How well do generative models solve inverse problems? A benchmark study

TL;DR

This paper benchmarks various generative models against traditional Bayesian methods for inverse problems, specifically in gas turbine design, highlighting the superior performance of Conditional Flow Matching.

Contribution

It provides a comprehensive comparison of generative models and Bayesian approaches for inverse problems, introducing evaluation metrics and analyzing dataset size effects.

Findings

Conditional Flow Matching outperforms other models in accuracy and diversity.

Generative models can effectively solve inverse problems in engineering.

Performance improves with larger training datasets.

Abstract

Generative learning generates high dimensional data based on low dimensional conditions, also called prompts. Therefore, generative learning algorithms are eligible for solving (Bayesian) inverse problems. In this article we compare a traditional Bayesian inverse approach based on a forward regression model and a prior sampled with the Markov Chain Monte Carlo method with three state of the art generative learning models, namely conditional Generative Adversarial Networks, Invertible Neural Networks and Conditional Flow Matching. We apply them to a problem of gas turbine combustor design where we map six independent design parameters to three performance labels. We propose several metrics for the evaluation of this inverse design approaches and measure the accuracy of the labels of the generated designs along with the diversity. We also study the performance as a function of the training dataset size. Our benchmark has a clear winner, as Conditional Flow Matching consistently outperforms all competing approaches.