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We propose a novel modular inference approach combining two differentgenerative models -- generative adversarial networks (GAN) and normalizingflows -- to approximate the posterior distribution of physics-based Bayesianinverse problems framed in high-dimensional ambient spaces. We dub the proposedframework GAN-Flow. The proposed method leverages the intrinsic dimensionreduction and superior sample generation capabilities of GANs to define alow-dimensional data-driven prior distribution. Once a trained GAN-prior isavailable, the inverse problem is solved entirely in the latent space of theGAN using variational Bayesian inference with normalizing flow-basedvariational distribution, which approximates low-dimensional posteriordistribution by transforming realizations from the low-dimensional latent prior(Gaussian) to corresponding realizations of a low-dimensional variationalposterior distribution. The trained GAN generator then maps realizations fromthis approximate posterior distribution in the latent space back to thehigh-dimensional ambient space. We also propose a two-stage training strategyfor GAN-Flow wherein we train the two generative models sequentially.Thereafter, GAN-Flow can estimate the statistics of posterior-predictivequantities of interest at virtually no additional computational cost. Thesynergy between the two types of generative models allows us to overcome manychallenges associated with the application of Bayesian inference to large-scaleinverse problems, chief among which are describing an informative prior andsampling from the high-dimensional posterior. We demonstrate the efficacy andflexibility of GAN-Flow on various physics-based inverse problems of varyingambient dimensionality and prior knowledge using different types of GANs andnormalizing flows.

A dimension-reduced variational approach for solving physics-based  inverse problems using generative adversarial network priors and normalizing  flows