Parameter Estimation and Inverse Problems

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

Publisher: Elsevier

ISBN: 0128134232

Category: Science

Page: 404

View: 6819


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 and Methods for Model Parameter Estimation

Author: Albert Tarantola

Publisher: SIAM

ISBN: 9780898717921

Category: Engineering

Page: 342

View: 2281


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: 3497


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.

Parameter Identification and Inverse Problems in Hydrology, Geology and Ecology

Author: Johannes Gottlieb,Paul DuChateau

Publisher: Springer Science & Business Media

ISBN: 940091704X

Category: Science

Page: 302

View: 4444


The Workshop on Parameter Identification and Inverse Problems in Hydrology, Geology and Ecology, Karlsruhe, April 10-12, 1995, was organized to bring to gether an interdisciplinary group drawn from the areas of science, engineering and mathematics for the following purposes: - to promote, encourage and influence more understanding and cooperation in the community of parameter identifiers from various disciplines, - to forge unity in diversity by bringing together a variety of disciplines that attempt to understand the reconstruction of inner model parameters, un known nonlinear constitutive relations, heterogeneous structures inside of geological objects, sources or sinks from observational data, - to discuss modern regularization tools for handling improperly posed pro blems and strategies of incorporating a priori knowledge from the applied problem into the model and its treatment. These proceedings contain some of the results of the workshop, representing a bal anced selection of contributions from the various groups of participants. The reviewed invited and contributed articles are grouped according to the broad headings of hydrology, non-linear diffusion and soil physics, geophysical methods, mathematical analysis of inverse and ill-posed problems and parallel algorithms for inverse problems. Some of the issues adressed by the articles in these proceedings include the rela tion between least squares and direct formulations of inverse problems for partial differential equations, nonlinear regularization, identification of nonlinear consti tutive relations, fast parallel algorithms for large scale inverse problems, reduction of model structures, geostatistical inversion techniques.

Stable Solution of Inverse Problems

Author: Johann Baumeister

Publisher: Vieweg + Teubner Verlag


Category: Language Arts & Disciplines

Page: 254

View: 2993


These notes are intended to describe the basic concepts of solving inverse problems in a stable way. Since almost all in­ verse problems are ill-posed in its original formulation the discussion of methods to overcome difficulties which result from this fact is the main subject of this book. Over the past fifteen years, the number of publications on inverse problems has grown rapidly. Therefore, these notes can be neither a comprehensive introduction nor a complete mono­ graph on the topics considered; it is designed to provide the main ideas and methods. Throughout, we have not striven for the most general statement, but the clearest one which would cover the most situations. The presentation is intended to be accessible to students whose mathematical background includes basic courses in ad­ vanced calculus, linear algebra and functional analysis. Each chapter contains bibliographical comments. At the end of Chap­ ter 1 references are given which refer to topics which are not studied in this book. I am very grateful to Mrs. B. Brodt for typing and to W. Scondo and u. Schuch for inspecting the manuscript.

Introduction to Inverse Problems in Imaging

Author: M. Bertero,P. Boccacci

Publisher: CRC Press

ISBN: 9781439822067

Category: Technology & Engineering

Page: 352

View: 8953


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.

Inverse problems in engineering

theory and practice

Author: Nicholas Zabaras,Engineering Foundation (U.S.),American Society of Mechanical Engineers

Publisher: Amer Society of Mechanical


Category: Technology & Engineering

Page: 369

View: 5177


Numerical Methods for Inverse Problems

Author: Michel Kern

Publisher: John Wiley & Sons

ISBN: 1848218184

Category: Mathematics

Page: 232

View: 6787


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.

Modeling and Inverse Problems in Imaging Analysis

Author: Bernard Chalmond

Publisher: Springer Science & Business Media

ISBN: 9780387955476

Category: Computers

Page: 309

View: 2209


More mathematics 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. Through concrete image analysis problems, the author develops consistent modeling, a know-how generally hidden in the proposed solutions. The book is divided into three main parts. The first two parts describe the theory behind the applications that are presented in the third part. These materials include splines (variational approach, regression spline, spline in high dimension) and random fields (Markovian field, parametric estimation, stochastic and deterministic optimization, continuous Gaussian field). Most of these applications come from industrial projects in which the author was involved in robot vision and radiography: tracking 3-D lines, radiographic image processing, 3-D reconstruction and tomography, matching and deformation learning. Numerous graphical illustrations accompany the text showing the performance of the proposed models. This book will be useful to researchers and graduate students in mathematics, physics, computer science, and engineering.

Computational Methods for Inverse Problems

Author: Curtis R. Vogel

Publisher: SIAM

ISBN: 0898715504

Category: Mathematics

Page: 183

View: 1237


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: 9401719705

Category: Science

Page: 338

View: 6576


... 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.

Inverse Problems, Design and Optimization - vol. 2

Author: Marcelo J. Colaço,Helcio R. B. Orlande,George S. Dulikravich

Publisher: Editora E-papers

ISBN: 8576500302


Page: 354

View: 1014


This book contains the papers presented in the Inverse Problems, Design and Optimization (IPDO) Symposium, held in Rio de Janeiro, Brazil, during March 17-19, 2004

Dynamic Systems Models

New Methods of Parameter and State Estimation

Author: Josif A. Boguslavskiy

Publisher: Springer

ISBN: 3319040367

Category: Science

Page: 201

View: 9768


This monograph is an exposition of a novel method for solving inverse problems, a method of parameter estimation for time series data collected from simulations of real experiments. These time series might be generated by measuring the dynamics of aircraft in flight, by the function of a hidden Markov model used in bioinformatics or speech recognition or when analyzing the dynamics of asset pricing provided by the nonlinear models of financial mathematics. Dynamic Systems Models demonstrates the use of algorithms based on polynomial approximation which have weaker requirements than already-popular iterative methods. Specifically, they do not require a first approximation of a root vector and they allow non-differentiable elements in the vector functions being approximated. The text covers all the points necessary for the understanding and use of polynomial approximation from the mathematical fundamentals, through algorithm development to the application of the method in, for instance, aeroplane flight dynamics or biological sequence analysis. The technical material is illustrated by the use of worked examples and methods for training the algorithms are included. Dynamic Systems Models provides researchers in aerospatial engineering, bioinformatics and financial mathematics (as well as computer scientists interested in any of these fields) with a reliable and effective numerical method for nonlinear estimation and solving boundary problems when carrying out control design. It will also be of interest to academic researchers studying inverse problems and their solution.

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: 7444


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.


Praxisorientierter Leitfaden zur numerischen Modellierung von Beschaffenheit, Kontamination und Sanierung aquatischer Systeme

Author: Broder J. Merkel,Britta Planer-Friedrich

Publisher: Springer-Verlag

ISBN: 366207611X

Category: Science

Page: 219

View: 796


Die Autoren konzentrieren sich in ihrem Werk auf die Lösung praxisorientierter hydrogeochemischer Fragestellungen und schließen damit eine Lücke im Bereich anwendungsorientierter Lehrbücher. Ein erster Teil fasst dabei die Theorie soweit zusammen, daß es auch Neulingen im Bereich der Modellierung und Nichtchemikern leicht gemacht wird, das anspruchsvolle Thema zu erfassen. Akademikern mit hydrogeologischer oder chemischer Grundausbildung sowie Studenten höherer Semester in den relevanten Fachgebieten erlaubt das Buch, anhand der beschriebenen Beispiele und Lösungen, eine eigenständige Erarbeitung der Sachverhalte. Die beiliegende CD-ROM ermöglicht zudem eine rasche Überprüfung der Ergebnisse, bzw. das Nachvollziehen aller Aufgaben und Lösungen anhand der beigefügten PhreeC-Eingabedateien. Da das Programm PhreeC kostenfrei verfügbar ist und mit Windows-Oberfläche auf der CD-ROM vorhanden ist, kann sofort mit der Modellierung begonnen werden.

Inverse Problems in Diffusion Processes

Proceedings of the GAMM-SIAM Symposium

Author: Heinz W. Engl,William Rundell

Publisher: SIAM

ISBN: 9780898713510

Category: Science

Page: 232

View: 3906


This collection of expository papers encompasses both the theoretical and physical application side of inverse problems in diffusion processes.

Inverse Problems and Related Topics

Author: Gen Nakamura,Saburou Saitoh,Jin Kean Seo

Publisher: CRC Press

ISBN: 9781584881919

Category: Mathematics

Page: 248

View: 545


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 compiles papers authored by some of the top researchers in Korea and Japan. It presents a number of original and useful results and offers a unique opportunity to explore the current trends of research in inverse problems in these countries. Highlighting the existence and active work of several Japanese and Korean groups, it also serves as a guide to those seeking future scientific exchange with researchers in these countries.