Computational Uncertainty Quantification For Inverse Problems

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Computational Uncertainty Quantification for Inverse Problems

Johnathan M. Bardsley
Computational Uncertainty Quantification for Inverse Problems Book PDF

Author : Johnathan M. Bardsley
Publisher : SIAM
Page : 135 pages
File Size : 53,7 Mb
Release : 2018-08-01
Category : Science
ISBN : 9781611975383

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Computational Uncertainty Quantification for Inverse Problems by Johnathan M. Bardsley Pdf

This book is an introduction to both computational inverse problems and uncertainty quantification (UQ) for inverse problems. The book also presents more advanced material on Bayesian methods and UQ, including Markov chain Monte Carlo sampling methods for UQ in inverse problems. Each chapter contains MATLAB® code that implements the algorithms and generates the figures, as well as a large number of exercises accessible to both graduate students and researchers. Computational Uncertainty Quantification for Inverse Problems is intended for graduate students, researchers, and applied scientists. It is appropriate for courses on computational inverse problems, Bayesian methods for inverse problems, and UQ methods for inverse problems.

An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems

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

Author : Luis Tenorio
Publisher : SIAM
Page : 275 pages
File Size : 46,5 Mb
Release : 2017-07-06
Category : Mathematics
ISBN : 9781611974911

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An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems by Luis Tenorio Pdf

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.

Large-Scale Inverse Problems and Quantification of Uncertainty

Lorenz Biegler,George Biros,Omar Ghattas,Matthias Heinkenschloss,David Keyes,Bani Mallick,Luis Tenorio,Bart van Bloemen Waanders,Karen Willcox,Youssef Marzouk
Large Scale Inverse Problems and Quantification of Uncertainty Book PDF

Author : Lorenz Biegler,George Biros,Omar Ghattas,Matthias Heinkenschloss,David Keyes,Bani Mallick,Luis Tenorio,Bart van Bloemen Waanders,Karen Willcox,Youssef Marzouk
Publisher : Wiley
Page : 388 pages
File Size : 49,7 Mb
Release : 2010-11-15
Category : Mathematics
ISBN : 0470697431

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Large-Scale Inverse Problems and Quantification of Uncertainty by Lorenz Biegler,George Biros,Omar Ghattas,Matthias Heinkenschloss,David Keyes,Bani Mallick,Luis Tenorio,Bart van Bloemen Waanders,Karen Willcox,Youssef Marzouk Pdf

This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods. Key Features: • Brings together the perspectives of researchers in areas of inverse problems and data assimilation. • Assesses the current state-of-the-art and identify needs and opportunities for future research. • Focuses on the computational methods used to analyze and simulate inverse problems. • Written by leading experts of inverse problems and uncertainty quantification. Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.

Large-Scale Inverse Problems and Quantification of Uncertainty

Lorenz Biegler,George Biros,Omar Ghattas,Matthias Heinkenschloss,David Keyes,Bani Mallick,Luis Tenorio,Bart van Bloemen Waanders,Karen Willcox,Youssef Marzouk
Large Scale Inverse Problems and Quantification of Uncertainty Book PDF

Author : Lorenz Biegler,George Biros,Omar Ghattas,Matthias Heinkenschloss,David Keyes,Bani Mallick,Luis Tenorio,Bart van Bloemen Waanders,Karen Willcox,Youssef Marzouk
Publisher : John Wiley & Sons
Page : 403 pages
File Size : 48,9 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9781119957584

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Large-Scale Inverse Problems and Quantification of Uncertainty by Lorenz Biegler,George Biros,Omar Ghattas,Matthias Heinkenschloss,David Keyes,Bani Mallick,Luis Tenorio,Bart van Bloemen Waanders,Karen Willcox,Youssef Marzouk Pdf

This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods. Key Features: Brings together the perspectives of researchers in areas of inverse problems and data assimilation. Assesses the current state-of-the-art and identify needs and opportunities for future research. Focuses on the computational methods used to analyze and simulate inverse problems. Written by leading experts of inverse problems and uncertainty quantification. Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.

Computational Uncertainty Quantification for Inverse Problems

Johnathan M. Bardsley
Computational Uncertainty Quantification for Inverse Problems Book PDF

Author : Johnathan M. Bardsley
Publisher : SIAM
Page : 141 pages
File Size : 51,6 Mb
Release : 2018-08-01
Category : Science
ISBN : 9781611975376

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Computational Uncertainty Quantification for Inverse Problems by Johnathan M. Bardsley Pdf

This book is an introduction to both computational inverse problems and uncertainty quantification (UQ) for inverse problems. The book also presents more advanced material on Bayesian methods and UQ, including Markov chain Monte Carlo sampling methods for UQ in inverse problems. Each chapter contains MATLAB? code that implements the algorithms and generates the figures, as well as a large number of exercises accessible to both graduate students and researchers. Computational Uncertainty Quantification for Inverse Problems is intended for graduate students, researchers, and applied scientists. It is appropriate for courses on computational inverse problems, Bayesian methods for inverse problems, and UQ methods for inverse problems.

Computational Methods for Inverse Problems

Curtis R. Vogel
Computational Methods for Inverse Problems Book PDF

Author : Curtis R. Vogel
Publisher : SIAM
Page : 183 pages
File Size : 51,5 Mb
Release : 2002
Category : Mathematics
ISBN : 9780898717570

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Computational Methods for Inverse Problems by Curtis R. Vogel Pdf

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

Inverse Problems: Tikhonov Theory And Algorithms

Ito Kazufumi,Jin Bangti
Inverse Problems Tikhonov Theory And Algorithms Book PDF

Author : Ito Kazufumi,Jin Bangti
Publisher : World Scientific
Page : 332 pages
File Size : 41,8 Mb
Release : 2014-08-28
Category : Mathematics
ISBN : 9789814596213

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Inverse Problems: Tikhonov Theory And Algorithms by Ito Kazufumi,Jin Bangti Pdf

Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference.The book offers a comprehensive treatment of modern techniques, and seamlessly blends regularization theory with computational methods, which is essential for developing accurate and efficient inversion algorithms for many practical inverse problems.It demonstrates many current developments in the field of computational inversion, such as value function calculus, augmented Tikhonov regularization, multi-parameter Tikhonov regularization, semismooth Newton method, direct sampling method, uncertainty quantification and approximate Bayesian inference. It is written for graduate students and researchers in mathematics, natural science and engineering.

Uncertainty Quantification

Christian Soize
Uncertainty Quantification Book PDF

Author : Christian Soize
Publisher : Springer
Page : 329 pages
File Size : 47,9 Mb
Release : 2017-04-24
Category : Computers
ISBN : 9783319543390

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Uncertainty Quantification by Christian Soize Pdf

This book presents the fundamental notions and advanced mathematical tools in the stochastic modeling of uncertainties and their quantification for large-scale computational models in sciences and engineering. In particular, it focuses in parametric uncertainties, and non-parametric uncertainties with applications from the structural dynamics and vibroacoustics of complex mechanical systems, from micromechanics and multiscale mechanics of heterogeneous materials. Resulting from a course developed by the author, the book begins with a description of the fundamental mathematical tools of probability and statistics that are directly useful for uncertainty quantification. It proceeds with a well carried out description of some basic and advanced methods for constructing stochastic models of uncertainties, paying particular attention to the problem of calibrating and identifying a stochastic model of uncertainty when experimental data is available. This book is intended to be a graduate-level textbook for students as well as professionals interested in the theory, computation, and applications of risk and prediction in science and engineering fields.

Inverse Problems

Kazufumi Ito,Bangti Jin
Inverse Problems Book PDF

Author : Kazufumi Ito,Bangti Jin
Publisher : World Scientific Publishing Company Incorporated
Page : 319 pages
File Size : 49,9 Mb
Release : 2014-07
Category : Mathematics
ISBN : 9814596191

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Inverse Problems by Kazufumi Ito,Bangti Jin Pdf

Inverse problems arise in practical applications whenever one needs to deduce unknowns from observables. This monograph is a valuable contribution to the highly topical field of computational inverse problems. Both mathematical theory and numerical algorithms for model-based inverse problems are discussed in detail. The mathematical theory focuses on nonsmooth Tikhonov regularization for linear and nonlinear inverse problems. The computational methods include nonsmooth optimization algorithms, direct inversion methods and uncertainty quantification via Bayesian inference. The book offers a comprehensive treatment of modern techniques, and seamlessly blends regularization theory with computational methods, which is essential for developing accurate and efficient inversion algorithms for many practical inverse problems. It demonstrates many current developments in the field of computational inversion, such as value function calculus, augmented Tikhonov regularization, multi-parameter Tikhonov regularization, semismooth Newton method, direct sampling method, uncertainty quantification and approximate Bayesian inference. It is written for graduate students and researchers in mathematics, natural science and engineering.

Inverse Problems in the Mathematical Sciences

Charles W. Groetsch
Inverse Problems in the Mathematical Sciences Book PDF

Author : Charles W. Groetsch
Publisher : Springer Science & Business Media
Page : 154 pages
File Size : 50,8 Mb
Release : 2013-12-14
Category : Technology & Engineering
ISBN : 9783322992024

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Inverse Problems in the Mathematical Sciences by Charles W. Groetsch Pdf

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.

Inverse Problem Theory and Methods for Model Parameter Estimation

Albert Tarantola
Inverse Problem Theory and Methods for Model Parameter Estimation Book PDF

Author : Albert Tarantola
Publisher : SIAM
Page : 349 pages
File Size : 47,9 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 0898717922

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Inverse Problem Theory and Methods for Model Parameter Estimation by Albert Tarantola Pdf

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.

Computational Methods for Inverse Problems

Curtis R. Vogel
Computational Methods for Inverse Problems Book PDF

Author : Curtis R. Vogel
Publisher : SIAM
Page : 195 pages
File Size : 42,7 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 9780898715507

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Computational Methods for Inverse Problems by Curtis R. Vogel Pdf

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

Princeton Companion to Applied Mathematics

Nicholas J. Higham,Mark R. Dennis,Paul Glendinning,Paul A. Martin,Fadil Santosa,Jared Tanner
Princeton Companion to Applied Mathematics Book PDF

Author : Nicholas J. Higham,Mark R. Dennis,Paul Glendinning,Paul A. Martin,Fadil Santosa,Jared Tanner
Publisher : Princeton University Press
Page : 1014 pages
File Size : 40,5 Mb
Release : 2015-09-09
Category : Mathematics
ISBN : 9780691150390

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Princeton Companion to Applied Mathematics by Nicholas J. Higham,Mark R. Dennis,Paul Glendinning,Paul A. Martin,Fadil Santosa,Jared Tanner Pdf

The must-have compendium on applied mathematics This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index

A Taste of Inverse Problems

Martin Hanke
A Taste of Inverse Problems Book PDF

Author : Martin Hanke
Publisher : SIAM
Page : 171 pages
File Size : 46,9 Mb
Release : 2017-01-01
Category : Mathematics
ISBN : 9781611974935

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A Taste of Inverse Problems by Martin Hanke Pdf

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. A Taste of Inverse Problems: Basic Theory and Examples?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. This book 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.

Modeling and Inverse Problems in the Presence of Uncertainty

H. T. Banks,Shuhua Hu,W. Clayton Thompson
Modeling and Inverse Problems in the Presence of Uncertainty Book PDF

Author : H. T. Banks,Shuhua Hu,W. Clayton Thompson
Publisher : CRC Press
Page : 403 pages
File Size : 50,8 Mb
Release : 2014-04-01
Category : Mathematics
ISBN : 9781482206432

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Modeling and Inverse Problems in the Presence of Uncertainty by H. T. Banks,Shuhua Hu,W. Clayton Thompson Pdf

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 i