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

2026-01-30

AI Summary

This study addresses the inverse design problem of gas turbine combustors by systematically evaluating the effectiveness of generative models in Bayesian inverse problems. For the first time in an engineering inverse design context, we benchmark conditional generative adversarial networks (cGAN), invertible neural networks (INN), conditional flow matching (CFM), and traditional Markov chain Monte Carlo (MCMC) methods, introducing a comprehensive evaluation metric that balances accuracy and diversity. Experimental results demonstrate that CFM significantly outperforms all other approaches across all metrics: it not only produces designs whose performance metrics align more closely with target specifications but also exhibits greater solution diversity and enhanced robustness to variations in training data size.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Calibration & Uncertainty Quantification
• Natural Language Processing: Generation

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success

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.

Problem

• inverse problems
• generative models
• combustor design
• Bayesian inference
• conditional generation

Innovation

• Conditional Flow Matching
• Inverse Problems
• Generative Models
• Bayesian Inference
• Combustor Design