Inverse Problem Theory And Methods For Model Parameter Estimation

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Inverse Problem Theory and Methods for Model Parameter Estimation

Author : Albert Tarantola
Publisher : SIAM
ISBN 13 : 9780898717921
Total Pages : 349 pages
Book Rating : 4.7/5 (179 download)

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Book Synopsis Inverse Problem Theory and Methods for Model Parameter Estimation by : Albert Tarantola

Download or read book Inverse Problem Theory and Methods for Model Parameter Estimation written by Albert Tarantola and published by SIAM. This book was released on 2005-01-01 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Parameter Estimation and Inverse Problems

Author : Richard C. Aster
Publisher : Elsevier
ISBN 13 : 0128134232
Total Pages : 404 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Parameter Estimation and Inverse Problems by : Richard C. Aster

Download or read book Parameter Estimation and Inverse Problems written by Richard C. Aster and published by Elsevier. This book was released on 2018-10-16 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. 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

Author : A. Tarantola
Publisher : Elsevier
ISBN 13 : 0444599673
Total Pages : 644 pages
Book Rating : 4.4/5 (445 download)

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Book Synopsis Inverse Problem Theory by : A. Tarantola

Download or read book Inverse Problem Theory written by A. Tarantola and published by Elsevier. This book was released on 2013-10-14 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Computational Methods for Inverse Problems

Author : Curtis R. Vogel
Publisher : SIAM
ISBN 13 : 0898717574
Total Pages : 183 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Computational Methods for Inverse Problems by : Curtis R. Vogel

Download or read book Computational Methods for Inverse Problems written by Curtis R. Vogel and published by SIAM. This book was released on 2002 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

Inverse Problems in Groundwater Modeling

Author : Ne-Zheng Sun
Publisher : Springer Science & Business Media
ISBN 13 : 9401719705
Total Pages : 346 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Inverse Problems in Groundwater Modeling by : Ne-Zheng Sun

Download or read book Inverse Problems in Groundwater Modeling written by Ne-Zheng Sun and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: ... 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 Data Analysis and Uncertainty Quantification for Inverse Problems

Author : Luis Tenorio
Publisher : SIAM
ISBN 13 : 1611974917
Total Pages : 275 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems by : Luis Tenorio

Download or read book An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems written by Luis Tenorio and published by SIAM. This book was released on 2017-07-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 the Mathematical Sciences

Author : Charles W. Groetsch
Publisher : Springer Science & Business Media
ISBN 13 : 3322992020
Total Pages : 154 pages
Book Rating : 4.3/5 (229 download)

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Book Synopsis Inverse Problems in the Mathematical Sciences by : Charles W. Groetsch

Download or read book Inverse Problems in the Mathematical Sciences written by Charles W. Groetsch and published by Springer Science & Business Media. This book was released on 2013-12-14 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geophysical Data Analysis: Understanding Inverse Problem Theory and Practice

Author : Max A. Meju
Publisher : SEG Books
ISBN 13 : 156080257X
Total Pages : 305 pages
Book Rating : 4.5/5 (68 download)

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Book Synopsis Geophysical Data Analysis: Understanding Inverse Problem Theory and Practice by : Max A. Meju

Download or read book Geophysical Data Analysis: Understanding Inverse Problem Theory and Practice written by Max A. Meju and published by SEG Books. This book was released on 1994 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This publication is designed to provide a practical understanding of methods of parameter estimation and uncertainty analysis. The practical problems covered range from simple processing of time- and space-series data to inversion of potential field, seismic, electrical, and electromagnetic data. The various formulations are reconciled with field data in the numerous examples provided in the book; well-documented computer programmes are also given to show how easy it is to implement inversion algorithms.

Computational Methods for Applied Inverse Problems

Author : Yanfei Wang
Publisher : Walter de Gruyter
ISBN 13 : 3110259052
Total Pages : 552 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Computational Methods for Applied Inverse Problems by : Yanfei Wang

Download or read book Computational Methods for Applied Inverse Problems written by Yanfei Wang and published by Walter de Gruyter. This book was released on 2012-10-30 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays inverse problems and applications in science and engineering represent an extremely active research field. The subjects are related to mathematics, physics, geophysics, geochemistry, oceanography, geography and remote sensing, astronomy, biomedicine, and other areas of applications. This monograph reports recent advances of inversion theory and recent developments with practical applications in frontiers of sciences, especially inverse design and novel computational methods for inverse problems. The practical applications include inverse scattering, chemistry, molecular spectra data processing, quantitative remote sensing inversion, seismic imaging, oceanography, and astronomical imaging. The book serves as a reference book and readers who do research in applied mathematics, engineering, geophysics, biomedicine, image processing, remote sensing, and environmental science will benefit from the contents since the book incorporates a background of using statistical and non-statistical methods, e.g., regularization and optimization techniques for solving practical inverse problems.

Parameter Estimation and Inverse Problems

Author : Richard C. Aster
Publisher : Academic Press
ISBN 13 : 0123850487
Total Pages : 377 pages
Book Rating : 4.1/5 (238 download)

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Book Synopsis Parameter Estimation and Inverse Problems by : Richard C. Aster

Download or read book Parameter Estimation and Inverse Problems written by Richard C. Aster and published by Academic Press. This book was released on 2013 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface -- 1. Introduction -- 2. Linear Regression -- 3. Discretizing Continuous Inverse Problems -- 4. Rank Deficiency and Ill-Conditioning -- 5. Tikhonov Regularization -- 6. Iterative Methods -- 7. Other Regularization Techniques -- 8. Fourier Techniques -- 9. Nonlinear Regression -- 10. Nonlinear Inverse Problems -- 11. Bayesian Methods -- Appendix A: Review of Linear Algebra -- Appendix B: Review of Probability and Statistics -- Appendix C: Glossary of Notation -- Bibliography -- IndexLinear Regression -- Discretizing Continuous Inverse Problems -- Rank Deficiency and Ill-Conditioning -- Tikhonov Regularization -- Iterative Methods -- Other Regularization Techniques -- Fourier Techniques -- Nonlinear Regression -- Nonlinear Inverse Problems -- Bayesian Methods.

Mathematical Modelling

Author : Seppo Pohjolainen
Publisher : Springer
ISBN 13 : 3319278363
Total Pages : 242 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Mathematical Modelling by : Seppo Pohjolainen

Download or read book Mathematical Modelling written by Seppo Pohjolainen and published by Springer. This book was released on 2016-07-14 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.

Geophysical Inverse Theory

Author : Robert L. Parker
Publisher : Princeton University Press
ISBN 13 : 069120683X
Total Pages : 400 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Geophysical Inverse Theory by : Robert L. Parker

Download or read book Geophysical Inverse Theory written by Robert L. Parker and published by Princeton University Press. This book was released on 2019-12-31 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many physical sciences, the most natural description of a system is with a function of position or time. In principle, infinitely many numbers are needed to specify that function, but in practice only finitely many measurements can be made. Inverse theory concerns the mathematical techniques that enable researchers to use the available information to build a model of the unknown system or to determine its essential properties. In Geophysical Inverse Theory, Robert Parker provides a systematic development of inverse theory at the graduate and professional level that emphasizes a rigorous yet practical solution of inverse problems, with examples from experimental observations in geomagnetism, seismology, gravity, electromagnetic sounding, and interpolation. Although illustrated with examples from geophysics, this book has broad implications for researchers in applied disciplines from materials science and engineering to astrophysics, oceanography, and meteorology. Parker's approach is to avoid artificial statistical constructs and to emphasize instead the reasonable assumptions researchers must make to reduce the ambiguity that inevitably arises in complex problems. The structure of the book follows a natural division in the subject into linear theory, in which the measured quantities are linear functionals of the unknown models, and nonlinear theory, which covers all other systems but is not nearly so well understood. The book covers model selection as well as techniques for drawing firm conclusions about the earth independent of any particular model.

Material Parameter Identification and Inverse Problems in Soft Tissue Biomechanics

Author : Stéphane Avril
Publisher : Springer
ISBN 13 : 3319450719
Total Pages : 144 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Material Parameter Identification and Inverse Problems in Soft Tissue Biomechanics by : Stéphane Avril

Download or read book Material Parameter Identification and Inverse Problems in Soft Tissue Biomechanics written by Stéphane Avril and published by Springer. This book was released on 2016-10-12 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this book review hybrid experimental-computational methods applied to soft tissues which have been developed by worldwide specialists in the field. People developing computational models of soft tissues and organs will find solutions for calibrating the material parameters of their models; people performing tests on soft tissues will learn what to extract from the data and how to use these data for their models and people worried about the complexity of the biomechanical behavior of soft tissues will find relevant approaches to address this complexity.

Mathematical Physiology

Author : James Keener
Publisher : Springer Science & Business Media
ISBN 13 : 038775847X
Total Pages : 547 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Mathematical Physiology by : James Keener

Download or read book Mathematical Physiology written by James Keener and published by Springer Science & Business Media. This book was released on 2010-06-04 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: Divided into two volumes, the book begins with a pedagogical presentation of some of the basic theory, with chapters on biochemical reactions, diffusion, excitability, wave propagation and cellular homeostasis. The second, more extensive part discusses particular physiological systems, with chapters on calcium dynamics, bursting oscillations and secretion, cardiac cells, muscles, intercellular communication, the circulatory system, the immune system, wound healing, the respiratory system, the visual system, hormone physiology, renal physiology, digestion, the visual system and hearing. New chapters on Calcium Dynamics, Neuroendocrine Cells and Regulation of Cell Function have been included. Reviews from first edition: Keener and Sneyd's Mathematical Physiology is the first comprehensive text of its kind that deals exclusively with the interplay between mathematics and physiology. Writing a book like this is an audacious act! -Society of Mathematical Biology Keener and Sneyd's is unique in that it attempts to present one of the most important subfields of biology and medicine, physiology, in terms of mathematical "language", rather than organizing materials around mathematical methodology. -SIAM review

Handbook of Mathematical Methods in Imaging

Author : Otmar Scherzer
Publisher : Springer Science & Business Media
ISBN 13 : 0387929193
Total Pages : 1626 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Handbook of Mathematical Methods in Imaging by : Otmar Scherzer

Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Numerical Methods for Inverse Problems

Author : Michel Kern
Publisher : John Wiley & Sons
ISBN 13 : 1848218184
Total Pages : 232 pages
Book Rating : 4.8/5 (482 download)

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Book Synopsis Numerical Methods for Inverse Problems by : Michel Kern

Download or read book Numerical Methods for Inverse Problems written by Michel Kern and published by John Wiley & Sons. This book was released on 2016-06-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Statistical and Computational Inverse Problems

Author : Jari Kaipio
Publisher : Springer Science & Business Media
ISBN 13 : 0387271325
Total Pages : 340 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Statistical and Computational Inverse Problems by : Jari Kaipio

Download or read book Statistical and Computational Inverse Problems written by Jari Kaipio and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the statistical mechanics approach to computational solution of inverse problems, an innovative area of current research with very promising numerical results. The techniques are applied to a number of real world applications such as limited angle tomography, image deblurring, electical impedance tomography, and biomagnetic inverse problems. Contains detailed examples throughout and includes a chapter on case studies where such methods have been implemented in biomedical engineering.