The efficacy and generalizability of conditional GANs for posterior inference in physics-based inverse problems

Abstract

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.

Conditional Generative Learning for Medical Image Imputation

“…where W 1 is Wasserstein-1 metric [33]. The Lipschitz constraint on the critic can be weakly imposed using a gradient penalty term while training D [4,26] (also see Supplementary Note 3).…”

“…It is typical to use residual blocks to introduce non-linearity in the U-Net, which is what was also done in [26]. However, in the present work, we make use of dense blocks since they lead to superior performance compared to residual blocks while reducing the number of trainable parameters [13].…”

“…The architecture of the generator and critic is based on those considered in [26]. The generator G has a U-Net architecture, as shown in Figure 2(a), taking as input the measured sequence y (after linear reconstruction of the missing phase) and the latent variable z.…”

“…The generator G has a U-Net architecture, as shown in Figure 2(a), taking as input the measured sequence y (after linear reconstruction of the missing phase) and the latent variable z. The latent information is injected at every scale of the contracting and expanding branches of the U-Net using conditional instance normalization (CIN) [8], which has two advantages: i) the latent dimension N Z can be chosen independently of N X or N Y , thus allowing for significant dimension reduction, and ii) stochasticity is introduced at all scales of the U-Net, which overcomes the issue of mode collapse [26].…”

“…In the probabilistic framework, we treat both the incomplete and complete image sequences as random vectors. Then, using data which consists complete sequences and their incomplete counterparts (generated by decimating an image at random), we train a conditional generative adversarial (cGAN) network [4,22,26]. This network takes samples from the joint distribution of two random vectors and learns to efficiently sample from the conditional distribution.…”