High performance computing methods for nonlinear Bayesian uncertainty quantification

Abstract

Bayesian uncertainty quantification (UQ) for nonlinear inverse problems requires the application of numerical integration (sampling) to estimate the posterior probability density since no closed-form expressions exist. Nonlinear problems are common in geophysics, in particular, in applications of studying the seabed with sound. The computational cost of applying UQ can be daunting and we present several approaches that improve efficiency for large inverse problems. Fundamentally, Bayesian sampling includes both fine-grained parallelism in the forward model (data prediction) as well as coarse grained parallelism in the sampling. Fine grained parallelism can be addressed efficiently by implementation on massively parallel accelerators, such as graphics processing units, and application to reflection coefficient computation is shown. The coarse grained parallelism of sampling is ideally addressed by traditional parallelization with message passing across a cluster of computers. We consider implementation of parallel sampling algorithms that scale efficiently to 103 computer cores. Finally, computational efficiency is closely tied to parametrization efficiency, which is addressed by self-adapting parametrizations of unknown complexity that lead to parsimonious representations of complex environments with few parameters. These three aspects of efficiency will be illustrated for several inverse and imaging problems in seabed acoustics and seismology. [Funded by the Natural Sciences and Engineering Research Council of Canada.]