Uncertainty Quantification and Predictive Computational Science [electronic resource] : A Foundation for Physical Scientists and Engineers / by Ryan G. McClarren
- Part I Fundamentals -- Introduction -- Probability and Statistics Preliminaries -- Input Parameter Distributions -- Part II Local Sensitivity Analysis -- Derivative Approximations -- Regression Approximations -- Adjoint-based Local Sensitivity Analysis -- Part III Parametric Uncertainty Quantification -- From Sensitivity Analysis to UQ -- Sampling-Based UQ -- Reliability Methods -- Polynomial Chaos Methods -- Part IV Predictive Science -- Emulators and Surrogate Models -- Reduced Order Models -- Predictive Models -- Epistemic Uncertainties -- Appendices -- A. A cookbook of distributions.
- 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 R and 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 first year 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. Organizes interdisciplinary topics of uncertainty quantification into a single teaching text Reviews the fundamentals of probability and statistics Guides the transition from merely performing calculations to making confident predictions Builds readers' confidence in the validity of their simulations Illustrates concepts with real-world examples and models from the physical sciences and engineering Includes R and python code, enabling readers to perform the analysis.
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