests show that this system has exactly one real solution. Exact solutions are analytically obtained for a couple of special cases.

Resolving the existence of Higgsinos in the LHC inverse problem

International Nuclear Information System (INIS)

Jung, Sunghoon

2014-01-01

The LHC inverse problem is infamously challenging when neutralinos and charginos are heavy and pure and other superparticles are decoupled. This limit is becoming more relevant to particle physics nowadays. Fortunately, in this limit, Higgsinos produce a distinctive signature if they are the LSPs or NLSPs. The identifying signature is the presence of equal numbers of Z bosons and Higgs bosons in NLSP productions and subsequent decays at hadron colliders. The signature is derived from the Goldstone equivalence theorem by which partial widths into Z and Higgs bosons are inherently related and from the fact that Higgsinos consist of two indistinguishable neutralinos. Thus it is valid in general for many supersymmetry models; exceptions may happen when Higgsino NLSPs decay to weakly coupled LSPs such as axinos or gravitinos.

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

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

Science.gov (United States)

CUI, C.; Hou, W.

2017-12-01

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

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

Solving Inverse Detection Problems Using Passive Radiation Signatures

International Nuclear Information System (INIS)

Favorite, Jeffrey A.; Armstrong, Jerawan C.; Vaquer, Pablo A.

2012-01-01

The ability to reconstruct an unknown radioactive object based on its passive gamma-ray and neutron signatures is very important in homeland security applications. Often in the analysis of unknown radioactive objects, for simplicity or speed or because there is no other information, they are modeled as spherically symmetric regardless of their actual geometry. In these presentation we discuss the accuracy and implications of this approximation for decay gamma rays and for neutron-induced gamma rays. We discuss an extension of spherical raytracing (for uncollided fluxes) that allows it to be used when the exterior shielding is flat or cylindrical. We revisit some early results in boundary perturbation theory, showing that the Roussopolos estimate is the correct one to use when the quantity of interest is the flux or leakage on the boundary. We apply boundary perturbation theory to problems in which spherically symmetric systems are perturbed in asymmetric nonspherical ways. We apply mesh adaptive direct search (MADS) algorithms to object reconstructions. We present a benchmark test set that may be used to quantitatively evaluate inverse detection methods.

Multi-scattering inversion for low model wavenumbers

KAUST Repository

Alkhalifah, Tariq Ali

2015-08-19

A successful full wavenumber inversion (FWI) implementation updates the low wavenumber model components first for proper wavefield propagation description, and slowly adds the high-wavenumber potentially scattering parts of the model. The low-wavenumber components can be extracted from the transmission parts of the recorded data given by direct arrivals or the transmission parts of the single and double-scattering wave-fields developed from a predicted scatter field. We develop a combined inversion of data modeled from the source and those corresponding to single and double scattering to update both the velocity model and the component of the velocity (perturbation) responsible for the single and double scattering. The combined inversion helps us access most of the potential model wavenumber information that may be embedded in the data. A scattering angle filter is used to divide the gradient of the combined inversion so initially the high wavenumber (low scattering angle) components of the gradient is directed to the perturbation model and the low wavenumber (high scattering angle) components to the velocity model. As our background velocity matures, the scattering angle divide is slowly lowered to allow for more of the higher wavenumbers to contribute the velocity model.

Greedy solution of ill-posed problems: error bounds and exact inversion

International Nuclear Information System (INIS)

Denis, L; Lorenz, D A; Trede, D

2009-01-01

The orthogonal matching pursuit (OMP) is a greedy algorithm to solve sparse approximation problems. Sufficient conditions for exact recovery are known with and without noise. In this paper we investigate the applicability of the OMP for the solution of ill-posed inverse problems in general, and in particular for two deconvolution examples from mass spectrometry and digital holography, respectively. In sparse approximation problems one often has to deal with the problem of redundancy of a dictionary, i.e. the atoms are not linearly independent. However, one expects them to be approximatively orthogonal and this is quantified by the so-called incoherence. This idea cannot be transferred to ill-posed inverse problems since here the atoms are typically far from orthogonal. The ill-posedness of the operator probably causes the correlation of two distinct atoms to become huge, i.e. that two atoms look much alike. Therefore, one needs conditions which take the structure of the problem into account and work without the concept of coherence. In this paper we develop results for the exact recovery of the support of noisy signals. In the two examples, mass spectrometry and digital holography, we show that our results lead to practically relevant estimates such that one may check a priori if the experimental setup guarantees exact deconvolution with OMP. Especially in the example from digital holography, our analysis may be regarded as a first step to calculate the resolution power of droplet holography

Inverse 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.

Adaptive forward-inverse modeling of reservoir fluids away from wellbores; TOPICAL

International Nuclear Information System (INIS)

Ziagos, J P; Gelinas, R J; Doss, S K; Nelson, R G

1999-01-01

This Final Report contains the deliverables of the DeepLook Phase I project entitled, ''Adaptive Forward-Inverse Modeling of Reservoir Fluids Away from Wellbores''. The deliverables are: (i) a description of 2-D test problem results, analyses, and technical descriptions of the techniques used, (ii) a listing of program setup commands that construct and execute the codes for selected test problems (these commands are in mathematical terminology, which reinforces technical descriptions in the text), and (iii) an evaluation and recommendation regarding continuance of this project, including considerations of possible extensions to 3-D codes, additional technical scope, and budget for the out-years. The far-market objective in this project is to develop advanced technologies that can help locate and enhance the recovery of oil from heterogeneous rock formations. The specific technical objective in Phase I was to develop proof-of-concept of new forward and inverse (F-I) modeling techniques[Gelinas et al, 1998] that seek to enhance estimates (images) of formation permeability distributions and fluid motion away from wellbore volumes. This goes to the heart of improving industry's ability to jointly image reservoir permeability and flow predictions of trapped and recovered oil versus time. The estimation of formation permeability away from borehole measurements is an ''inverse'' problem. It is an inseparable part of modeling fluid flows throughout the reservoir in efforts to increase the efficiency of oil recovery at minimum cost. Classic issues of non-uniqueness, mathematical instability, noise effects, and inadequate numerical solution techniques have historically impeded progress in reservoir parameter estimations. Because information pertaining to fluid and rock properties is always sampled sparsely by wellbore measurements, a successful method for interpolating permeability and fluid data between the measurements must be: (i) physics-based, (ii) conditioned by signal

Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods.

Science.gov (United States)

Gramfort, Alexandre; Kowalski, Matthieu; Hämäläinen, Matti

2012-04-07

Magneto- and electroencephalography (M/EEG) measure the electromagnetic fields produced by the neural electrical currents. Given a conductor model for the head, and the distribution of source currents in the brain, Maxwell's equations allow one to compute the ensuing M/EEG signals. Given the actual M/EEG measurements and the solution of this forward problem, one can localize, in space and in time, the brain regions that have produced the recorded data. However, due to the physics of the problem, the limited number of sensors compared to the number of possible source locations, and measurement noise, this inverse problem is ill-posed. Consequently, additional constraints are needed. Classical inverse solvers, often called minimum norm estimates (MNE), promote source estimates with a small ℓ₂ norm. Here, we consider a more general class of priors based on mixed norms. Such norms have the ability to structure the prior in order to incorporate some additional assumptions about the sources. We refer to such solvers as mixed-norm estimates (MxNE). In the context of M/EEG, MxNE can promote spatially focal sources with smooth temporal estimates with a two-level ℓ₁/ℓ₂ mixed-norm, while a three-level mixed-norm can be used to promote spatially non-overlapping sources between different experimental conditions. In order to efficiently solve the optimization problems of MxNE, we introduce fast first-order iterative schemes that for the ℓ₁/ℓ₂ norm give solutions in a few seconds making such a prior as convenient as the simple MNE. Furthermore, thanks to the convexity of the optimization problem, we can provide optimality conditions that guarantee global convergence. The utility of the methods is demonstrated both with simulations and experimental MEG data.

Modeling and forecasting foreign exchange daily closing prices with normal inverse Gaussian

Science.gov (United States)

Teneng, Dean

2013-09-01

We fit the normal inverse Gaussian(NIG) distribution to foreign exchange closing prices using the open software package R and select best models by Käärik and Umbleja (2011) proposed strategy. We observe that daily closing prices (12/04/2008 - 07/08/2012) of CHF/JPY, AUD/JPY, GBP/JPY, NZD/USD, QAR/CHF, QAR/EUR, SAR/CHF, SAR/EUR, TND/CHF and TND/EUR are excellent fits while EGP/EUR and EUR/GBP are good fits with a Kolmogorov-Smirnov test p-value of 0.062 and 0.08 respectively. It was impossible to estimate normal inverse Gaussian parameters (by maximum likelihood; computational problem) for JPY/CHF but CHF/JPY was an excellent fit. Thus, while the stochastic properties of an exchange rate can be completely modeled with a probability distribution in one direction, it may be impossible the other way around. We also demonstrate that foreign exchange closing prices can be forecasted with the normal inverse Gaussian (NIG) Lévy process, both in cases where the daily closing prices can and cannot be modeled by NIG distribution.

Angle-domain inverse scattering migration/inversion in isotropic media

Science.gov (United States)

Li, Wuqun; Mao, Weijian; Li, Xuelei; Ouyang, Wei; Liang, Quan

2018-07-01

The classical seismic asymptotic inversion can be transformed into a problem of inversion of generalized Radon transform (GRT). In such methods, the combined parameters are linearly attached to the scattered wave-field by Born approximation and recovered by applying an inverse GRT operator to the scattered wave-field data. Typical GRT-style true-amplitude inversion procedure contains an amplitude compensation process after the weighted migration via dividing an illumination associated matrix whose elements are integrals of scattering angles. It is intuitional to some extent that performs the generalized linear inversion and the inversion of GRT together by this process for direct inversion. However, it is imprecise to carry out such operation when the illumination at the image point is limited, which easily leads to the inaccuracy and instability of the matrix. This paper formulates the GRT true-amplitude inversion framework in an angle-domain version, which naturally degrades the external integral term related to the illumination in the conventional case. We solve the linearized integral equation for combined parameters of different fixed scattering angle values. With this step, we obtain high-quality angle-domain common-image gathers (CIGs) in the migration loop which provide correct amplitude-versus-angle (AVA) behavior and reasonable illumination range for subsurface image points. Then we deal with the over-determined problem to solve each parameter in the combination by a standard optimization operation. The angle-domain GRT inversion method keeps away from calculating the inaccurate and unstable illumination matrix. Compared with the conventional method, the angle-domain method can obtain more accurate amplitude information and wider amplitude-preserved range. Several model tests demonstrate the effectiveness and practicability.

A Parametric Empirical Bayesian framework for the EEG/MEG inverse problem: generative models for multisubject and multimodal integration

Directory of Open Access Journals (Sweden)

Richard N Henson

2011-08-01

Full Text Available We review recent methodological developments within a Parametric Empirical Bayesian (PEB framework for reconstructing intracranial sources of extracranial electroencephalographic (EEG and magnetoencephalographic (MEG data under linear Gaussian assumptions. The PEB framework offers a natural way to integrate multiple constraints (spatial priors on this inverse problem, such as those derived from different modalities (e.g., from functional magnetic resonance imaging, fMRI or from multiple replications (e.g., subjects. Using variations of the same basic generative model, we illustrate the application of PEB to three cases: 1 symmetric integration (fusion of MEG and EEG; 2 asymmetric integration of MEG or EEG with fMRI, and 3 group-optimisation of spatial priors across subjects. We evaluate these applications on multimodal data acquired from 18 subjects, focusing on energy induced by face perception within a time-frequency window of 100-220ms, 8-18Hz. We show the benefits of multi-modal, multi-subject integration in terms of the model evidence and the reproducibility (over subjects of cortical responses to faces.

Trimming and procrastination as inversion techniques

Science.gov (United States)

Backus, George E.

1996-12-01

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

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.

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.

A hybrid finite difference and integral equation method for modeling and inversion of marine CSEM data

DEFF Research Database (Denmark)

Yoon, Daeung; Zhdanov, Michael; Cai, Hongzhu

2015-01-01

One of the major problems in the modeling and inversion of marine controlled source electromagnetic (MCSEM) data is related to the need for accurate representation of very complex geoelectrical models typical for marine environment. At the same time, the corresponding forward modeling algorithms...

Anisotropic magnetotelluric inversion using a mutual information constraint

Science.gov (United States)

Mandolesi, E.; Jones, A. G.

2012-12-01

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

Comparative study of direct and inverse problems of cracked beams

Directory of Open Access Journals (Sweden)

Mahieddine Chettah

2018-01-01

Full Text Available In recent decades, the analysis and evaluation of the cracked structures were hot spots in several engineering fields and has been the subject of great interest with important and comprehensive surveys covering various methodologies and applications, in order to obtain reliable and effective methods to maintain the safety and performance of structures on a proactive basis. The presence of a crack, not only causes a local variation in the structural parameters (e.g., the stiffness of a beam at its location, but it also has a global effect which affects the overall dynamic behavior of the structure (such as the natural frequencies. For this reason, the dynamic characterization of the cracked structures can be used to detect damage from non-destructive testing. The objective of this paper is to compare the accuracy and ability of two methods to correctly predict the results for both direct problem to find natural frequencies and inverse problem to find crack’s locations and depths of a cracked simply supported beam. Several cases of crack depths and crack locations are investigated. The crack is supposed to remain open. The Euler–Bernoulli beam theory is employed to model the cracked beam and the crack is represented as a rotational spring with a sectional flexibility. In the first method, the transfer matrix method is used; the cracked beam is modeled as two uniform sub-segments connected by a rotational spring located at the cracked section. In the second method which is based on the Rayleigh’s method, the mode shape of the cracked beam is constructed by adding a cubic polynomial function to that of the undamaged beam. By applying the compatibility conditions at crack’s location and the corresponding boundary conditions, the general forms of characteristic equations for this cracked system are obtained. The two methods are then utilized to determine the locations and depths by using any two natural frequencies of a cracked simply

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...

Voxel inversion of airborne electromagnetic data for improved model integration

Science.gov (United States)

Fiandaca, Gianluca; Auken, Esben; Kirkegaard, Casper; Vest Christiansen, Anders

2014-05-01

Inversion of electromagnetic data has migrated from single site interpretations to inversions including entire surveys using spatial constraints to obtain geologically reasonable results. Though, the model space is usually linked to the actual observation points. For airborne electromagnetic (AEM) surveys the spatial discretization of the model space reflects the flight lines. On the contrary, geological and groundwater models most often refer to a regular voxel grid, not correlated to the geophysical model space, and the geophysical information has to be relocated for integration in (hydro)geological models. We have developed a new geophysical inversion algorithm working directly in a voxel grid disconnected from the actual measuring points, which then allows for informing directly geological/hydrogeological models. The new voxel model space defines the soil properties (like resistivity) on a set of nodes, and the distribution of the soil properties is computed everywhere by means of an interpolation function (e.g. inverse distance or kriging). Given this definition of the voxel model space, the 1D forward responses of the AEM data are computed as follows: 1) a 1D model subdivision, in terms of model thicknesses, is defined for each 1D data set, creating "virtual" layers. 2) the "virtual" 1D models at the sounding positions are finalized by interpolating the soil properties (the resistivity) in the center of the "virtual" layers. 3) the forward response is computed in 1D for each "virtual" model. We tested the new inversion scheme on an AEM survey carried out with the SkyTEM system close to Odder, in Denmark. The survey comprises 106054 dual mode AEM soundings, and covers an area of approximately 13 km X 16 km. The voxel inversion was carried out on a structured grid of 260 X 325 X 29 xyz nodes (50 m xy spacing), for a total of 2450500 inversion parameters. A classical spatially constrained inversion (SCI) was carried out on the same data set, using 106054

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

The inverse problem of brain energetics: ketone bodies as alternative substrates

Energy Technology Data Exchange (ETDEWEB)

Calvetti, D; Occhipinti, R [Case Western Reserve University, Department of Mathematics, 10900 Euclid Avenue, Cleveland, OH 44106 (United States); Somersalo, E [Helsinki University of Technology, Institute of Mathematics, P. O. Box 1100, FIN-02015 HUT (Finland)], E-mail: daniela.calvetti@case.edu, E-mail: rossana.occhipinti@case.edu, E-mail: erkki.somersalo@tkk.fi

2008-07-15

Little is known about brain energy metabolism under ketosis, although there is evidence that ketone bodies have a neuroprotective role in several neurological disorders. We investigate the inverse problem of estimating reaction fluxes and transport rates in the different cellular compartments of the brain, when the data amounts to a few measured arterial venous concentration differences. By using a recently developed methodology to perform Bayesian Flux Balance Analysis and a new five compartment model of the astrocyte-glutamatergic neuron cellular complex, we are able to identify the preferred biochemical pathways during shortage of glucose and in the presence of ketone bodies in the arterial blood. The analysis is performed in a minimally biased way, therefore revealing the potential of this methodology for hypothesis testing.

The inverse problem of brain energetics: ketone bodies as alternative substrates

International Nuclear Information System (INIS)

Calvetti, D; Occhipinti, R; Somersalo, E

2008-01-01

Little is known about brain energy metabolism under ketosis, although there is evidence that ketone bodies have a neuroprotective role in several neurological disorders. We investigate the inverse problem of estimating reaction fluxes and transport rates in the different cellular compartments of the brain, when the data amounts to a few measured arterial venous concentration differences. By using a recently developed methodology to perform Bayesian Flux Balance Analysis and a new five compartment model of the astrocyte-glutamatergic neuron cellular complex, we are able to identify the preferred biochemical pathways during shortage of glucose and in the presence of ketone bodies in the arterial blood. The analysis is performed in a minimally biased way, therefore revealing the potential of this methodology for hypothesis testing

The inverse problem of brain energetics: ketone bodies as alternative substrates

Science.gov (United States)

Calvetti, D.; Occhipinti, R.; Somersalo, E.

2008-07-01

Little is known about brain energy metabolism under ketosis, although there is evidence that ketone bodies have a neuroprotective role in several neurological disorders. We investigate the inverse problem of estimating reaction fluxes and transport rates in the different cellular compartments of the brain, when the data amounts to a few measured arterial venous concentration differences. By using a recently developed methodology to perform Bayesian Flux Balance Analysis and a new five compartment model of the astrocyte-glutamatergic neuron cellular complex, we are able to identify the preferred biochemical pathways during shortage of glucose and in the presence of ketone bodies in the arterial blood. The analysis is performed in a minimally biased way, therefore revealing the potential of this methodology for hypothesis testing.

Inverse modelling of European CH4 emissions during 2006-2012 using different inverse models and reassessed atmospheric observations

Science.gov (United States)

Bergamaschi, Peter; Karstens, Ute; Manning, Alistair J.; Saunois, Marielle; Tsuruta, Aki; Berchet, Antoine; Vermeulen, Alexander T.; Arnold, Tim; Janssens-Maenhout, Greet; Hammer, Samuel; Levin, Ingeborg; Schmidt, Martina; Ramonet, Michel; Lopez, Morgan; Lavric, Jost; Aalto, Tuula; Chen, Huilin; Feist, Dietrich G.; Gerbig, Christoph; Haszpra, László; Hermansen, Ove; Manca, Giovanni; Moncrieff, John; Meinhardt, Frank; Necki, Jaroslaw; Galkowski, Michal; O'Doherty, Simon; Paramonova, Nina; Scheeren, Hubertus A.; Steinbacher, Martin; Dlugokencky, Ed

2018-01-01

We present inverse modelling (top down) estimates of European methane (CH4) emissions for 2006-2012 based on a new quality-controlled and harmonised in situ data set from 18 European atmospheric monitoring stations. We applied an ensemble of seven inverse models and performed four inversion experiments, investigating the impact of different sets of stations and the use of a priori information on emissions. The inverse models infer total CH4 emissions of 26.8 (20.2-29.7) Tg CH4 yr-1 (mean, 10th and 90th percentiles from all inversions) for the EU-28 for 2006-2012 from the four inversion experiments. For comparison, total anthropogenic CH4 emissions reported to UNFCCC (bottom up, based on statistical data and emissions factors) amount to only 21.3 Tg CH4 yr-1 (2006) to 18.8 Tg CH4 yr-1 (2012). A potential explanation for the higher range of top-down estimates compared to bottom-up inventories could be the contribution from natural sources, such as peatlands, wetlands, and wet soils. Based on seven different wetland inventories from the Wetland and Wetland CH4 Inter-comparison of Models Project (WETCHIMP), total wetland emissions of 4.3 (2.3-8.2) Tg CH4 yr-1 from the EU-28 are estimated. The hypothesis of significant natural emissions is supported by the finding that several inverse models yield significant seasonal cycles of derived CH4 emissions with maxima in summer, while anthropogenic CH4 emissions are assumed to have much lower seasonal variability. Taking into account the wetland emissions from the WETCHIMP ensemble, the top-down estimates are broadly consistent with the sum of anthropogenic and natural bottom-up inventories. However, the contribution of natural sources and their regional distribution remain rather uncertain. Furthermore, we investigate potential biases in the inverse models by comparison with regular aircraft profiles at four European sites and with vertical profiles obtained during the Infrastructure for Measurement of the European Carbon

The inverse problem of determining several coefficients in a nonlinear Lotka–Volterra system

International Nuclear Information System (INIS)

Roques, Lionel; Cristofol, Michel

2012-01-01

In this paper, we prove a uniqueness result in the inverse problem of determining several non-constant coefficients of a system of two parabolic equations, which corresponds to a Lotka–Volterra competition model. Our result gives a sufficient condition for the uniqueness of the determination of four coefficients of the system. This sufficient condition only involves pointwise measurements of the solution (u, v) of the system and of the spatial derivative ∂u/∂x or ∂v/∂x of one component at a single point x 0 , during a time interval (0, ε). Our results are illustrated by numerical computations. (paper)

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)

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)

Thermal measurements and inverse techniques

CERN Document Server

Orlande, Helcio RB; Maillet, Denis; Cotta, Renato M

2011-01-01

With its uncommon presentation of instructional material regarding mathematical modeling, measurements, and solution of inverse problems, Thermal Measurements and Inverse Techniques is a one-stop reference for those dealing with various aspects of heat transfer. Progress in mathematical modeling of complex industrial and environmental systems has enabled numerical simulations of most physical phenomena. In addition, recent advances in thermal instrumentation and heat transfer modeling have improved experimental procedures and indirect measurements for heat transfer research of both natural phe

Eigenvalue based inverse model of beam for structural modification and diagnostics: examples of using

Directory of Open Access Journals (Sweden)

Leszek Majkut

Full Text Available In the work, in order to solve the inverse problem, i.e. the problem of finding values of the additional quantities (mass, elasticity, the beam inverse model was proposed. Analysis of this model allows finding such a value of additional mass (elasticity as a function of its localization so that the free vibration frequency changes to desirable value. The criteria for choice of the “proper” pair (mass - its position, including the criterion allowing changing the position of the vibration node of the second mode of the free vibrations, were given. Analysis of the influence of uncertainties in the determination of the additional quantity value and its position on the desired free vibration frequency was carried out, too. The proposed beam inverse model can be employing to identification of the beam cracks. In such a case, the input quantity is free vibration frequency measured on the damaged object. Each determined free-vibration frequency allows determining the flexibility curve for the spring modeling crack as a function of its position. The searched parameters of the crack (its depth and position are indicated by the common point of two arbitrary curves. Accuracy of crack parameters determination depends on accuracy (uncertainty of frequency measurement. Only some regions containing the searched crack parameters can be obtained in such a situation.

Inverse Ising problem in continuous time: A latent variable approach

Science.gov (United States)

Donner, Christian; Opper, Manfred

2017-12-01

We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.

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

Nonlinear inversion of resistivity sounding data for 1-D earth models using the Neighbourhood Algorithm

Science.gov (United States)

Ojo, A. O.; Xie, Jun; Olorunfemi, M. O.

2018-01-01

To reduce ambiguity related to nonlinearities in the resistivity model-data relationships, an efficient direct-search scheme employing the Neighbourhood Algorithm (NA) was implemented to solve the 1-D resistivity problem. In addition to finding a range of best-fit models which are more likely to be global minimums, this method investigates the entire multi-dimensional model space and provides additional information about the posterior model covariance matrix, marginal probability density function and an ensemble of acceptable models. This provides new insights into how well the model parameters are constrained and make assessing trade-offs between them possible, thus avoiding some common interpretation pitfalls. The efficacy of the newly developed program is tested by inverting both synthetic (noisy and noise-free) data and field data from other authors employing different inversion methods so as to provide a good base for comparative performance. In all cases, the inverted model parameters were in good agreement with the true and recovered model parameters from other methods and remarkably correlate with the available borehole litho-log and known geology for the field dataset. The NA method has proven to be useful whilst a good starting model is not available and the reduced number of unknowns in the 1-D resistivity inverse problem makes it an attractive alternative to the linearized methods. Hence, it is concluded that the newly developed program offers an excellent complementary tool for the global inversion of the layered resistivity structure.

Dynamic Inversion for Hydrological Process Monitoring with Electrical Resistance Tomography Under Model Uncertainty

Energy Technology Data Exchange (ETDEWEB)

Lehikoinen, A.; Huttunen, J.M.J.; Finsterle, S.; Kowalsky, M.B.; Kaipio, J.P.

2009-08-01

We propose an approach for imaging the dynamics of complex hydrological processes. The evolution of electrically conductive fluids in porous media is imaged using time-lapse electrical resistance tomography. The related dynamic inversion problem is solved using Bayesian filtering techniques, that is, it is formulated as a sequential state estimation problem in which the target is an evolving posterior probability density of the system state. The dynamical inversion framework is based on the state space representation of the system, which involves the construction of a stochastic evolution model and an observation model. The observation model used in this paper consists of the complete electrode model for ERT, with Archie's law relating saturations to electrical conductivity. The evolution model is an approximate model for simulating flow through partially saturated porous media. Unavoidable modeling and approximation errors in both the observation and evolution models are considered by computing approximate statistics for these errors. These models are then included in the construction of the posterior probability density of the estimated system state. This approximation error method allows the use of approximate - and therefore computationally efficient - observation and evolution models in the Bayesian filtering. We consider a synthetic example and show that the incorporation of an explicit model for the model uncertainties in the state space representation can yield better estimates than a frame-by-frame imaging approach.

A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations

Science.gov (United States)

Zhang, Ye; Gong, Rongfang; Cheng, Xiaoliang; Gulliksson, Mårten

2018-06-01

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

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.

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.

Constraint on Parameters of Inverse Compton Scattering Model for ...

Indian Academy of Sciences (India)

B2319+60, two parameters of inverse Compton scattering model, the initial Lorentz factor and the factor of energy loss of relativistic particles are constrained. Key words. Pulsar—inverse Compton scattering—emission mechanism. 1. Introduction. Among various kinds of models for pulsar radio emission, the inverse ...

Inverse problems using ANN in long range atmospheric dispersion with signature analysis picked scattered numerical sensors from CFD

International Nuclear Information System (INIS)

Sharma, Pavan K.; Gera, B.; Ghosh, A.K.; Kushwaha, H.S.

2010-01-01

Scalar dispersion in the atmosphere is an important area wherein different approaches are followed in development of good analytical model. The analyses based on Computational Fluid Dynamics (CFD) codes offer an opportunity of model development based on first principles of physics and hence such models have an edge over the existing models. Both forward and backward calculation methods are being developed for atmospheric dispersion around NPPs at BARC Forward modeling methods, which describe the atmospheric transport from sources to receptors, use forward-running transport and dispersion models or computational fluid dynamics models which are run many times, and the resulting dispersion field is compared to observations from multiple sensors. Backward or inverse modeling methods use only one model run in the reverse direction from the receptors to estimate the upwind sources. Inverse modeling methods include adjoint and tangent linear models, Kalman filters, and variational data assimilation, and neural network. The present paper is aimed at developing a new approach where the identified specific signatures at receptor points form the basis for source estimation or inversions. This approach is expected to reduce the large transient data sets to reduced and meaningful data sets. In fact this reduces the inherently transient data set into a time independent mean data set. Forward computation were carried out with CFD code for various case to generate a large set of data to train the ANN. Specific signature analysis was carried out to find the parameters of interest for ANN training like peak concentration, time to reach peak concentration and time to fall, the ANN was trained with data and source strength and location were predicted from ANN. Inverse problem was performed using ANN approach in long range atmospheric dispersion. An illustration of application of CFD code for atmospheric dispersion studies for a hypothetical case is also included in the paper. (author)

Convex blind image deconvolution with inverse filtering

Science.gov (United States)

Lv, Xiao-Guang; Li, Fang; Zeng, Tieyong

2018-03-01

Blind image deconvolution is the process of estimating both the original image and the blur kernel from the degraded image with only partial or no information about degradation and the imaging system. It is a bilinear ill-posed inverse problem corresponding to the direct problem of convolution. Regularization methods are used to handle the ill-posedness of blind deconvolution and get meaningful solutions. In this paper, we investigate a convex regularized inverse filtering method for blind deconvolution of images. We assume that the support region of the blur object is known, as has been done in a few existing works. By studying the inverse filters of signal and image restoration problems, we observe the oscillation structure of the inverse filters. Inspired by the oscillation structure of the inverse filters, we propose to use the star norm to regularize the inverse filter. Meanwhile, we use the total variation to regularize the resulting image obtained by convolving the inverse filter with the degraded image. The proposed minimization model is shown to be convex. We employ the first-order primal-dual method for the solution of the proposed minimization model. Numerical examples for blind image restoration are given to show that the proposed method outperforms some existing methods in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), visual quality and time consumption.

Direct and inverse problems in dispersive time-of-flight photocurrent revisited

Science.gov (United States)

Sagues, Francesc; Sokolov, Igor M.

2017-10-01

Using the fact that the continuous time random walk (CTRW) scheme is a random process subordinated to a simple random walk under the operational time given by the number of steps taken by the walker up to a given time, we revisit the problem of strongly dispersive transport in disordered media, which first lead Scher and Montroll to introducing the power law waiting time distributions. Using a subordination approach permits to disentangle the complexity of the problem, separating the solution of the boundary value problem (which is solved on the level of normal diffusive transport) from the influence of the waiting times, which allows for the solution of the direct problem in the whole time domain (including short times, out of reach of the initial approach), and simplifying strongly the analysis of the inverse problem. This analysis shows that the current traces do not contain information sufficient for unique restoration of the waiting time probability densities, but define a single-parametric family of functions that can be restored, all leading to the same photocurrent forms. The members of the family have the power-law tails which differ only by a prefactor, but may look astonishingly different at their body. The same applies to the multiple trapping model, mathematically equivalent to a special limiting case of CTRW. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

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

ANNIT - An Efficient Inversion Algorithm based on Prediction Principles

Science.gov (United States)

Růžek, B.; Kolář, P.

2009-04-01

Solution of inverse problems represents meaningful job in geophysics. The amount of data is continuously increasing, methods of modeling are being improved and the computer facilities are also advancing great technical progress. Therefore the development of new and efficient algorithms and computer codes for both forward and inverse modeling is still up to date. ANNIT is contributing to this stream since it is a tool for efficient solution of a set of non-linear equations. Typical geophysical problems are based on parametric approach. The system is characterized by a vector of parameters p, the response of the system is characterized by a vector of data d. The forward problem is usually represented by unique mapping F(p)=d. The inverse problem is much more complex and the inverse mapping p=G(d) is available in an analytical or closed form only exceptionally and generally it may not exist at all. Technically, both forward and inverse mapping F and G are sets of non-linear equations. ANNIT solves such situation as follows: (i) joint subspaces {pD, pM} of original data and model spaces D, M, resp. are searched for, within which the forward mapping F is sufficiently smooth that the inverse mapping G does exist, (ii) numerical approximation of G in subspaces {pD, pM} is found, (iii) candidate solution is predicted by using this numerical approximation. ANNIT is working in an iterative way in cycles. The subspaces {pD, pM} are searched for by generating suitable populations of individuals (models) covering data and model spaces. The approximation of the inverse mapping is made by using three methods: (a) linear regression, (b) Radial Basis Function Network technique, (c) linear prediction (also known as "Kriging"). The ANNIT algorithm has built in also an archive of already evaluated models. Archive models are re-used in a suitable way and thus the number of forward evaluations is minimized. ANNIT is now implemented both in MATLAB and SCILAB. Numerical tests show good

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.

Splines employment for inverse problem of nonstationary thermal conduction

International Nuclear Information System (INIS)

Nikonov, S.P.; Spolitak, S.I.

1985-01-01

An analytical solution has been obtained for an inverse problem of nonstationary thermal conduction which is faced in nonstationary heat transfer data processing when the rewetting in channels with uniform annular fuel element imitators is investigated. In solving the problem both boundary conditions and power density within the imitator are regularized via cubic splines constructed with the use of Reinsch algorithm. The solution can be applied for calculation of temperature distribution in the imitator and the heat flux in two-dimensional approximation (r-z geometry) under the condition that the rewetting front velocity is known, and in one-dimensional r-approximation in cases with negligible axial transport or when there is a lack of data about the temperature disturbance source velocity along the channel

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

Science.gov (United States)

Kalenichenko, V. V.

A method of the absolute mass scale calibration is suggested for solving the inverse problem of the physical theory of fireballs. The method is based on the data on the masses of the fallen meteorites whose fireballs have been photographed in their flight. The method may be applied to those fireballs whose bodies have not experienced considerable fragmentation during their destruction in the atmosphere and have kept their form well enough. Statistical analysis of the inverse problem solution for a sufficiently representative sample makes it possible to separate a subsample of such fireballs. The data on the Lost City and Innisfree meteorites are used to obtain calibration coefficients.

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