Inverse problems are notoriously difficult to solve because they can have no
solutions, multiple solutions, or have solutions that vary significantly in
response to small perturbations in measurements. Bayesian inference, which
poses an inverse problem as a stochastic inference problem, addresses these
difficulties and provides quantitative estimates of the inferred field and the
associated uncertainty. However, it is difficult to employ when inferring
vectors of large dimensions, and/or when prior information is available through
previously acquired samples. In this paper, we describe how deep generative
adversarial networks can be used to represent the prior distribution in
Bayesian inference and overcome these challenges. We apply these ideas to
inverse problems that are diverse in terms of the governing physical
principles, sources of prior knowledge, type of measurement, and the extent of
available information about measurement noise. In each case we apply the
proposed approach to infer the most likely solution and quantitative estimates
of uncertainty.Comment: Paper: 18 pages, 5 figures. Supplementary: 9 pages, 6 Figures, 2
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