General descriptionThe behavior of many physical systems can be mathematically modeled by deterministic ordinary or partial differential equations (ODEs or PDEs). These models however differ from reality for two main reasons: (1) an intrinsic variability of the physical system (aleatoric uncertainty); and/or (2) our inability to accurately characterize all parameters of the mathematical model (epistemic uncertainty). Uncertainty is therefore a fundamental feature of physical systems and needs to be taken into account when building a mathematical model. Examples appear in the description of flows in porous media, behavior of living tissues, combustion problems, deformation of composite materials, earthquake motions, etc. In order to understand the uncertainties inherent in the model, and often represented in a probabilistic setting, we need a process called uncertainty quantification (UQ).
In this course we consider different types of ODEs/PDEs with stochastic input parameters (coefficients, forcing terms, initial/boundary conditions, etc.) and study various numerical techniques for solving both forward and inverse stochastic problems.
Office hours1) TBA SMLC 216 (Motamed)     2) TBA SMLC 314 (Huerta)
Assignment 1 (Probability and Karhunen-Loeve)
Assignment 2 (Monte Carlo Sampling)
Assignment 3 (Polynomial Approximation)
Assignment 4 (Bayesian Inference)
Assignment 5 (MCMC)
Assignment 6 (Advanced methods)