Parameter Estimation and Inverse Problems

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

Publisher: Academic Press

ISBN: 0123850487

Category: Science

Page: 360

View: 3803

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: 5553

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,Clifford H. Thurber,Brian Borchers

Publisher: Academic Press

ISBN: 0120656043

Category: Mathematics

Page: 301

View: 6379

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 contains Matlab code corresponding to all examples. * 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

Inverse Problem Theory and Methods for Model Parameter Estimation

Author: Albert Tarantola

Publisher: SIAM

ISBN: 9780898717921

Category: Engineering

Page: 342

View: 2545

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.

Inverse Problem Theory

Methods for Data Fitting and Model Parameter Estimation

Author: A. Tarantola

Publisher: Elsevier

ISBN: 0444599673

Category: Mathematics

Page: 644

View: 3182

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.

Introduction to Inverse Problems in Imaging

Author: M. Bertero,P. Boccacci

Publisher: CRC Press

ISBN: 9781439822067

Category: Technology & Engineering

Page: 352

View: 8002

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: 6515

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: 1749

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.

Linear and Nonlinear Inverse Problems with Practical Applications

Author: Jennifer L. Mueller,Samuli Siltanen

Publisher: SIAM

ISBN: 9781611972344

Category: Mathematics

Page: 351

View: 7930

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.

Computational Methods for Inverse Problems

Author: Curtis R. Vogel

Publisher: SIAM

ISBN: 0898715504

Category: Mathematics

Page: 183

View: 3752

Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

A Taste of Inverse Problems

Basic Theory and Examples

Author: Martin Hanke

Publisher: SIAM

ISBN: 1611974941

Category: Inverse problems (Differential equations)

Page: 162

View: 7520

Inverse problems need to be solved in order to properly interpret indirect measurements. Often, inverse problems are ill-posed and sensitive to data errors. Therefore one has to incorporate some sort of regularization to reconstruct significant information from the given data. This book presents the main achievements that have emerged in regularization theory over the past 50 years, focusing on linear ill-posed problems and the development of methods that can be applied to them. Some of this material has previously appeared only in journal articles. A Taste of Inverse Problems: Basic Theory and Examples rigorously discusses state-of-the-art inverse problems theory, focusing on numerically relevant aspects and omitting subordinate generalizations;presents diverse real-world applications, important test cases, and possible pitfalls; and treats these applications with the same rigor and depth as the theory.

Numerical Methods for Inverse Problems

Author: Michel Kern

Publisher: John Wiley & Sons

ISBN: 1848218184

Category: Mathematics

Page: 232

View: 2725

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.

Geophysical Data Analysis

Discrete Inverse Theory

Author: William Menke

Publisher: Academic Press

ISBN: 0123971608

Category: Mathematics

Page: 293

View: 4488

Please use extracts from reviews of first edition Key Features * Updated and thoroughly revised edition * additional material on geophysical/acoustic tomography * Detailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studies

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: 5419

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: 3963

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 Groundwater Modeling

Author: Ne-Zheng Sun

Publisher: Springer Science & Business Media

ISBN: 9401719705

Category: Science

Page: 338

View: 8929

... 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.

An Introduction to Inverse Problems with Applications

Author: Francisco Duarte Moura Neto,Antônio José da Silva Neto

Publisher: Springer Science & Business Media

ISBN: 3642325564

Category: Mathematics

Page: 246

View: 5265

Computational engineering/science uses a blend of applications, mathematical models and computations. Mathematical models require accurate approximations of their parameters, which are often viewed as solutions to inverse problems. Thus, the study of inverse problems is an integral part of computational engineering/science. This book presents several aspects of inverse problems along with needed prerequisite topics in numerical analysis and matrix algebra. If the reader has previously studied these prerequisites, then one can rapidly move to the inverse problems in chapters 4-8 on image restoration, thermal radiation, thermal characterization and heat transfer. “This text does provide a comprehensive introduction to inverse problems and fills a void in the literature”. Robert E White, Professor of Mathematics, North Carolina State University

Model Calibration and Parameter Estimation

For Environmental and Water Resource Systems

Author: Ne-Zheng Sun,Alexander Sun

Publisher: Springer

ISBN: 1493923234

Category: Mathematics

Page: 621

View: 3337

This three-part book provides a comprehensive and systematic introduction to these challenging topics such as model calibration, parameter estimation, reliability assessment, and data collection design. Part 1 covers the classical inverse problem for parameter estimation in both deterministic and statistical frameworks, Part 2 is dedicated to system identification, hyperparameter estimation, and model dimension reduction, and Part 3 considers how to collect data and construct reliable models for prediction and decision-making. For the first time, topics such as multiscale inversion, stochastic field parameterization, level set method, machine learning, global sensitivity analysis, data assimilation, model uncertainty quantification, robust design, and goal-oriented modeling, are systematically described and summarized in a single book from the perspective of model inversion, and elucidated with numerical examples from environmental and water resources modeling. Readers of this book will not only learn basic concepts and methods for simple parameter estimation, but also get familiar with advanced methods for modeling complex systems. Algorithms for mathematical tools used in this book, such as numerical optimization, automatic differentiation, adaptive parameterization, hierarchical Bayesian, metamodeling, Markov chain Monte Carlo, are covered in details. This book can be used as a reference for graduate and upper level undergraduate students majoring in environmental engineering, hydrology, and geosciences. It also serves as an essential reference book for professionals such as petroleum engineers, mining engineers, chemists, mechanical engineers, biologists, biology and medical engineering, applied mathematicians, and others who perform mathematical modeling.

Numerical Treatment of Inverse Problems in Differential and Integral Equations

Proceedings of an International Workshop, Heidelberg, Fed. Rep. of Germany, August 30 — September 3, 1982

Author: Deuflhard,Hairer

Publisher: Springer Science & Business Media

ISBN: 1468473247

Category: Mathematics

Page: 357

View: 5890

In many scientific or engineering applications, where ordinary differen tial equation (OOE),partial differential equation (POE), or integral equation (IE) models are involved, numerical simulation is in common use for prediction, monitoring, or control purposes. In many cases, however, successful simulation of a process must be preceded by the solution of the so-called inverse problem, which is usually more complex: given meas ured data and an associated theoretical model, determine unknown para meters in that model (or unknown functions to be parametrized) in such a way that some measure of the "discrepancy" between data and model is minimal. The present volume deals with the numerical treatment of such inverse probelms in fields of application like chemistry (Chap. 2,3,4, 7,9), molecular biology (Chap. 22), physics (Chap. 8,11,20), geophysics (Chap. 10,19), astronomy (Chap. 5), reservoir simulation (Chap. 15,16), elctrocardiology (Chap. 14), computer tomography (Chap. 21), and control system design (Chap. 12,13). In the actual computational solution of inverse problems in these fields, the following typical difficulties arise: (1) The evaluation of the sen sitivity coefficients for the model. may be rather time and storage con suming. Nevertheless these coefficients are needed (a) to ensure (local) uniqueness of the solution, (b) to estimate the accuracy of the obtained approximation of the solution, (c) to speed up the iterative solution of nonlinear problems. (2) Often the inverse problems are ill-posed. To cope with this fact in the presence of noisy or incomplete data or inev itable discretization errors, regularization techniques are necessary.

Estimation Techniques for Distributed Parameter Systems

Author: H.T. Banks,K. Kunisch

Publisher: Springer Science & Business Media

ISBN: 1461237009

Category: Juvenile Nonfiction

Page: 316

View: 4390

The research detailed in this monograph was originally motivated by our interest in control problems involving partial and delay differential equations. Our attempts to apply control theory techniques to such prob lems in several areas of science convinced us that in the need for better and more detailed models of distributed/ continuum processes in biology and mechanics lay a rich, interesting, and challenging class of fundamen tal questions. These questions, which involve science and mathematics, are typical of those arising in inverse or parameter estimation problems. Our efforts on inverse problems for distributed parameter systems, which are infinite dimensional in the most common realizations, began about seven years ago at a time when rapid advances in computing capabilities and availability held promise for significant progress in the development of a practically useful as well as theoretically sound methodology for such problems. Much of the research reported in our presentation was not begun when we outlined the plans for this monograph some years ago. By publishing this monograph now, when only a part of the originally intended topics are covered (see Chapter VII in this respect), we hope to stimulate the research and interest of others in an area of scientific en deavor which has exceeded even our optimistic expectations with respect to excitement, opportunity, and stimulation. The computer revolution alluded to above and the development of new codes allow one to solve rather routinely certain estimation problems that would have been out of the question ten years ago.