Fundamentals Of Uncertainty Quantification For Engineers
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Fundamentals of Uncertainty Quantification for Engineers
Fundamentals of Uncertainty Quantification for Engineers: Methods and Models provides a comprehensive introduction to uncertainty quantification (UQ) accompanied by a wide variety of applied examples and implementation details to reinforce the concepts outlined in the book. Sections start with an introduction to the history of probability theory and an overview of recent developments of UQ methods in the domains of applied mathematics and data science. Major concepts of copula, Monte Carlo sampling, Markov chain Monte Carlo, polynomial regression, Gaussian process regression, polynomial chaos expansion, stochastic collocation, Bayesian inference, modelform uncertainty, multi-fidelity modeling, model validation, local and global sensitivity analyses, linear and nonlinear dimensionality reduction are included. Advanced UQ methods are also introduced, including stochastic processes, stochastic differential equations, random fields, fractional stochastic differential equations, hidden Markov model, linear Gaussian state space model, as well as non-probabilistic methods such as robust Bayesian analysis, Dempster-Shafer theory, imprecise probability, and interval probability. The book also includes example applications in multiscale modeling, reliability, fatigue, materials design, machine learning, and decision making. • Introduces all major topics of uncertainty quantification with engineering examples and implementation details• Features examples from a wide variety of science and engineering disciplines (e.g., fluids, structural dynamics, materials, manufacturing, multiscale simulation)• Discusses sampling methods, surrogate modeling, stochastic expansion, sensitivity analysis, dimensionality reduction and more
Uncertainty Quantification and Predictive Computational Science
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.
Uncertainty Quantification
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.