Markov Chain Generative Adversarial Neural Networks for Solving Bayesian Inverse Problems in Physics Applications

TL;DR

This paper introduces MCGANs, a novel method combining GANs and Markov Chain Monte Carlo techniques to efficiently solve Bayesian inverse problems in physics, significantly reducing computational costs while maintaining accuracy.

Contribution

The paper presents a new MCGAN framework that efficiently samples from complex posterior distributions in Bayesian inverse problems, with proven convergence and superior performance.

Findings

Up to 100x faster sampling compared to existing methods.

Achieved two orders of magnitude higher accuracy in test cases.

Successfully applied to leak detection in pipelines.

Abstract

In the context of solving inverse problems for physics applications within a Bayesian framework, we present a new approach, Markov Chain Generative Adversarial Neural Networks (MCGANs), to alleviate the computational costs associated with solving the Bayesian inference problem. GANs pose a very suitable framework to aid in the solution of Bayesian inference problems, as they are designed to generate samples from complicated high-dimensional distributions. By training a GAN to sample from a low-dimensional latent space and then embedding it in a Markov Chain Monte Carlo method, we can highly efficiently sample from the posterior, by replacing both the high-dimensional prior and the expensive forward map. We prove that the proposed methodology converges to the true posterior in the Wasserstein-1 distance and that sampling from the latent space is equivalent to sampling in the high-dimensional space in a weak sense. The method is showcased on two test cases where we perform both state and parameter estimation simultaneously. The approach is shown to be up to two orders of magnitude more accurate than alternative approaches while also being up to two orders of magnitude computationally faster, in multiple test cases, including the important engineering setting of detecting leaks in pipelines.