  In this work, we train conditional Wasserstein generative adversarial
networks to effectively sample from the posterior of physics-based Bayesian
inference problems. The generator is constructed using a U-Net architecture,
with the latent information injected using conditional instance normalization.
The former facilitates a multiscale inverse map, while the latter enables the
decoupling of the latent space dimension from the dimension of the measurement,
and introduces stochasticity at all scales of the U-Net. We solve PDE-based
inverse problems to demonstrate the performance of our approach in quantifying
the uncertainty in the inferred field. Further, we show the generator can learn
inverse maps which are local in nature, which in turn promotes generalizability
when testing with out-of-distribution samples.
