Handbook of Uncertainty Quantification
Handbook of Uncertainty Quantification

Author: Roger Ghanem

Publisher: Springer

Published: 2016-05-08

Total Pages: 0

ISBN-13: 9783319123844

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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 and Predictive Computational Science
Uncertainty Quantification and Predictive Computational Science

Author: Ryan G. McClarren

Publisher: Springer

Published: 2018-11-23

Total Pages: 349

ISBN-13: 3319995251

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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.

Princeton Companion to Applied Mathematics
Princeton Companion to Applied Mathematics

Author: Nicholas J. Higham

Publisher: Princeton University Press

Published: 2015-09-09

Total Pages: 1014

ISBN-13: 0691150397

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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
Uncertainty Quantification

Author: Ralph C. Smith

Publisher: SIAM

Published: 2013-12-02

Total Pages: 400

ISBN-13: 161197321X

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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.

Model Validation and Uncertainty Quantification, Volume 3
Model Validation and Uncertainty Quantification, Volume 3

Author: Roland Platz

Publisher: Springer Nature

Published: 2023-10-06

Total Pages: 208

ISBN-13: 3031370031

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Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 41st IMAC, A Conference and Exposition on Structural Dynamics, 2023, the third volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on: Introduction of Uncertainty Quantification Uncertainty Quantification in Dynamics Model Form Uncertainty and Selection incl. Round Robin Challenge Sensor and Information Fusion Virtual Sensing, Certification, and Real-Time Monitoring Surrogate Modeling

Model Validation and Uncertainty Quantification, Volume 3
Model Validation and Uncertainty Quantification, Volume 3

Author: Sez Atamturktur

Publisher: Springer

Published: 2016-06-27

Total Pages: 366

ISBN-13: 3319297546

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Model Validation and Uncertainty Quantifi cation, Volume 3. Proceedings of the 34th IMAC, A Conference and Exposition on Dynamics of Multiphysical Systems: From Active Materials to Vibroacoustics, 2016, the third volume of ten from the Conference brings together contributions to this important area of research and engineering. Th e collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: • Uncertainty Quantifi cation & Model Validation • Uncertainty Propagation in Structural Dynamics • Bayesian & Markov Chain Monte Carlo Methods • Practical Applications of MVUQ • Advances in MVUQ & Model Updating • Robustness in Design & Validation • Verifi cation & Validation Methods

Model Validation and Uncertainty Quantification, Volume 3
Model Validation and Uncertainty Quantification, Volume 3

Author: Zhu Mao

Publisher: Springer Nature

Published: 2020-10-27

Total Pages: 426

ISBN-13: 3030476383

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Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 38th IMAC, A Conference and Exposition on Structural Dynamics, 2020, the third volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on: Uncertainty Quantification in Material Models Uncertainty Propagation in Structural Dynamics Practical Applications of MVUQ Advances in Model Validation & Uncertainty Quantification: Model Updating Model Validation & Uncertainty Quantification: Industrial Applications Controlling Uncertainty Uncertainty in Early Stage Design Modeling of Musical Instruments Overview of Model Validation and Uncertainty

Uncertainty Quantification and Stochastic Modeling with Matlab
Uncertainty Quantification and Stochastic Modeling with Matlab

Author: Eduardo Souza de Cursi

Publisher: Elsevier

Published: 2015-04-09

Total Pages: 457

ISBN-13: 0081004710

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Uncertainty Quantification (UQ) is a relatively new research area which describes the methods and approaches used to supply quantitative descriptions of the effects of uncertainty, variability and errors in simulation problems and models. It is rapidly becoming a field of increasing importance, with many real-world applications within statistics, mathematics, probability and engineering, but also within the natural sciences. Literature on the topic has up until now been largely based on polynomial chaos, which raises difficulties when considering different types of approximation and does not lead to a unified presentation of the methods. Moreover, this description does not consider either deterministic problems or infinite dimensional ones. This book gives a unified, practical and comprehensive presentation of the main techniques used for the characterization of the effect of uncertainty on numerical models and on their exploitation in numerical problems. In particular, applications to linear and nonlinear systems of equations, differential equations, optimization and reliability are presented. Applications of stochastic methods to deal with deterministic numerical problems are also discussed. Matlab® illustrates the implementation of these methods and makes the book suitable as a textbook and for self-study. - Discusses the main ideas of Stochastic Modeling and Uncertainty Quantification using Functional Analysis - Details listings of Matlab® programs implementing the main methods which complete the methodological presentation by a practical implementation - Construct your own implementations from provided worked examples

Uncertainty Quantification in Multiscale Materials Modeling
Uncertainty Quantification in Multiscale Materials Modeling

Author: Yan Wang

Publisher: Woodhead Publishing

Published: 2020-03-12

Total Pages: 604

ISBN-13: 0081029411

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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.

Model Validation and Uncertainty Quantification, Volume 3
Model Validation and Uncertainty Quantification, Volume 3

Author: Robert Barthorpe

Publisher: Springer

Published: 2017-06-07

Total Pages: 368

ISBN-13: 3319548581

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Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 35th IMAC, A Conference and Exposition on Structural Dynamics, 2017, the third volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on: Uncertainty Quantification in Material Models Uncertainty Propagation in Structural Dynamics Practical Applications of MVUQ Advances in Model Validation & Uncertainty Quantification: Model Updating Model Validation & Uncertainty Quantification: Industrial Applications Controlling Uncertainty Uncertainty in Early Stage Design Modeling of Musical Instruments Overview of Model Validation and Uncertainty