High Performance Uncertainty Quantification with Parallelized Multilevel Markov Chain Monte Carlo

TL;DR

This paper introduces a parallelized multilevel Markov Chain Monte Carlo framework and software for scalable uncertainty quantification in high-performance computing environments, demonstrated on large-scale models including tsunami source identification.

Contribution

It presents a novel parallelization strategy and software implementation for MLMCMC, enabling large-scale UQ in complex models with strong data dependencies.

Findings

Achieved scalable parallel MLMCMC performance

Successfully applied to tsunami source identification

Demonstrated integration with DUNE and ExaHyPE engines

Abstract

Numerical models of complex real-world phenomena often necessitate High Performance Computing (HPC). Uncertainties increase problem dimensionality further and pose even greater challenges. We present a parallelization strategy for multilevel Markov chain Monte Carlo, a state-of-the-art, algorithmically scalable Uncertainty Quantification (UQ) algorithm for Bayesian inverse problems, and a new software framework allowing for large-scale parallelism across forward model evaluations and the UQ algorithms themselves. The main scalability challenge presents itself in the form of strong data dependencies introduced by the MLMCMC method, prohibiting trivial parallelization. Our software is released as part of the modular and open-source MIT UQ Library (MUQ), and can easily be coupled with arbitrary user codes. We demonstrate it using the DUNE and the ExaHyPE Engine. The latter provides a realistic, large-scale tsunami model in which identify the source of a tsunami from buoy-elevation data.