How well do generative models solve inverse problems? A benchmark study
This work provides a benchmark for evaluating generative models in inverse design, which is incremental but useful for engineers and researchers in computational design.
The study compared traditional Bayesian inverse methods with three generative models for solving inverse design problems in gas turbine combustors, finding that Conditional Flow Matching consistently outperformed others in accuracy and diversity metrics.
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.