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.
Auteur
Ryan McClarren has been teaching uncertainty quantification and predictive computational science to students from various engineering and physical science departments at since 2009. He is currently Associate Professor of Aerospace and Mechanical Engineering at the University of Notre Dame. Prior to joining Notre Dame in 2017, he was Assistant Professor of Nuclear Engineering at Texas A&M University, an institution well-known in the nuclear engineering community for its computational research and education. He has authored numerous publications in refereed journals, is the author of a book that teaches python and numerical methods to undergraduates, Computational Nuclear Engineering and Radiological Science Using Python, and was the editor of a special issue of the journal Transport Theory and Statistical Physics. A well-known member of the computational nuclear engineering community, he has won research awards from NSF, DOE, and three national labs. While an undergraduate at the University of Michigan he won three awards for creative writing. Before joining the faculty of Texas A&M, Dr. McClarren was a research scientist at Los Alamos National Laboratory in the Computational Physics and Methods group.
Contenu
Part I Fundamentals1. Introduction1.1. What is Uncertainty Quantification1.2. Selecting Quantities of Interest (QoIs)1.3. Identifying Uncertainties1.4. Physics-based uncertainty quantification1.5. From simulation to prediction1.6. Notes and References1.7. Exercises 2. Probability and Statistics Preliminaries2.1. Random Variables2.2. Moments and Expectation Values 2.3. Sampling Random variables2.4. Notes and References2.5. Exercises 3. Input Parameter Distributions3.1. Principle Components Analysis3.2. Copulas3.3. Choosing input parameter distributions3.4. Implications of distribution selection3.5. Notes and References3.6. Exercises Part II Local Sensitivity Analysis4. Derivative Approximations4.1. First-order approximations4.2. Scaled Sensitivity Coefficients4.3. Sensitivity Indices4.4. Automatic Differentiation4.5. Notes and References4.6. Exercises 5. Regression Approximations5.1. Sensitivity analyses with many parameters5.2. Least-squares regression5.3. Regularized regression5.4. Notes and References5.5. Exercises 6. Adjoint-based Local Sensitivity Analysis6.1. Adjoint equations for linear, steady-state models6.2. Adjoints for nonlinear, time-dependent models6.3. Notes and References6.4. Exercises Part III Parametric Uncertainty Quantification7. From Sensitivity Analysis to UQ7.1. Applying distributions to SA results7.2. Limitations of SA for UQ7.3. Approximate QoI variance due to covariance of inputs7.4. Variable Selection 7.5. Notes and References7.6. Exercises 8. Sampling-Based UQ8.1. Basic Monte Carlo Method8.2. Pseudo-Monte Carlo 8.3. Quasi-Monte Carlo8.4. Notes and References8.5. Exercises9. Reliability Methods9.1. General Statement of Reliability Analysis9.2. First-Order Reliability Methods9.3. First-Order Second-Moment Reliability Methods9.4. Higher-Order approaches 9.5. Notes and References9.6. Exercises 10. Polynomial Chaos Methods10.1. The Polynomial Chaos Expansion10.2. Estimating Expansion Parameters using Quadrature10.3. Sparse Quadrature Rules10.4. Regression-based PCE10.5. Stochastic Finite Elements 10.6. Notes and References10.7. ExercisesPart IV Predictive Science11. Emulators and Surrogate Models11.1. Simple Surrogate Models11.2. Markov Chain Monte Carlo11.3. Gaussian Process Regression11.4. Bayesian MARS11.5. Notes and References11.6. Exercises 12. Reduced Order Models12.1. Proper Orthogonal Decomposition12.2. Active Subspace Methods 12.3. Notes and References12.4. Exercises 13. Predictive Models13.1. The Kennedy-O'Hagan Model13.2. Calibration and Data Assimilation13.3. Hierarchical Models13.4. Notes and References13.5. Exercises 14. Epistemic Uncertainties14.1. Horsetail Plots14.2. The Minkowski Metric14.3. Dempster-Shafer Theory14.4. Kolmogorov-Smirnoff Confidence Bounds14.5. The Method of Cauchy Deviates14.6. Notes and References14.7. Exercises AppendicesA. A cookbook of distributions