Paired Autoencoders for Likelihood-free Estimation in Inverse Problems

TL;DR

This paper introduces a paired autoencoder framework for likelihood-free estimation in nonlinear inverse problems, improving solution efficiency and assessment capabilities in complex PDE-based scenarios.

Contribution

The work presents a novel paired autoencoder architecture that enhances likelihood-free inverse problem solving, addressing generalization and accuracy limitations.

Findings

Efficient solution construction for inverse problems.

Ability to assess and improve solution quality.

Successful application to waveform inversion and electromagnetic imaging.

Abstract

We consider the solution of nonlinear inverse problems where the forward problem is a discretization of a partial differential equation. Such problems are notoriously difficult to solve in practice and require minimizing a combination of a data-fit term and a regularization term. The main computational bottleneck of typical algorithms is the direct estimation of the data misfit. Therefore, likelihood-free approaches have become appealing alternatives. Nonetheless, difficulties in generalization and limitations in accuracy have hindered their broader utility and applicability. In this work, we use a paired autoencoder framework as a likelihood-free estimator for inverse problems. We show that the use of such an architecture allows us to construct a solution efficiently and to overcome some known open problems when using likelihood-free estimators. In particular, our framework can assess the quality of the solution and improve on it if needed. We demonstrate the viability of our approach using examples from full waveform inversion and inverse electromagnetic imaging.