The efficacy and generalizability of conditional GANs for posterior inference in physics-based inverse problems
This work addresses uncertainty quantification in physics-based inverse problems, which is incremental as it applies existing GAN methods to a specific domain.
The authors tackled the problem of sampling from posterior distributions in physics-based Bayesian inverse problems by training conditional Wasserstein GANs, achieving effective uncertainty quantification in PDE-based scenarios and demonstrating generalizability with out-of-distribution samples.
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.