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 underuncertainty, 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.

• parametric uncertainty quantification
• sensitivity analysis
• Reliability Methods
• Monte Carlo Methods
• Polynomial Chaos Methods
• Emulators and Surrogate Models
• Reduced Order Models
• Epistemic Uncertainties
• Regressive Approximations
• Derivative Approximations

• Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, USA

  Ryan G. McClarren

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.

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