对比生成模型解决逆问题，流匹配表现最佳。
How well do generative models solve inverse problems? A benchmark study
- 用条件流匹配等生成模型求解燃气轮机设计逆问题。
- 流匹配在标签准确率和设计多样性上均领先。
- 适合关注生成模型逆向设计的工程师与研究者。
生成模型可根据低维条件生成高维数据，适用于（贝叶斯）逆问题求解。本文将基于前向回归模型与马尔可夫链蒙特卡洛采样的传统贝叶斯方法，与三种先进生成模型——条件生成对抗网络、可逆神经网络和条件流匹配进行对比，应用于六维设计参数映射至三维性能指标的燃气轮机燃烧室设计问题。提出多项评估指标，衡量生成设计方案的标签精度与多样性，并分析训练数据量对性能的影响。结果表明，条件流匹配在所有测试条件下均显著优于其他方法。
原文摘要 · Abstract (English)
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.
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