Solution of physics-based Bayesian inverse problems with deep generative priors

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