Uncertainty Quantification and Predictive Computational Science: A Foundation for Physical Scientists and Engineers

Description

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. Front Matter ....Pages i-xvii Front Matter ....Pages 1-1 Introduction to Uncertainty Quantification and Predictive Science (Ryan G. McClarren)....Pages 3-17 Probability and Statistics Preliminaries (Ryan G. McClarren)....Pages 19-51 Input Parameter Distributions (Ryan G. McClarren)....Pages 53-91 Front Matter ....Pages 93-93 Local Sensitivity Analysis Based on Derivative Approximations (Ryan G. McClarren)....Pages 95-109 Regression Approximations to Estimate Sensitivities (Ryan G. McClarren)....Pages 111-128 Adjoint-Based Local Sensitivity Analysis (Ryan G. McClarren)....Pages 129-143 Front Matter ....Pages 145-145 Sampling-Based Uncertainty Quantification: Monte Carlo and Beyond (Ryan G. McClarren)....Pages 147-173 Reliability Methods for Estimating the Probability of Failure (Ryan G. McClarren)....Pages 175-187 Stochastic Projection and Collocation (Ryan G. McClarren)....Pages 189-254 Front Matter ....Pages 255-255 Gaussian Process Emulators and Surrogate Models (Ryan G. McClarren)....Pages 257-274 Predictive Models Informed by Simulation, Measurement, and Surrogates (Ryan G. McClarren)....Pages 275-304 Epistemic Uncertainties: Dealing with a Lack of Knowledge (Ryan G. McClarren)....Pages 305-322 Back Matter ....Pages 323-345