Parameterizing uncertainty by deep invertible networks, an application to reservoir characterization

Uncertainty quantification for full-waveform inversion provides a probabilistic characterization of the ill-conditioning of the problem, comprising the sensitivity of the solution with respect to the starting model and data noise. This analysis allows to assess the confidence in the candidate solution and how it is reflected in the tasks that are typically performed after imaging (e.g., stratigraphic segmentation following reservoir characterization). Classically, uncertainty comes in the form of a probability distribution formulated from Bayesian principles, from which we seek to obtain samples. A popular solution involves Monte Carlo sampling. Here, we propose instead an approach characterized by training a deep network that "pushes forward" Gaussian random inputs into the model space (representing, for example, density or velocity) as if they were sampled from the actual posterior distribution. Such network is designed to solve a variational optimization problem based on the Kullback-Leibler divergence between the posterior and the network output distributions. This work is fundamentally rooted in recent developments for invertible networks. Special invertible architectures, besides being computational advantageous with respect to traditional networks, do also enable analytic computation of the output density function. Therefore, after training, these networks can be readily used as a new prior for a related inversion problem. This stands in stark contrast with Monte-Carlo methods, which only produce samples. We validate these ideas with an application to angle-versus-ray parameter analysis for reservoir characterization

Improving GAN Training with Probability Ratio Clipping and Sample Reweighting

Despite success on a wide range of problems related to vision, generative adversarial networks (GANs) often suffer from inferior performance due to unstable training, especially for text generation. To solve this issue, we propose a new variational GAN training framework which enjoys superior training stability. Our approach is inspired by a connection of GANs and reinforcement learning under a variational perspective. The connection leads to (1) probability ratio clipping that regularizes generator training to prevent excessively large updates, and (2) a sample re-weighting mechanism that improves discriminator training by downplaying bad-quality fake samples. Moreover, our variational GAN framework can provably overcome the training issue in many GANs that an optimal discriminator cannot provide any informative gradient to training generator. By plugging the training approach in diverse state-of-the-art GAN architectures, we obtain significantly improved performance over a range of tasks, including text generation, text style transfer, and image generation.Comment: NeurIPS 2020 camera ready version (citations updated