Georgia Institute of Technology College of Sciences

Mathematical models of physical phenomena often include parameters that are hard or impossible to measure directly or are subject to variability, and are thus considered uncertain. Different aspects of modeling under uncertainty include forward uncertainty propagation, statistical inver- sion of uncertain parameters, optimal design of experiments, and optimization under uncertainty. I will focus on recent advances in numerical methods for infinite-dimensional Bayesian inverse problems and optimal experimental de- sign. I will also discuss the problem of risk-averse optimization under uncertainty with applications to control of PDEs with uncertain parameters. The driving applications are systems governed by PDEs with uncertain parameter fields, such as ow in the subsurface with an uncertain permeability field, or the diffusive transport of a contaminant with an uncertain initial condition. Such problems are computationally challenging due to expensive forward PDE solves and infinite-dimensional (high-dimensional when discretized) parameter spaces.