Large Scale Inverse Problems And Quantification Of Uncertainty

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Large-Scale Inverse Problems and Quantification of Uncertainty

Author : Lorenz Biegler
Publisher : Wiley
ISBN 13 : 9780470685853
Total Pages : 0 pages
Book Rating : 4.6/5 (858 download)

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Book Synopsis Large-Scale Inverse Problems and Quantification of Uncertainty by : Lorenz Biegler

Download or read book Large-Scale Inverse Problems and Quantification of Uncertainty written by Lorenz Biegler and published by Wiley. This book was released on 2010-10-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Lorenz Biegler
Publisher : John Wiley & Sons
ISBN 13 : 1119957583
Total Pages : 403 pages
Book Rating : 4.1/5 (199 download)

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Book Synopsis Large-Scale Inverse Problems and Quantification of Uncertainty by : Lorenz Biegler

Download or read book Large-Scale Inverse Problems and Quantification of Uncertainty written by Lorenz Biegler and published by John Wiley & Sons. This book was released on 2011-06-24 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems

Author : Luis Tenorio
Publisher : SIAM
ISBN 13 : 1611974917
Total Pages : 275 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems by : Luis Tenorio

Download or read book An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems written by Luis Tenorio and published by SIAM. This book was released on 2017-07-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book 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.

Computational Uncertainty Quantification for Inverse Problems

Author : Johnathan M. Bardsley
Publisher : SIAM
ISBN 13 : 1611975387
Total Pages : 135 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Computational Uncertainty Quantification for Inverse Problems by : Johnathan M. Bardsley

Download or read book Computational Uncertainty Quantification for Inverse Problems written by Johnathan M. Bardsley and published by SIAM. This book was released on 2018-08-01 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Curtis R. Vogel
Publisher : SIAM
ISBN 13 : 0898717574
Total Pages : 195 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Computational Methods for Inverse Problems by : Curtis R. Vogel

Download or read book Computational Methods for Inverse Problems written by Curtis R. Vogel and published by SIAM. This book was released on 2002-01-01 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.

Handbook of Mathematical Methods in Imaging

Author : Otmar Scherzer
Publisher : Springer Science & Business Media
ISBN 13 : 0387929193
Total Pages : 1626 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Handbook of Mathematical Methods in Imaging by : Otmar Scherzer

Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Princeton Companion to Applied Mathematics

Author : Nicholas J. Higham
Publisher : Princeton University Press
ISBN 13 : 0691150397
Total Pages : 1014 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Princeton Companion to Applied Mathematics by : Nicholas J. Higham

Download or read book Princeton Companion to Applied Mathematics written by Nicholas J. Higham and published by Princeton University Press. This book was released on 2015-09-09 with total page 1014 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Christian Soize
Publisher : Springer
ISBN 13 : 3319543393
Total Pages : 329 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Uncertainty Quantification by : Christian Soize

Download or read book Uncertainty Quantification written by Christian Soize and published by Springer. This book was released on 2017-04-24 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems

Author : Luis Tenorio
Publisher :
ISBN 13 :
Total Pages : 269 pages
Book Rating : 4.:/5 (21 download)

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Book Synopsis An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems by : Luis Tenorio

Download or read book An Introduction to Data Analysis and Uncertainty Quantification for Inverse Problems written by Luis Tenorio and published by . This book was released on 2017 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: 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

Bayesian Approach to Inverse Problems

Author : Jérôme Idier
Publisher : John Wiley & Sons
ISBN 13 : 111862369X
Total Pages : 322 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis Bayesian Approach to Inverse Problems by : Jérôme Idier

Download or read book Bayesian Approach to Inverse Problems written by Jérôme Idier and published by John Wiley & Sons. This book was released on 2013-03-01 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data. Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation. The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.

Handbook of Dynamic Data Driven Applications Systems

Author : Frederica Darema
Publisher : Springer Nature
ISBN 13 : 3031279867
Total Pages : 937 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Handbook of Dynamic Data Driven Applications Systems by : Frederica Darema

Download or read book Handbook of Dynamic Data Driven Applications Systems written by Frederica Darema and published by Springer Nature. This book was released on 2023-10-16 with total page 937 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Second Volume in the series Handbook of Dynamic Data Driven Applications Systems (DDDAS) expands the scope of the methods and the application areas presented in the first Volume and aims to provide additional and extended content of the increasing set of science and engineering advances for new capabilities enabled through DDDAS. The methods and examples of breakthroughs presented in the book series capture the DDDAS paradigm and its scientific and technological impact and benefits. The DDDAS paradigm and the ensuing DDDAS-based frameworks for systems’ analysis and design have been shown to engender new and advanced capabilities for understanding, analysis, and management of engineered, natural, and societal systems (“applications systems”), and for the commensurate wide set of scientific and engineering fields and applications, as well as foundational areas. The DDDAS book series aims to be a reference source of many of the important research and development efforts conducted under the rubric of DDDAS, and to also inspire the broader communities of researchers and developers about the potential in their respective areas of interest, of the application and the exploitation of the DDDAS paradigm and the ensuing frameworks, through the examples and case studies presented, either within their own field or other fields of study. As in the first volume, the chapters in this book reflect research work conducted over the years starting in the 1990’s to the present. Here, the theory and application content are considered for: Foundational Methods Materials Systems Structural Systems Energy Systems Environmental Systems: Domain Assessment & Adverse Conditions/Wildfires Surveillance Systems Space Awareness Systems Healthcare Systems Decision Support Systems Cyber Security Systems Design of Computer Systems The readers of this book series will benefit from DDDAS theory advances such as object estimation, information fusion, and sensor management. The increased interest in Artificial Intelligence (AI), Machine Learning and Neural Networks (NN) provides opportunities for DDDAS-based methods to show the key role DDDAS plays in enabling AI capabilities; address challenges that ML-alone does not, and also show how ML in combination with DDDAS-based methods can deliver the advanced capabilities sought; likewise, infusion of DDDAS-like approaches in NN-methods strengthens such methods. Moreover, the “DDDAS-based Digital Twin” or “Dynamic Digital Twin”, goes beyond the traditional DT notion where the model and the physical system are viewed side-by-side in a static way, to a paradigm where the model dynamically interacts with the physical system through its instrumentation, (per the DDDAS feed-back control loop between model and instrumentation).

Uncertainty Quantification

Author : Ralph C. Smith
Publisher : SIAM
ISBN 13 : 161197321X
Total Pages : 400 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Uncertainty Quantification by : Ralph C. Smith

Download or read book Uncertainty Quantification written by Ralph C. Smith and published by SIAM. This book was released on 2013-12-02 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of uncertainty quantification is evolving rapidly because of increasing emphasis on models that require quantified uncertainties for large-scale applications, novel algorithm development, and new computational architectures that facilitate implementation of these algorithms. Uncertainty Quantification: Theory, Implementation, and Applications provides readers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models arising in a broad range of disciplines. The book begins with a detailed discussion of applications where uncertainty quantification is critical for both scientific understanding and policy. It then covers concepts from probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, surrogate model construction, and local and global sensitivity analysis. The author maintains a complementary web page where readers can find data used in the exercises and other supplementary material.

Discrete Inverse Problems

Author : Per Christian Hansen
Publisher : SIAM
ISBN 13 : 089871883X
Total Pages : 220 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Discrete Inverse Problems by : Per Christian Hansen

Download or read book Discrete Inverse Problems written by Per Christian Hansen and published by SIAM. This book was released on 2010-01-01 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.

Numerical Analysis and Optimization

Author : Mehiddin Al-Baali
Publisher : Springer
ISBN 13 : 3319176897
Total Pages : 344 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Numerical Analysis and Optimization by : Mehiddin Al-Baali

Download or read book Numerical Analysis and Optimization written by Mehiddin Al-Baali and published by Springer. This book was released on 2015-07-16 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the latest findings in the field of numerical analysis and optimization, this volume balances pure research with practical applications of the subject. Accompanied by detailed tables, figures, and examinations of useful software tools, this volume will equip the reader to perform detailed and layered analysis of complex datasets. Many real-world complex problems can be formulated as optimization tasks. Such problems can be characterized as large scale, unconstrained, constrained, non-convex, non-differentiable, and discontinuous, and therefore require adequate computational methods, algorithms, and software tools. These same tools are often employed by researchers working in current IT hot topics such as big data, optimization and other complex numerical algorithms on the cloud, devising special techniques for supercomputing systems. The list of topics covered include, but are not limited to: numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, optimal control, approximation theory, applied mathematics, algorithms and software developments, derivative free optimization methods and programming models. The volume also examines challenging applications to various types of computational optimization methods which usually occur in statistics, econometrics, finance, physics, medicine, biology, engineering and industrial sciences.

Recent Numerical Advances in Fluid Mechanics

Author : Omer San
Publisher : MDPI
ISBN 13 : 3039364022
Total Pages : 302 pages
Book Rating : 4.0/5 (393 download)

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Book Synopsis Recent Numerical Advances in Fluid Mechanics by : Omer San

Download or read book Recent Numerical Advances in Fluid Mechanics written by Omer San and published by MDPI. This book was released on 2020-07-03 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent decades, the field of computational fluid dynamics has made significant advances in enabling advanced computing architectures to understand many phenomena in biological, geophysical, and engineering fluid flows. Almost all research areas in fluids use numerical methods at various complexities: from molecular to continuum descriptions; from laminar to turbulent regimes; from low speed to hypersonic, from stencil-based computations to meshless approaches; from local basis functions to global expansions, as well as from first-order approximation to high-order with spectral accuracy. Many successful efforts have been put forth in dynamic adaptation strategies, e.g., adaptive mesh refinement and multiresolution representation approaches. Furthermore, with recent advances in artificial intelligence and heterogeneous computing, the broader fluids community has gained the momentum to revisit and investigate such practices. This Special Issue, containing a collection of 13 papers, brings together researchers to address recent numerical advances in fluid mechanics.

Monte Carlo and Quasi-Monte Carlo Methods 2010

Author : Leszek Plaskota
Publisher : Springer Science & Business Media
ISBN 13 : 3642274404
Total Pages : 732 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Monte Carlo and Quasi-Monte Carlo Methods 2010 by : Leszek Plaskota

Download or read book Monte Carlo and Quasi-Monte Carlo Methods 2010 written by Leszek Plaskota and published by Springer Science & Business Media. This book was released on 2012-08-23 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the refereed proceedings of the Ninth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Warsaw (Poland) in August 2010. These biennial conferences are major events for Monte Carlo and the premiere event for quasi-Monte Carlo research. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. The reader will be provided with information on latest developments in these very active areas. The book is an excellent reference for theoreticians and practitioners interested in solving high-dimensional computational problems arising, in particular, in finance and statistics.

Numerical Methods for Stochastic Computations

Author : Dongbin Xiu
Publisher : Princeton University Press
ISBN 13 : 1400835348
Total Pages : 142 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Numerical Methods for Stochastic Computations by : Dongbin Xiu

Download or read book Numerical Methods for Stochastic Computations written by Dongbin Xiu and published by Princeton University Press. This book was released on 2010-07-01 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: The@ first graduate-level textbook to focus on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial chaos (gPC). These fast, efficient, and accurate methods are an extension of the classical spectral methods of high-dimensional random spaces. Designed to simulate complex systems subject to random inputs, these methods are widely used in many areas of computer science and engineering. The book introduces polynomial approximation theory and probability theory; describes the basic theory of gPC methods through numerical examples and rigorous development; details the procedure for converting stochastic equations into deterministic ones; using both the Galerkin and collocation approaches; and discusses the distinct differences and challenges arising from high-dimensional problems. The last section is devoted to the application of gPC methods to critical areas such as inverse problems and data assimilation. Ideal for use by graduate students and researchers both in the classroom and for self-study, Numerical Methods for Stochastic Computations provides the required tools for in-depth research related to stochastic computations. The first graduate-level textbook to focus on the fundamentals of numerical methods for stochastic computations Ideal introduction for graduate courses or self-study Fast, efficient, and accurate numerical methods Polynomial approximation theory and probability theory included Basic gPC methods illustrated through examples