Solving Bayesian Inverse Problems via Variational Autoencoders

TL;DR

This paper introduces UQ-VAE, a novel framework that adapts variational autoencoders for efficient uncertainty quantification in scientific inverse problems, leveraging divergence-based inference and adaptive optimization.

Contribution

It presents a flexible, hybrid data/model-informed VAE framework with adjustable hyperparameters for posterior modeling in inverse problems.

Findings

Effective posterior modeling in inverse problems

Flexible hyperparameter for distance measure

Adaptive learning of posterior uncertainty

Abstract

In recent years, the field of machine learning has made phenomenal progress in the pursuit of simulating real-world data generation processes. One notable example of such success is the variational autoencoder (VAE). In this work, with a small shift in perspective, we leverage and adapt VAEs for a different purpose: uncertainty quantification in scientific inverse problems. We introduce UQ-VAE: a flexible, adaptive, hybrid data/model-informed framework for training neural networks capable of rapid modelling of the posterior distribution representing the unknown parameter of interest. Specifically, from divergence-based variational inference, our framework is derived such that most of the information usually present in scientific inverse problems is fully utilized in the training procedure. Additionally, this framework includes an adjustable hyperparameter that allows selection of the notion of distance between the posterior model and the target distribution. This introduces more flexibility in controlling how optimization directs the learning of the posterior model. Further, this framework possesses an inherent adaptive optimization property that emerges through the learning of the posterior uncertainty.