Georgia Institute of Technology College of Sciences

Uncertainty is ubiquitous: both data and physical models inherently contain uncertainty. Therefore, it is crucial to identify the sources of uncertainty and control its propagation over time. In this talk, I will introduce two approaches to address this uncertainty propagation problem—one for the inverse problem and one for the forward problem. The main idea is to work directly with probability measures, treating the underlying PDE as a pushforward map. In the inverse setting, we will explore various variational formulations, focusing on the characterization of minimizers and their stability. In the forward setting, we aim to propose a new approach to tackle high-dimensional uncertainties.