Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priors

TL;DR

This paper introduces a novel Bayesian inversion method that leverages deep generative models, specifically GANs, to efficiently solve large-scale inverse problems while preserving physics and providing reliable uncertainty estimates.

Contribution

The work presents a new approach combining GAN-based priors with Bayesian inference in the latent space to address high-dimensional inverse problems efficiently and accurately.

Findings

Effective in solving large-scale inverse problems

Provides reliable uncertainty quantification

Works with both synthetic and real data

Abstract

Inverse problems are ubiquitous in nature, arising in almost all areas of science and engineering ranging from geophysics and climate science to astrophysics and biomechanics. One of the central challenges in solving inverse problems is tackling their ill-posed nature. Bayesian inference provides a principled approach for overcoming this by formulating the inverse problem into a statistical framework. However, it is challenging to apply when inferring fields that have discrete representations of large dimensions (the so-called "curse of dimensionality") and/or when prior information is available only in the form of previously acquired solutions. In this work, we present a novel method for efficient and accurate Bayesian inversion using deep generative models. Specifically, we demonstrate how using the approximate distribution learned by a Generative Adversarial Network (GAN) as a prior in a Bayesian update and reformulating the resulting inference problem in the low-dimensional latent space of the GAN, enables the efficient solution of large-scale Bayesian inverse problems. Our statistical framework preserves the underlying physics and is demonstrated to yield accurate results with reliable uncertainty estimates, even in the absence of information about underlying noise model, which is a significant challenge with many existing methods. We demonstrate the effectiveness of proposed method on a variety of inverse problems which include both synthetic as well as experimentally observed data.