Parameter Estimation and Inverse Problems

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

Publisher: Elsevier

ISBN: 0128134232

Category: Science

Page: 404

View: 9456

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: 6347

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: 9992

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: 4261

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: 4927

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.

Time Series Analysis and Inverse Theory for Geophysicists

Author: David Gubbins

Publisher: Cambridge University Press

ISBN: 9780521525695

Category: Mathematics

Page: 255

View: 4131

The first textbook covering spectral analysis and geophysical data inversion for undergraduate and graduate students.

Introduction to Inverse Problems in Imaging

Author: M. Bertero,P. Boccacci

Publisher: CRC Press

ISBN: 9781439822067

Category: Technology & Engineering

Page: 352

View: 9742

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: 9840

Modeling and Inverse Problems in the Presence of Uncertainty

Author: H. T. Banks,Shuhua Hu,W. Clayton Thompson

Publisher: CRC Press

ISBN: 1482206439

Category: Mathematics

Page: 405

View: 1901

Modeling and Inverse Problems in the Presence of Uncertainty collects recent research—including the authors’ own substantial projects—on uncertainty propagation and quantification. It covers two sources of uncertainty: where uncertainty is present primarily due to measurement errors and where uncertainty is present due to the modeling formulation itself. After a useful review of relevant probability and statistical concepts, the book summarizes mathematical and statistical aspects of inverse problem methodology, including ordinary, weighted, and generalized least-squares formulations. It then discusses asymptotic theories, bootstrapping, and issues related to the evaluation of correctness of assumed form of statistical models. The authors go on to present methods for evaluating and comparing the validity of appropriateness of a collection of models for describing a given data set, including statistically based model selection and comparison techniques. They also explore recent results on the estimation of probability distributions when they are embedded in complex mathematical models and only aggregate (not individual) data are available. In addition, they briefly discuss the optimal design of experiments in support of inverse problems for given models. The book concludes with a focus on uncertainty in model formulation itself, covering the general relationship of differential equations driven by white noise and the ones driven by colored noise in terms of their resulting probability density functions. It also deals with questions related to the appropriateness of discrete versus continuum models in transitions from small to large numbers of individuals. With many examples throughout addressing problems in physics, biology, and other areas, this book is intended for applied mathematicians interested in deterministic and/or stochastic models and their interactions. It is also suitable for scientists in biology, medicine, engineering, and physics working on basic modeling and inverse problems, uncertainty in modeling, propagation of uncertainty, and statistical modeling.

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: 8379

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

Inverse Problems in Groundwater Modeling

Author: Ne-Zheng Sun

Publisher: Springer Science & Business Media

ISBN: 9401719705

Category: Science

Page: 338

View: 4947

... 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.

Computational Methods for Inverse Problems

Author: Curtis R. Vogel

Publisher: SIAM

ISBN: 0898715504

Category: Mathematics

Page: 183

View: 793

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


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: 8440

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.

Numerical Methods for Inverse Problems

Author: Michel Kern

Publisher: John Wiley & Sons

ISBN: 1848218184

Category: Mathematics

Page: 232

View: 7562

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.

Optimale Steuerung partieller Differentialgleichungen

Theorie, Verfahren und Anwendungen

Author: Fredi Tröltzsch

Publisher: Springer-Verlag

ISBN: 3322968448

Category: Mathematics

Page: 298

View: 2325

Die mathematische Theorie der optimalen Steuerung hat sich im Zusammenhang mit Berechnungen für die Luft- und Raumfahrt schnell zu einem wichtigen und eigenständigen Gebiet der angewandten Mathematik entwickelt. Die optimale Steuerung durch partielle Differentialgleichungen modellierter Prozesse wird eine numerische Herausforderung der Zukunft sein. Sie erfordert die Analysis nichtlinearer partieller Differentialgleichungen, Optimierung im Funktionenraum, nichtlineare Funktionalanalysis sowie Optimierungsverfahren für extrem große Aufgaben. Im Buch werden entsprechende Grundlagen mit langsam steigendem Schwierigkeitsgrad entwickelt. Grundkenntnisse zu partiellen Differentialgleichungen und der Funktionalanalysis werden jeweils dort gebracht, wo sie konkret nötig sind. Das Buch enthält viele Beispiele und eignet sich als Grundlage für Vorlesungen und Seminare.

Bayesian inference for inverse problems

Author: Society of photo-optical instrumentation engineers

Publisher: SPIE-International Society for Optical Engineering


Category: Technology & Engineering

Page: 380

View: 1975

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: 9209

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.

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: 7698

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

Modeling and Inverse Problems in Imaging Analysis

Author: Bernard Chalmond

Publisher: Springer Science & Business Media

ISBN: 9780387955476

Category: Computers

Page: 309

View: 2172

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.

Inverse Problems and High-Dimensional Estimation

Stats in the Château Summer School, August 31 - September 4, 2009

Author: Pierre Alquier,Eric Gautier,Gilles Stoltz

Publisher: Springer Science & Business Media

ISBN: 9783642199899

Category: Mathematics

Page: 198

View: 562

The “Stats in the Château” summer school was held at the CRC château on the campus of HEC Paris, Jouy-en-Josas, France, from August 31 to September 4, 2009. This event was organized jointly by faculty members of three French academic institutions ─ ENSAE ParisTech, the Ecole Polytechnique ParisTech, and HEC Paris ─ which cooperate through a scientific foundation devoted to the decision sciences. The scientific content of the summer school was conveyed in two courses, one by Laurent Cavalier (Université Aix-Marseille I) on "Ill-posed Inverse Problems", and one by Victor Chernozhukov (Massachusetts Institute of Technology) on "High-dimensional Estimation with Applications to Economics". Ten invited researchers also presented either reviews of the state of the art in the field or of applications, or original research contributions. This volume contains the lecture notes of the two courses. Original research articles and a survey complement these lecture notes. Applications to economics are discussed in various contributions.