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.

翻译：生成学习基于低维条件（亦称提示）生成高维数据，因此生成学习算法适用于解决（贝叶斯）逆问题。本文比较了基于前向回归模型、采用马尔可夫链蒙特卡罗方法进行先验采样的传统贝叶斯逆问题求解方法，与三种前沿生成学习模型——条件生成对抗网络、可逆神经网络和条件流匹配——的性能。我们将这些方法应用于燃气轮机燃烧室设计问题，将六个独立设计参数映射至三个性能指标。针对此类逆设计方法，我们提出了多项评估指标，测量生成设计的指标准确性及多样性，并研究了训练数据集规模对性能的影响。本基准测试存在明确优胜者：条件流匹配方法在所有对比方法中均表现出持续优势。