Computational and Applied Mathematics seminar

Abstract: We investigate the Bayesian approach to certain elliptic boundary value problems of determining a Robin coefficient on a hidden part of the boundary from Cauchy data on the observable part. Such a nonlinear inverse problem arises naturally in the initialisation of large-scale ice sheet models. In this talk we will specifically focus on the computational routine to estimate posterior densities for the Robin coefficient.

The Bayesian approach is motivated for a prototypical Robin inverse problem by showing that the posterior mean converges in probability to the data-generating ground truth as the number of observations increases. Related to the stability theory for inverse Robin problems, a logarithmic convergence rate for Sobolev-regular Robin coefficients is established, whereas for analytic coefficients an algebraic rate can be attained. Our numerical results on synthetic data illustrate the convergence property in two observation settings. (Joint work with Aksel Kaastrup Rasmussen, Ieva Kazlauskaite and Mark Girolami).