Computational Uncertainty Quantification For Inverse Problems
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Computational Uncertainty Quantification For Inverse Problems
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Author : Johnathan M. Bardsley
language : en
Publisher: SIAM
Release Date : 2018-08-01
Computational Uncertainty Quantification For Inverse Problems written by Johnathan M. Bardsley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-01 with Science categories.
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
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Author : Luis Tenorio
language : en
Publisher: SIAM
Release Date : 2017-07-06
An Introduction To Data Analysis And Uncertainty Quantification For Inverse Problems written by Luis Tenorio and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-06 with Mathematics categories.
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.
Computational Uncertainty Quantification For Inverse Problems
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Author : Johnathan M. Bardsley
language : en
Publisher: SIAM
Release Date : 2018-08-01
Computational Uncertainty Quantification For Inverse Problems written by Johnathan M. Bardsley and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-01 with Science categories.
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
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Author : Curtis R. Vogel
language : en
Publisher: SIAM
Release Date : 2002-01-01
Computational Methods For Inverse Problems written by Curtis R. Vogel and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.
Princeton Companion To Applied Mathematics
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Author : Nicholas J. Higham
language : en
Publisher: Princeton University Press
Release Date : 2015-09-09
Princeton Companion To Applied Mathematics written by Nicholas J. Higham and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-09 with Mathematics categories.
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
Uncertainty Quantification
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Author : Ralph C. Smith
language : en
Publisher: SIAM
Release Date : 2024-09-13
Uncertainty Quantification written by Ralph C. Smith and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-13 with Mathematics categories.
Uncertainty quantification serves a fundamental role when establishing the predictive capabilities of simulation models. This book provides a comprehensive and unified treatment of the mathematical, statistical, and computational theory and methods employed to quantify uncertainties associated with models from a wide range of applications. Expanded and reorganized, the second edition includes advances in the field and provides a comprehensive sensitivity analysis and uncertainty quantification framework for models from science and engineering. It contains new chapters on random field representations, observation models, parameter identifiability and influence, active subspace analysis, and statistical surrogate models, and a completely revised chapter on local sensitivity analysis. Other updates to the second edition are the inclusion of over 100 exercises and many new examples — several of which include data — and UQ Crimes listed throughout the text to identify common misconceptions and guide readers entering the field. Uncertainty Quantification: Theory, Implementation, and Applications, Second Edition is intended for advanced undergraduate and graduate students as well as researchers in mathematics, statistics, engineering, physical and biological sciences, operations research, and computer science. Readers are assumed to have a basic knowledge of probability, linear algebra, differential equations, and introductory numerical analysis. The book can be used as a primary text for a one-semester course on sensitivity analysis and uncertainty quantification or as a supplementary text for courses on surrogate and reduced-order model construction and parameter identifiability analysis.
Inverse Problem Theory And Methods For Model Parameter Estimation
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Author : Albert Tarantola
language : en
Publisher: SIAM
Release Date : 2005-01-01
Inverse Problem Theory And Methods For Model Parameter Estimation written by Albert Tarantola and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
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.
Uncertainty Quantification In Variational Inequalities
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Author : Joachim Gwinner
language : en
Publisher: CRC Press
Release Date : 2021-12-21
Uncertainty Quantification In Variational Inequalities written by Joachim Gwinner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-21 with Mathematics categories.
Uncertainty Quantification (UQ) is an emerging and extremely active research discipline which aims to quantitatively treat any uncertainty in applied models. The primary objective of Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications is to present a comprehensive treatment of UQ in variational inequalities and some of its generalizations emerging from various network, economic, and engineering models. Some of the developed techniques also apply to machine learning, neural networks, and related fields. Features First book on UQ in variational inequalities emerging from various network, economic, and engineering models Completely self-contained and lucid in style Aimed for a diverse audience including applied mathematicians, engineers, economists, and professionals from academia Includes the most recent developments on the subject which so far have only been available in the research literature
Linear And Nonlinear Inverse Problems With Practical Applications
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Author : Jennifer L. Mueller
language : en
Publisher: SIAM
Release Date : 2012-11-30
Linear And Nonlinear Inverse Problems With Practical Applications written by Jennifer L. Mueller and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-30 with Mathematics categories.
Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. This book explains how to identify ill-posed inverse problems arising in practice and gives a hands-on guide to designing computational solution methods for them, with related codes on an accompanying website. The guiding linear inversion examples are the problem of image deblurring, x-ray tomography, and backward parabolic problems, including heat transfer. A thorough treatment of electrical impedance tomography is used as the guiding nonlinear inversion example which combines the analytic-geometric research tradition and the regularization-based school of thought in a fruitful manner. This book is complete with exercises and project topics, making it ideal as a classroom textbook or self-study guide for graduate and advanced undergraduate students in mathematics, engineering or physics who wish to learn about computational inversion. It also acts as a useful guide for researchers who develop inversion techniques in high-tech industry.
Methods In Computational Science
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Author : Johan Hoffman
language : en
Publisher: SIAM
Release Date : 2021-10-19
Methods In Computational Science written by Johan Hoffman and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-19 with Computers categories.
Computational methods are an integral part of most scientific disciplines, and a rudimentary understanding of their potential and limitations is essential for any scientist or engineer. This textbook introduces computational science through a set of methods and algorithms, with the aim of familiarizing the reader with the field’s theoretical foundations and providing the practical skills to use and develop computational methods. Centered around a set of fundamental algorithms presented in the form of pseudocode, this self-contained textbook extends the classical syllabus with new material, including high performance computing, adjoint methods, machine learning, randomized algorithms, and quantum computing. It presents theoretical material alongside several examples and exercises and provides Python implementations of many key algorithms. Methods in Computational Science is for advanced undergraduate and graduate-level students studying computer science and data science. It can also be used to support continuous learning for practicing mathematicians, data scientists, computer scientists, and engineers in the field of computational science. It is appropriate for courses in advanced numerical analysis, data science, numerical optimization, and approximation theory.