Fundamentals of Uncertainty Quantification for Engineers

Dr. Yan Wang is a Professor of Mechanical Engineering at the Georgia Institute of Technology. He leads the Multiscale Systems Engineering Research Group at Georgia Tech. His research interests include probabilistic and non‐probabilistic approaches to quantify uncertainty in both physics‐based and data‐driven models for multiscale systems engineering for materials design. He has over 200 publications, including the first book on uncertainty quantification in multiscale materials modelling co‐edited with David McDowell. Dr. Anh V. Tran is a research staff member at the Department of Scientific Machine Learning, Sandia National Laboratories. His research areas include uncertainty quantification, optimization, machine learning for multiscale computational materials science. David L. McDowell Ph.D. is Regents’ Professor Emeritus at the Georgia Institute of Technology, having joined Georgia Tech as a faculty member in 1983. His research focuses on multiscale modelling of materials with emphasis on multiscale modeling of the inelastic behavior of metals, microstructure-sensitive computational fatigue analysis of microstructures, methods for materials design that are robust against uncertainty, and coarse-grained atomistic modelling methods.

• PART 1 Fundamentals of uncertainty quantification1. Uncertainty quantification for engineering decision making2. Probability and statistics in uncertainty quantification3. Sampling methods in uncertainty quantification 854. Surrogate modeling in uncertainty quantification5. Stochastic expansion methods in uncertainty quantification6. Bayesian inference in uncertainty quantification7. Sensitivity analysis in uncertainty quantification8. Linear and nonlinear dimensionality reduction techniques in uncertainty quantification9. Applications of uncertainty quantification in engineeringPART 2 Advanced topics of uncertainty quantification10. Stochastic processes in uncertainty quantification11. Markov models in uncertainty quantification12. Nonprobabilistic methods in uncertainty quantification