Parameter Estimation and Inverse Problems Book

Parameter Estimation and Inverse Problems

  • Author : Richard C. Aster
  • Publisher : Academic Press
  • Release Date : 2013
  • Genre: Computers
  • Pages : 377
  • ISBN 10 : 9780123850485

Parameter Estimation and Inverse Problems 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.

Inverse Problem Theory and Methods for Model Parameter Estimation Book

Inverse Problem Theory and Methods for Model Parameter Estimation

  • Author : Albert Tarantola
  • Publisher : SIAM
  • Release Date : 2005-01-01
  • Genre: Mathematics
  • Pages : 354
  • ISBN 10 : 0898717922

Inverse Problem Theory and Methods for Model Parameter Estimation 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.

Geophysical Inverse Theory Book

Geophysical Inverse Theory

  • Author : Robert L. Parker
  • Publisher : Princeton University Press
  • Release Date : 2019-12-31
  • Genre: Science
  • Pages : null
  • ISBN 10 : 9780691206837

Geophysical Inverse Theory 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.

Computational Methods for Inverse Problems Book

Computational Methods for Inverse Problems

  • Author : Curtis R. Vogel
  • Publisher : SIAM
  • Release Date : 2002
  • Genre: Mathematics
  • Pages : 183
  • ISBN 10 : 9780898717570

Computational Methods for Inverse Problems Excerpt :

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

Inverse Problems in the Mathematical Sciences Book

Inverse Problems in the Mathematical Sciences

  • Author : Charles W. Groetsch
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-12-14
  • Genre: Technology & Engineering
  • Pages : 154
  • ISBN 10 : 9783322992024

Inverse Problems in the Mathematical Sciences 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.

Numerical Methods for Inverse Problems Book

Numerical Methods for Inverse Problems

  • Author : Michel Kern
  • Publisher : John Wiley & Sons
  • Release Date : 2016-06-07
  • Genre: Mathematics
  • Pages : 232
  • ISBN 10 : 9781848218185

Numerical Methods for Inverse Problems 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.

Advanced Data Assimilation for Geosciences Book

Advanced Data Assimilation for Geosciences

  • Author : Marc Bocquet
  • Publisher : Lecture Notes of the Les Houch
  • Release Date : 2014
  • Genre: Science
  • Pages : 609
  • ISBN 10 : 9780198723844

Advanced Data Assimilation for Geosciences Excerpt :

This volume gathers notes from lectures and seminars given during a three-week school on theoretical and applied data assimilation held in Les Houches in 2012. Data assimilation aims at determining as accurately as possible the state of a dynamical system by combining heterogeneous sources of information in an optimal way.

Inverse Problem Theory Book

Inverse Problem Theory

  • Author : A. Tarantola
  • Publisher : Elsevier
  • Release Date : 2013-10-14
  • Genre: Mathematics
  • Pages : 644
  • ISBN 10 : 9780444599674

Inverse Problem Theory 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.

Geophysical Data Analysis  Understanding Inverse Problem Theory and Practice Book

Geophysical Data Analysis Understanding Inverse Problem Theory and Practice

  • Author : Max A. Meju
  • Publisher : SEG Books
  • Release Date : 1994
  • Genre: Geophysics
  • Pages : 305
  • ISBN 10 : 9781560802570

Geophysical Data Analysis Understanding Inverse Problem Theory and Practice 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.

Inverse Problems and Related Topics Book

Inverse Problems and Related Topics

  • Author : Gen Nakamura
  • Publisher : CRC Press
  • Release Date : 2019-05-08
  • Genre: Mathematics
  • Pages : 147
  • ISBN 10 : 9780429530326

Inverse Problems and Related Topics Excerpt :

Inverse problems arise in many disciplines and hold great importance to practical applications. However, sound new methods are needed to solve these problems. Over the past few years, Japanese and Korean mathematicians have obtained a number of very interesting and unique results in inverse problems. Inverse Problems and Related Topics compi

Model Calibration and Parameter Estimation Book

Model Calibration and Parameter Estimation

  • Author : Ne-Zheng Sun
  • Publisher : Springer
  • Release Date : 2015-07-01
  • Genre: Mathematics
  • Pages : 621
  • ISBN 10 : 9781493923236

Model Calibration and Parameter Estimation Excerpt :

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.

An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems Book

An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems

  • Author : Luis Tenorio
  • Publisher : SIAM
  • Release Date : 2017-07-06
  • Genre: Mathematics
  • Pages : 275
  • ISBN 10 : 9781611974911

An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems 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 Heat Transfer Book

Inverse Heat Transfer

  • Author : M. Necat Ozisik
  • Publisher : Routledge
  • Release Date : 2018-05-02
  • Genre: Science
  • Pages : 174
  • ISBN 10 : 9781351436397

Inverse Heat Transfer Excerpt :

This book introduces the fundamental concepts of inverse heat transfer problems. It presents in detail the basic steps of four techniques of inverse heat transfer protocol, as a parameter estimation approach and as a function estimation approach. These techniques are then applied to the solution of the problems of practical engineering interest involving conduction, convection, and radiation. The text also introduces a formulation based on generalized coordinates for the solution of inverse heat conduction problems in two-dimensional regions.

Modeling and Inverse Problems in Imaging Analysis Book

Modeling and Inverse Problems in Imaging Analysis

  • Author : Bernard Chalmond
  • Publisher : Springer Science & Business Media
  • Release Date : 2003-01-14
  • Genre: Mathematics
  • Pages : 344
  • ISBN 10 : 038795547X

Modeling and Inverse Problems in Imaging Analysis Excerpt :

More mathematicians have been taking part in the development of digital image processing as a science and the contributions are reflected in the increasingly important role modeling has played solving complex problems. This book is mostly concerned with energy-based models. Most of these models come from industrial projects in which the author was involved in robot vision and radiography: tracking 3D lines, radiographic image processing, 3D reconstruction and tomography, matching, deformation learning. Numerous graphical illustrations accompany the text.

Inverse Engineering Handbook Book

Inverse Engineering Handbook

  • Author : Keith A. Woodbury
  • Publisher : CRC Press
  • Release Date : 2002-09-25
  • Genre: Mathematics
  • Pages : 480
  • ISBN 10 : 9781420041613

Inverse Engineering Handbook Excerpt :

Inverse problems have been the focus of a growing number of research efforts over the last 40 years-and rightly so. The ability to determine a "cause" from an observed "effect" is a powerful one. Researchers now have at their disposal a variety of techniques for solving inverse problems, techniques that go well beyond those useful for relatively simple parameter estimation problems. The question is, where can one find a single, comprehensive resource that details these methods? The answer is the Inverse Engineering Handbook. Leading experts in inverse problems have joined forces to produce the definitive reference that allows readers to understand, implement, and benefit from a variety of problem-solving techniques. Each chapter details a method developed or refined by its contributor, who provides clear explanations, examples, and in many cases, software algorithms. The presentation begins with methods for parameter estimation, which build a bridge to boundary function estimation problems. The techniques addressed include sequential function estimation, mollification, space marching techniques, and adjoint, Monte Carlo, and gradient-based methods. Discussions also cover important experimental aspects, including experiment design and the effects of uncertain parameters. While many of the examples presented focus on heat transfer, the techniques discussed are applicable to a wide range of inverse problems. Anyone interested in inverse problems, regardless of their specialty, will find the Inverse Engineering Handbook to be a unique and invaluable compendium of up-to-date techniques.