Abstract

We consider the task of characterizing and quantifying the effect of geometric uncertainties on the behavior of a system whose physics is described by partial differential equations (PDEs). We focus in particular on uncertainty in the shape of the physical domain or of an internal interface. We first address how such uncertainties can be modeled, and how to efficiently compute different realizations of the PDE solution. Then, we will address both the forward problem, that is the task of propagating the uncertainty from the geometry to the PDE solution, and the inverse problem in a Bayesian setting, that is using indirect measurement data to characterize the shape uncertainty. For both cases, we will discuss computational methods for efficient uncertainty quantification and their theoretical guarantees.