Introduction To Uncertainty Quantification

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Introduction to Uncertainty Quantification

T.J. Sullivan
Introduction to Uncertainty Quantification Book PDF

Author : T.J. Sullivan
Publisher : Springer
Page : 342 pages
File Size : 43,8 Mb
Release : 2015-12-14
Category : Mathematics
ISBN : 9783319233956

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Introduction to Uncertainty Quantification by T.J. Sullivan Pdf

This text provides a framework in which the main objectives of the field of uncertainty quantification (UQ) are defined and an overview of the range of mathematical methods by which they can be achieved. Complete with exercises throughout, the book will equip readers with both theoretical understanding and practical experience of the key mathematical and algorithmic tools underlying the treatment of uncertainty in modern applied mathematics. Students and readers alike are encouraged to apply the mathematical methods discussed in this book to their own favorite problems to understand their strengths and weaknesses, also making the text suitable for a self-study. Uncertainty quantification is a topic of increasing practical importance at the intersection of applied mathematics, statistics, computation and numerous application areas in science and engineering. This text is designed as an introduction to UQ for senior undergraduate and graduate students with a mathematical or statistical background and also for researchers from the mathematical sciences or from applications areas who are interested in the field. T. J. Sullivan was Warwick Zeeman Lecturer at the Mathematics Institute of the University of Warwick, United Kingdom, from 2012 to 2015. Since 2015, he is Junior Professor of Applied Mathematics at the Free University of Berlin, Germany, with specialism in Uncertainty and Risk Quantification.

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 : 53,8 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.

Handbook of Uncertainty Quantification

Roger Ghanem,David Higdon,Howman Owhadi
Handbook of Uncertainty Quantification Book PDF

Author : Roger Ghanem,David Higdon,Howman Owhadi
Publisher : Springer
Page : 0 pages
File Size : 50,5 Mb
Release : 2016-05-08
Category : Mathematics
ISBN : 331912384X

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Handbook of Uncertainty Quantification by Roger Ghanem,David Higdon,Howman Owhadi Pdf

The topic of Uncertainty Quantification (UQ) has witnessed massive developments in response to the promise of achieving risk mitigation through scientific prediction. It has led to the integration of ideas from mathematics, statistics and engineering being used to lend credence to predictive assessments of risk but also to design actions (by engineers, scientists and investors) that are consistent with risk aversion. The objective of this Handbook is to facilitate the dissemination of the forefront of UQ ideas to their audiences. We recognize that these audiences are varied, with interests ranging from theory to application, and from research to development and even execution.

Uncertainty Quantification

Christian Soize
Uncertainty Quantification Book PDF

Author : Christian Soize
Publisher : Springer
Page : 329 pages
File Size : 51,8 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.

Uncertainty Quantification

Ralph C. Smith
Uncertainty Quantification Book PDF

Author : Ralph C. Smith
Publisher : SIAM
Page : 400 pages
File Size : 45,5 Mb
Release : 2013-12-02
Category : Computers
ISBN : 9781611973211

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Uncertainty Quantification by Ralph C. Smith Pdf

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.

Uncertainty in Engineering

Louis J. M. Aslett,Frank P. A. Coolen,Jasper De Bock
Uncertainty in Engineering Book PDF

Author : Louis J. M. Aslett,Frank P. A. Coolen,Jasper De Bock
Publisher : Springer Nature
Page : 148 pages
File Size : 49,6 Mb
Release : 2022
Category : Electronic
ISBN : 9783030836405

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Uncertainty in Engineering by Louis J. M. Aslett,Frank P. A. Coolen,Jasper De Bock Pdf

This open access book provides an introduction to uncertainty quantification in engineering. Starting with preliminaries on Bayesian statistics and Monte Carlo methods, followed by material on imprecise probabilities, it then focuses on reliability theory and simulation methods for complex systems. The final two chapters discuss various aspects of aerospace engineering, considering stochastic model updating from an imprecise Bayesian perspective, and uncertainty quantification for aerospace flight modelling. Written by experts in the subject, and based on lectures given at the Second Training School of the European Research and Training Network UTOPIAE (Uncertainty Treatment and Optimization in Aerospace Engineering), which took place at Durham University (United Kingdom) from 2 to 6 July 2018, the book offers an essential resource for students as well as scientists and practitioners.

Uncertainty Quantification for Hyperbolic and Kinetic Equations

Shi Jin,Lorenzo Pareschi
Uncertainty Quantification for Hyperbolic and Kinetic Equations Book PDF

Author : Shi Jin,Lorenzo Pareschi
Publisher : Springer
Page : 277 pages
File Size : 50,5 Mb
Release : 2018-03-20
Category : Mathematics
ISBN : 9783319671109

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Uncertainty Quantification for Hyperbolic and Kinetic Equations by Shi Jin,Lorenzo Pareschi Pdf

This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.

Uncertainty Quantification and Predictive Computational Science

Ryan G. McClarren
Uncertainty Quantification and Predictive Computational Science Book PDF

Author : Ryan G. McClarren
Publisher : Springer
Page : 345 pages
File Size : 42,5 Mb
Release : 2018-11-23
Category : Science
ISBN : 9783319995250

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Uncertainty Quantification and Predictive Computational Science by Ryan G. McClarren Pdf

This textbook teaches the essential background and skills for understanding and quantifying uncertainties in a computational simulation, and for predicting the behavior of a system under those uncertainties. It addresses a critical knowledge gap in the widespread adoption of simulation in high-consequence decision-making throughout the engineering and physical sciences. Constructing sophisticated techniques for prediction from basic building blocks, the book first reviews the fundamentals that underpin later topics of the book including probability, sampling, and Bayesian statistics. Part II focuses on applying Local Sensitivity Analysis to apportion uncertainty in the model outputs to sources of uncertainty in its inputs. Part III demonstrates techniques for quantifying the impact of parametric uncertainties on a problem, specifically how input uncertainties affect outputs. The final section covers techniques for applying uncertainty quantification to make predictions under uncertainty, including treatment of epistemic uncertainties. It presents the theory and practice of predicting the behavior of a system based on the aggregation of data from simulation, theory, and experiment. The text focuses on simulations based on the solution of systems of partial differential equations and includes in-depth coverage of Monte Carlo methods, basic design of computer experiments, as well as regularized statistical techniques. Code references, in python, appear throughout the text and online as executable code, enabling readers to perform the analysis under discussion. Worked examples from realistic, model problems help readers understand the mechanics of applying the methods. Each chapter ends with several assignable problems. Uncertainty Quantification and Predictive Computational Science fills the growing need for a classroom text for senior undergraduate and early-career graduate students in the engineering and physical sciences and supports independent study by researchers and professionals who must include uncertainty quantification and predictive science in the simulations they develop and/or perform.

Spectral Methods for Uncertainty Quantification

Olivier Le Maitre,Omar M Knio
Spectral Methods for Uncertainty Quantification Book PDF

Author : Olivier Le Maitre,Omar M Knio
Publisher : Springer Science & Business Media
Page : 542 pages
File Size : 42,5 Mb
Release : 2010-03-11
Category : Science
ISBN : 9789048135202

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Spectral Methods for Uncertainty Quantification by Olivier Le Maitre,Omar M Knio Pdf

This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.

An Introduction to Uncertainty in Measurement

L. Kirkup,R. B. Frenkel
An Introduction to Uncertainty in Measurement Book PDF

Author : L. Kirkup,R. B. Frenkel
Publisher : Cambridge University Press
Page : 196 pages
File Size : 40,5 Mb
Release : 2006-06-01
Category : Science
ISBN : 9781139454902

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An Introduction to Uncertainty in Measurement by L. Kirkup,R. B. Frenkel Pdf

Measurement shapes scientific theories, characterises improvements in manufacturing processes and promotes efficient commerce. In concert with measurement is uncertainty, and students in science and engineering need to identify and quantify uncertainties in the measurements they make. This book introduces measurement and uncertainty to second and third year students of science and engineering. Its approach relies on the internationally recognised and recommended guidelines for calculating and expressing uncertainty (known by the acronym GUM). The statistics underpinning the methods are considered and worked examples and exercises are spread throughout the text. Detailed case studies based on typical undergraduate experiments are included to reinforce the principles described in the book. This guide is also useful to professionals in industry who are expected to know the contemporary methods in this increasingly important area. Additional online resources are available to support the book at www.cambridge.org/9780521605793.

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 : 44,6 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.

Quantifying Uncertainty in Subsurface Systems

Céline Scheidt,Lewis Li,Jef Caers
Quantifying Uncertainty in Subsurface Systems Book PDF

Author : Céline Scheidt,Lewis Li,Jef Caers
Publisher : John Wiley & Sons
Page : 306 pages
File Size : 50,7 Mb
Release : 2018-06-19
Category : Science
ISBN : 9781119325833

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Quantifying Uncertainty in Subsurface Systems by Céline Scheidt,Lewis Li,Jef Caers Pdf

Under the Earth's surface is a rich array of geological resources, many with potential use to humankind. However, extracting and harnessing them comes with enormous uncertainties, high costs, and considerable risks. The valuation of subsurface resources involves assessing discordant factors to produce a decision model that is functional and sustainable. This volume provides real-world examples relating to oilfields, geothermal systems, contaminated sites, and aquifer recharge. Volume highlights include: A multi-disciplinary treatment of uncertainty quantification Case studies with actual data that will appeal to methodology developers A Bayesian evidential learning framework that reduces computation and modeling time Quantifying Uncertainty in Subsurface Systems is a multidisciplinary volume that brings together five major fields: information science, decision science, geosciences, data science and computer science. It will appeal to both students and practitioners, and be a valuable resource for geoscientists, engineers and applied mathematicians. Read the Editors' Vox: eos.org/editors-vox/quantifying-uncertainty-about-earths-resources

Uncertainty Quantification in Multiscale Materials Modeling

Yan Wang,David L. McDowell
Uncertainty Quantification in Multiscale Materials Modeling Book PDF

Author : Yan Wang,David L. McDowell
Publisher : Woodhead Publishing Limited
Page : 604 pages
File Size : 51,7 Mb
Release : 2020-03-12
Category : Materials science
ISBN : 9780081029411

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Uncertainty Quantification in Multiscale Materials Modeling by Yan Wang,David L. McDowell Pdf

Uncertainty Quantification in Multiscale Materials Modeling provides a complete overview of uncertainty quantification (UQ) in computational materials science. It provides practical tools and methods along with examples of their application to problems in materials modeling. UQ methods are applied to various multiscale models ranging from the nanoscale to macroscale. This book presents a thorough synthesis of the state-of-the-art in UQ methods for materials modeling, including Bayesian inference, surrogate modeling, random fields, interval analysis, and sensitivity analysis, providing insight into the unique characteristics of models framed at each scale, as well as common issues in modeling across scales.

An Introduction to Error Analysis

John Robert Taylor
An Introduction to Error Analysis Book PDF

Author : John Robert Taylor
Publisher : Univ Science Books
Page : 327 pages
File Size : 48,9 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 0935702423

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An Introduction to Error Analysis by John Robert Taylor Pdf

Problems after each chapter

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 : 42,5 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.