CSE Community Seminar | April 25, 2025

Abstract

Operator learning involves data-driven models that accept continuum function data as inputs or outputs. Such models are robust to refinement of numerical discretizations and are thus well-suited for solving problems in computational science and engineering. This talk begins by reviewing the operator learning framework, and emphasizes the interplay between theory and algorithm development. Next, the talk showcases recent efforts to bring operator learning ideas to the field of inverse problems. The first effort considers end-to-end learning of inverse problem solution operators. Instability with respect to perturbations of the measurements is a fundamental barrier to successful estimation. The talk overcomes this barrier for the medical imaging problem of electrical impedance tomography. The second effort concerns Bayesian posterior distributions with approximate prior distributions. Prior approximations often arise for computational reasons, such as the need to discretize random field priors or empirically estimate priors from finite samples. The talk presents new convergence results and applications in this setting.