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Uncertainty Quantification and Predictive Computational Science

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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.


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.


Part I Fundamentals
1. Introduction
1.1. What is Uncertainty Quantification
1.2. Selecting Quantities of Interest (QoIs)
1.3. Identifying Uncertainties
1.4. Physics-based uncertainty quantification
1.5. From simulation to prediction
1.6. Notes and References
1.7. Exercises
2. Probability and Statistics Preliminaries
2.1. Random Variables
2.2. Moments and Expectation Values
2.3. Sampling Random variables
2.4. Notes and References
2.5. Exercises
3. Input Parameter Distributions
3.1. Principle Components Analysis
3.2. Copulas
3.3. Choosing input parameter distributions
3.4. Implications of distribution selection
3.5. Notes and References
3.6. Exercises
Part II Local Sensitivity Analysis
4. Derivative Approximations
4.1. First-order approximations
4.2. Scaled Sensitivity Coefficients
4.3. Sensitivity Indices
4.4. Automatic Differentiation
4.5. Notes and References
4.6. Exercises
5. Regression Approximations
5.1. Sensitivity analyses with many parameters
5.2. Least-squares regression
5.3. Regularized regression
5.4. Notes and References
5.5. Exercises
6. Adjoint-based Local Sensitivity Analysis
6.1. Adjoint equations for linear, steady-state models
6.2. Adjoints for nonlinear, time-dependent models
6.3. Notes and References
6.4. Exercises
Part III Parametric Uncertainty Quantification
7. From Sensitivity Analysis to UQ
7.1. Applying distributions to SA results
7.2. Limitations of SA for UQ
7.3. Approximate QoI variance due to covariance of inputs
7.4. Variable Selection
7.5. Notes and References
7.6. Exercises
8. Sampling-Based UQ
8.1. Basic Monte Carlo Method
8.2. Pseudo-Monte Carlo
8.3. Quasi-Monte Carlo
8.4. Notes and References
8.5. Exercises
9. Reliability Methods
9.1. General Statement of Reliability Analysis
9.2. First-Order Reliability Methods
9.3. First-Order Second-Moment Reliability Methods
9.4. Higher-Order approaches
9.5. Notes and References
9.6. Exercises
10. Polynomial Chaos Methods
10.1. The Polynomial Chaos Expansion
10.2. Estimating Expansion Parameters using Quadrature
10.3. Sparse Quadrature Rules
10.4. Regression-based PCE
10.5. Stochastic Finite Elements
10.6. Notes and References
10.7. ExercisesPart IV Predictive Science
11. Emulators and Surrogate Models
11.1. Simple Surrogate Models
11.2. Markov Chain Monte Carlo
11.3. Gaussian Process Regression
11.4. Bayesian MARS
11.5. Notes and References
11.6. Exercises
12. Reduced Order Models
12.1. Proper Orthogonal Decomposition
12.2. Active Subspace Methods
12.3. Notes and References
12.4. Exercises
13. Predictive Models
13.1. The Kennedy-O'Hagan Model
13.2. Calibration and Data Assimilation
13.3. Hierarchical Models
13.4. Notes and References
13.5. Exercises
14. Epistemic Uncertainties
14.1. Horsetail Plots
14.2. The Minkowski Metric
14.3. Dempster-Shafer Theory
14.4. Kolmogorov-Smirnoff Confidence Bounds
14.5. The Method of Cauchy Deviates
14.6. Notes and References
14.7. Exercises
A. A cookbook of distributions

Informations sur le produit

Titre: Uncertainty Quantification and Predictive Computational Science
Sous-titre: A Foundation for Physical Scientists and Engineers
Code EAN: 9783319995250
Protection contre la copie numérique: filigrane numérique
Format: eBook (pdf)
Producteur: Springer-Verlag GmbH
Genre: Physique, astronomie
nombre de pages: 345
Parution: 23.11.2018
Taille de fichier: 20.8 MB