  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.
