Good Things Come in Pairs: Paired Autoencoders for Inverse Problems

TL;DR

This paper introduces paired autoencoders for inverse problems, combining data-driven and model-based methods to improve reconstruction accuracy and uncertainty quantification in scientific computing tasks.

Contribution

It presents a novel paired autoencoder framework that projects data and quantities of interest into a latent space for improved inverse problem solving.

Findings

Effective in seismic imaging and inpainting tasks

Enables latent-space refinement for high-quality estimates

Supports uncertainty analysis through sampling variants

Abstract

In this book chapter, we discuss recent advances in data-driven approaches for inverse problems. In particular, we focus on the \emph{paired autoencoder} framework, which has proven to be a powerful tool for solving inverse problems in scientific computing. The paired autoencoder framework is a novel approach that leverages the strengths of both data-driven and model-based methods by projecting both the data and the quantity of interest into a latent space and mapping these latent spaces to provide surrogate forward and inverse mappings. We illustrate the advantages of this approach through numerical experiments, including seismic imaging and classical inpainting: nonlinear and linear inverse problems, respectively. Although the paired autoencoder framework is likelihood-free, it generates multiple data- and model-based reconstruction metrics that help assess whether examples are in or out of distribution. In addition to direct model estimates from data, the paired autoencoder enables latent-space refinement to fit the observed data accurately. Numerical experiments show that this procedure, combined with the latent-space initial guess, is essential for high-quality estimates, even when data noise exceeds the training regime. We also introduce two novel variants that combine variational and paired autoencoder ideas, maintaining the original benefits while enabling sampling for uncertainty analysis.