CHARLEMAGNE DISTINGUISHED LECTURE SERIES - Ghattas Seminar

Prof. Omar Ghattas, Ph.D. - Large-Scale Bayesian Inversion with Applications to the Flow of the Antarctic Ice Sheet

The University of Texas at Austin, USA

Institute for Computational Engineering Sciences (ICES)

Abstract

Many physical systems are characterized by complex nonlinear behavior coupling multiple physical processes over a wide rang of length and time scales. Mathematical and computational models of these systems often contain numerous uncertain parameters, making high-reliability predictive modeling a challenge. Rapidly expanding volumes of observational data--along with tremendous increases in HPC capability--present opportunities to reduce these uncertainties via solution of large-scale inverse probles. Bayesian inference provides a systematic framework for inferring model parameters with associated uncertainties from (possibly noisy) data and any prior information. However, solution of Bayesian inverse problems via conventional Markov chain Monte Carlo (MCMC) methods remains prohibitive for expensive models and high-dimensional parameterizations, as result from discretization of infinite dimensional problems with uncertain fields. Despite the large size of observational datasets, typically they inform only low dimensional manifolds in parameter space, due to ill-posedness of the inverse problem. Based on this property we design scalable Bayesian inversion algorithms that adapt to the structure and geometry of the posterior probability, thereby exploiting an effectively-reduced parameter dimension and making Bayesian inference tractable for some large-scale, high-dimensional inverse problems. We discuss an inverse problem for the flow of the Antarctic ice sheet, which has been solved for as many as one million uncertain parameters at a cost (measured in forward ice sheet flow solves) that is independent of both the parameter and data dimensions. This work is joint with Tobin Isaac, Noemi Petra, and Georg Stadler.