We adopt a Bayesian inference approach with persistent-homology-based prior to estimate a temporally dependent Robin coefficient arising in the analysis of convective heat transfer. And we also discuss the use of a hierarchical Bayesian method for automatic selection of the regularization parameter. Numerical results demonstrate that the PH prior shows consistent improvement compared to the Gaussian and the total variation prior.

翻译：本文采用基于持久同调的贝叶斯推断方法，用于估计对流换热分析中出现的时变Robin系数。同时，我们讨论了采用分层贝叶斯方法实现正则化参数的自动选择。数值结果表明，与高斯先验和全变分先验相比，持久同调先验展现出持续的性能改进。