Parameter Estimation and Inverse Problems

Author: Richard C. Aster,Brian Borchers,Clifford H. Thurber

Publisher: Academic Press

ISBN: 0123850487

Category: Science

Page: 360

View: 3355

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Parameter Estimation and Inverse Problems, 2e provides geoscience students and professionals with answers to common questions like how one can derive a physical model from a finite set of observations containing errors, and how one may determine the quality of such a model. This book takes on these fundamental and challenging problems, introducing students and professionals to the broad range of approaches that lie in the realm of inverse theory. The authors present both the underlying theory and practical algorithms for solving inverse problems. The authors' treatment is appropriate for geoscience graduate students and advanced undergraduates with a basic working knowledge of calculus, linear algebra, and statistics. Parameter Estimation and Inverse Problems, 2e introduces readers to both Classical and Bayesian approaches to linear and nonlinear problems with particular attention paid to computational, mathematical, and statistical issues related to their application to geophysical problems. The textbook includes Appendices covering essential linear algebra, statistics, and notation in the context of the subject. A companion website features computational examples (including all examples contained in the textbook) and useful subroutines using MATLAB. Includes appendices for review of needed concepts in linear, statistics, and vector calculus. Companion website contains comprehensive MATLAB code for all examples, which readers can reproduce, experiment with, and modify. Online instructor's guide helps professors teach, customize exercises, and select homework problems Accessible to students and professionals without a highly specialized mathematical background.

Parameter Estimation and Inverse Problems

Author: Richard C. Aster,Brian Borchers,Clifford H. Thurber

Publisher: Academic Press

ISBN: 0123850495

Category: Science

Page: 376

View: 3917

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Parameter Estimation and Inverse Problems, Second Edition provides geoscience students and professionals with answers to common questions like how one can derive a physical model from a finite set of observations containing errors, and how one may determine the quality of such a model. This book takes on these fundamental and challenging problems, introducing students and professionals to the broad range of approaches that lie in the realm of inverse theory. The authors present both the underlying theory and practical algorithms for solving inverse problems. The authors’ treatment is appropriate for geoscience graduate students and advanced undergraduates with a basic working knowledge of calculus, linear algebra, and statistics. Parameter Estimation and Inverse Problems, Second Edition introduces readers to both Classical and Bayesian approaches to linear and nonlinear problems with particular attention paid to computational, mathematical, and statistical issues related to their application to geophysical problems. The textbook includes Appendices covering essential linear algebra, statistics, and notation in the context of the subject. Includes appendices for review of needed concepts in linear, statistics, and vector calculus. Accessible to students and professionals without a highly specialized mathematical background.

Parameter Estimation and Inverse Problems

Author: Richard C. Aster,Brian Borchers,Clifford H. Thurber

Publisher: Elsevier

ISBN: 0080470556

Category: Mathematics

Page: 320

View: 5890

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Parameter Estimation and Inverse Problems primarily serves as a textbook for advanced undergraduate and introductory graduate courses. It promotes a fundamental understanding of parameter estimation and inverse problem philosophy and methodology. It introduces readers to Classical and Bayesian approaches to linear and nonlinear problems, with particular attention to computational, mathematical, and statistical issues related to their application to geophysical problems. Four appendices review foundational concepts in linear algebra, statistics, vector calculus, and notation. Pedagogy includes hundreds of highlighted equations, examples, and definitions; introductory chapter synopses; end-of-chapter exercises, both programming and theoretical; and suggestions for further reading. The text is designed to be accessible to graduate students and professionals in physical sciences without an extensive mathematical background. Designed to be accessible to graduate students and professionals in physical sciences without an extensive mathematical background Includes three appendices for review of linear algebra and crucial concepts in statistics Battle-tested in courses at several universities MATLAB exercises facilitate exploration of material

Parameter Estimation and Inverse Problems

Author: Richard C. Aster,Brian Borchers,Clifford H. Thurber

Publisher: Elsevier

ISBN: 0128134232

Category: Science

Page: 404

View: 8785

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Parameter Estimation and Inverse Problems, Third Edition, is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who do not have an extensive mathematical background. The book is complemented by a companion website that includes MATLAB codes that correspond to examples that are illustrated with simple, easy to follow problems that illuminate the details of particular numerical methods. Updates to the new edition include more discussions of Laplacian smoothing, an expansion of basis function exercises, the addition of stochastic descent, an improved presentation of Fourier methods and exercises, and more. Complemented by a companion website that includes MATLAB codes that correspond to all examples Features examples that are illustrated with simple, easy to follow problems that illuminate the details of a particular numerical method Includes an online instructor’s guide that helps professors teach and customize exercises and select homework problems Covers updated information on adjoint methods that are presented in an accessible manner

Inverse Problem Theory

Methods for Data Fitting and Model Parameter Estimation

Author: A. Tarantola

Publisher: Elsevier

ISBN: 0444599673

Category: Mathematics

Page: 644

View: 5270

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Inverse Problem Theory is written for physicists, geophysicists and all scientists facing the problem of quantitative interpretation of experimental data. Although it contains a lot of mathematics, it is not intended as a mathematical book, but rather tries to explain how a method of acquisition of information can be applied to the actual world. The book provides a comprehensive, up-to-date description of the methods to be used for fitting experimental data, or to estimate model parameters, and to unify these methods into the Inverse Problem Theory. The first part of the book deals with discrete problems and describes Maximum likelihood, Monte Carlo, Least squares, and Least absolute values methods. The second part deals with inverse problems involving functions. The book is almost completely self-contained, with all important concepts carefully introduced. Although theoretical concepts are strongly emphasized, the author has ensured that all the useful formulas are listed, with many special cases included. The book will thus serve equally well as a reference manual for researchers needing to refresh their memories on a given algorithm, or as a textbook in a course for undergraduate or graduate students.

Inverse Problem Theory and Methods for Model Parameter Estimation

Author: Albert Tarantola

Publisher: SIAM

ISBN: 9780898717921

Category: Engineering

Page: 342

View: 4941

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While the prediction of observations is a forward problem, the use of actual observations to infer the properties of a model is an inverse problem. Inverse problems are difficult because they may not have a unique solution. The description of uncertainties plays a central role in the theory, which is based on probability theory. This book proposes a general approach that is valid for linear as well as for nonlinear problems. The philosophy is essentially probabilistic and allows the reader to understand the basic difficulties appearing in the resolution of inverse problems. The book attempts to explain how a method of acquisition of information can be applied to actual real-world problems, and many of the arguments are heuristic.

Introduction to Inverse Problems in Imaging

Author: M. Bertero,P. Boccacci

Publisher: CRC Press

ISBN: 9781439822067

Category: Technology & Engineering

Page: 352

View: 1443

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This is a graduate textbook on the principles of linear inverse problems, methods of their approximate solution, and practical application in imaging. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of readers from different backgrounds in science and engineering. Mathematical prerequisites are first courses in analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms. With examples and exercised throughout, the book will provide the reader with the appropriate background for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems.

Discrete Inverse Problems

Insight and Algorithms

Author: Per Christian Hansen

Publisher: SIAM

ISBN: 089871883X

Category: Inverse problems (Differential equations)

Page: 213

View: 5049

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This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.

Inverse Problems

Activities for Undergraduates

Author: C. W. Groetsch

Publisher: Cambridge University Press

ISBN: 9780883857168

Category: Mathematics

Page: 222

View: 9200

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Problem solving in mathematics is often thought of as a one way process. For example: take two numbers and multiply them together. However for each problem there is also an inverse problem which runs in the opposite direction: now take a number and find a pair of factors. Such problems are considerably more important, in mathematics and throughout science, than they might first appear. This book concentrates on these inverse problems and how they can be usefully introduced to undergraduate students. A historical introduction sets the scene and gives a cultural context for what the rest of the book. Chapters dealing with inverse problems in calculus, differential equations and linear algebra then follow and the book concludes with suggestions for further reading. Whatever their own field of expertise, this will be an essential purchase for anyone interested in the teaching of mathematics.

Geophysical Data Analysis

Discrete Inverse Theory

Author: William Menke

Publisher: Academic Press

ISBN: 0128135565

Category: Science

Page: 352

View: 2081

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Geophysical Data Analysis: Diverse Inverse Theory, Fourth Edition is a revised and expanded introduction to inverse theory and tomography as it is practiced by geophysicists. It demonstrates the methods needed to analyze a broad spectrum of geophysical datasets, with special attention to those methods that generate images of the earth. Data analysis can be a mathematically complex activity, but the treatment in this volume is carefully designed to emphasize those mathematical techniques that readers will find the most familiar and to systematically introduce less-familiar ones. Using problems and case studies, along with MATLAB computer code and summaries of methods, the book provides data scientists and engineers in geophysics with the tools necessary to understand and apply mathematical techniques and inverse theory. Includes material on probability, including Bayesian influence, probability density function and metropolis algorithm Offers detailed discussion of the application of inverse theory to tectonic, gravitational and geomagnetic studies Contains numerous examples, color figures and end-of-chapter homework problems to help readers explore and further understand presented ideas Includes MATLAB examples and problem sets Updated and refined throughout to bring the text in line with current understanding and improved examples and case studies Expanded sections to cover material, such as second-derivation smoothing and chi-squared tests not covered in the previous edition

Linear and Nonlinear Inverse Problems with Practical Applications

Author: Jennifer L. Mueller,Samuli Siltanen

Publisher: SIAM

ISBN: 9781611972344

Category: Mathematics

Page: 351

View: 5932

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Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. This book explains how to identify ill-posed inverse problems arising in practice and gives a hands-on guide to designing computational solution methods for them, with related codes on an accompanying website. The guiding linear inversion examples are the problem of image deblurring, x-ray tomography, and backward parabolic problems, including heat transfer. A thorough treatment of electrical impedance tomography is used as the guiding nonlinear inversion example which combines the analytic-geometric research tradition and the regularization-based school of thought in a fruitful manner. This book is complete with exercises and project topics, making it ideal as a classroom textbook or self-study guide for graduate and advanced undergraduate students in mathematics, engineering or physics who wish to learn about computational inversion. It also acts as a useful guide for researchers who develop inversion techniques in high-tech industry.

Numerical Methods for Inverse Problems

Author: Michel Kern

Publisher: John Wiley & Sons

ISBN: 1848218184

Category: Mathematics

Page: 232

View: 5154

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This book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system. The author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications. This book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.

Inverse Problems

Mathematical and Analytical Techniques with Applications to Engineering

Author: Alexander G. Ramm

Publisher: Springer Science & Business Media

ISBN: 0387232184

Category: Mathematics

Page: 442

View: 6107

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Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.

Parameter Estimation for Scientists and Engineers

Author: Adriaan van den Bos

Publisher: John Wiley & Sons

ISBN: 9780470173855

Category: Technology & Engineering

Page: 296

View: 5067

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The subject of this book is estimating parameters of expectation models of statistical observations. The book describes the most important aspects of the subject for applied scientists and engineers. This group of users is often not aware of estimators other than least squares. Therefore one purpose of this book is to show that statistical parameter estimation has much more to offer than least squares estimation alone. In the approach of this book, knowledge of the distribution of the observations is involved in the choice of estimators. A further advantage of the chosen approach is that it unifies the underlying theory and reduces it to a relatively small collection of coherent, generally applicable principles and notions.

Inverse Problems in the Mathematical Sciences

Author: Charles W. Groetsch

Publisher: Springer Science & Business Media

ISBN: 3322992020

Category: Technology & Engineering

Page: 154

View: 4919

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Inverse problems are immensely important in modern science and technology. However, the broad mathematical issues raised by inverse problems receive scant attention in the university curriculum. This book aims to remedy this state of affairs by supplying an accessible introduction, at a modest mathematical level, to the alluring field of inverse problems. Many models of inverse problems from science and engineering are dealt with and nearly a hundred exercises, of varying difficulty, involving mathematical analysis, numerical treatment, or modelling of inverse problems, are provided. The main themes of the book are: causation problem modeled as integral equations; model identification problems, posed as coefficient determination problems in differential equations; the functional analytic framework for inverse problems; and a survey of the principal numerical methods for inverse problems. An extensive annotated bibliography furnishes leads on the history of inverse problems and a guide to the frontiers of current research.

An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems

Author: Luis Tenorio

Publisher: SIAM

ISBN: 1611974917

Category: Mathematics

Page: 269

View: 9842

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Inverse problems are found in many applications, such as medical imaging, engineering, astronomy, and geophysics, among others. To solve an inverse problem is to recover an object from noisy, usually indirect observations. Solutions to inverse problems are subject to many potential sources of error introduced by approximate mathematical models, regularization methods, numerical approximations for efficient computations, noisy data, and limitations in the number of observations; thus it is important to include an assessment of the uncertainties as part of the solution. Such assessment is interdisciplinary by nature, as it requires, in addition to knowledge of the particular application, methods from applied mathematics, probability, and statistics. This book bridges applied mathematics and statistics by providing a basic introduction to probability and statistics for uncertainty quantification in the context of inverse problems, as well as an introduction to statistical regularization of inverse problems. The author covers basic statistical inference, introduces the framework of ill-posed inverse problems, and explains statistical questions that arise in their applications. An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems÷includes many examples that explain techniques which are useful to address general problems arising in uncertainty quantification, Bayesian and non-Bayesian statistical methods and discussions of their complementary roles, and analysis of a real data set to illustrate the methodology covered throughout the book.

Inverse Problems in Engineering Mechanics III

Author: G.S. Dulikravich,Mana Tanaka

Publisher: Elsevier

ISBN: 9780080535142

Category: Science

Page: 432

View: 8078

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Inverse Problems are found in many areas of engineering mechanics and there are many successful applications e.g. in non-destructive testing and characterization of material properties by ultrasonic or X-ray techniques, thermography, etc. Generally speaking, inverse problems are concerned with the determination of the input and the characteristics of a system, given certain aspects of its output. Mathematically, such problems are ill-posed and have to be overcome through development of new computational schemes, regularization techniques, objective functionals, and experimental procedures. This volume contains a selection of peer-reviewed papers presented at the International Symposium on Inverse Problems in Engineering Mechanics (ISIP2001), held in February of 2001 in Nagano, Japan, where recent development in inverse problems in engineering mechanics and related topics were discussed. The following general areas in inverse problems in engineering mechanics were the subjects of the ISIP2001: mathematical and computational aspects of inverse problems, parameter or system identification, shape determination, sensitivity analysis, optimization, material property characterization, ultrasonic non-destructive testing, elastodynamic inverse problems, thermal inverse problems, and other engineering applications. These papers can provide a state-of-the-art review of the research on inverse problems in engineering mechanics.

Large-Scale Inverse Problems and Quantification of Uncertainty

Author: Lorenz Biegler,George Biros,Omar Ghattas,Matthias Heinkenschloss,David Keyes,Bani Mallick,Luis Tenorio,Bart van Bloemen Waanders,Karen Willcox,Youssef Marzouk

Publisher: John Wiley & Sons

ISBN: 1119957583

Category: Mathematics

Page: 388

View: 2356

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This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods. Key Features: • Brings together the perspectives of researchers in areas of inverse problems and data assimilation. • Assesses the current state-of-the-art and identify needs and opportunities for future research. • Focuses on the computational methods used to analyze and simulate inverse problems. • Written by leading experts of inverse problems and uncertainty quantification. Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.

Inverse Problems in Groundwater Modeling

Author: Ne-Zheng Sun

Publisher: Springer Science & Business Media

ISBN: 9401719705

Category: Science

Page: 338

View: 6352

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... A diskette with the updated programme of Appendix C and examples is available through the author at a small fee. email: [email protected] fax: 1--310--825--5435 ... This book systematically discusses basic concepts, theory, solution methods and applications of inverse problems in groundwater modeling. It is the first book devoted to this subject. The inverse problem is defined and solved in both deterministic and statistic frameworks. Various direct and indirect methods are discussed and compared. As a useful tool, the adjoint state method and its applications are given in detail. For a stochastic field, the maximum likelihood estimation and co-kriging techniques are used to estimate unknown parameters. The ill-posed problem of inverse solution is highlighted through the whole book. The importance of data collection strategy is specially emphasized. Besides the classical design criteria, the relationships between decision making, prediction, parameter identification and experimental design are considered from the point of view of extended identifiabilities. The problem of model structure identification is also considered. This book can be used as a textbook for graduate students majoring in hydrogeology or related subjects. It is also a reference book for hydrogeologists, petroleum engineers, environmental engineers, mining engineers and applied mathematicians.