Applied Math Colloquium: Alen Alexanderian (NCSU)

Title: Optimal path planning for mobile sensors in inverse problems governed by PDEs

Abstract: In this talk I will discuss infinite-dimensional Bayesian linear inverse problems constrained by PDEs where data are collected via moving sensors. In this context, I describe our recent work on methods for finding sensor paths that optimize the posterior uncertainty in a prediction functional of the inversion parameters. The mathematical formulations are first established in an infinite-dimensional Hilbert space setting. Subsequently, we consider discretization of the problem and present a scalable computational framework for finding optimal sensor paths. We also present illustrative numerical results, within the context of a model inverse problems governed by an advection-diffusion equation.