Uncertainty and Bayesian inference in inverse problems

Dr. Youssef Marzouk
Sandia National Laboratories, Livermore, CA

Abstract
Bayesian statistics provides a foundation for inference from noisy data and stochastic forward models, a natural mechanism for regularization in the form of prior information, and a quantitative assessment of uncertainty in the inferred results. Inverse problems—representing indirect estimation of model parameters, inputs, or structural components—can be fruitfully cast in this framework. Complex and computationally intensive forward models arising in physical applications, however, can render a Bayesian approach prohibitive. This difficulty is compounded by high-dimensional model spaces, as when the unknown is a spatiotemporal field.

We present new algorithmic developments for Bayesian inference in this context, showing strong connections with the forward propagation of uncertainty. In particular, we introduce a stochastic spectral formulation that dramatically accelerates the Bayesian solution of inverse problems via rapid evaluation of a surrogate posterior. We also pursue dimensionality reduction for the inference of spatiotemporal fields, using truncated spectral representations of Gaussian process priors. These new approaches are demonstrated on scalar transport problems arising in contaminant source inversion and in the inference of inhomogeneous material or transport properties. We also discuss extensions toward the inference of chemical models and reaction networks.

Monday, March 26th
2000 Vagelos Laboratories
11:00 – 12:00 noon