The reconstruction of time-dependent Robin coefficients is a challenging inverse heat transfer problem due to its inherent ill-posedness. This paper introduces a hierarchical Bayesian approach integrated with a persistent homology (PH) prior for robust coefficient estimation. By quantifying the birth and death of topological features, the PH-based prior provides a global structural constraint that transcends local derivative based penalties. Numerical experiments show that this topological perspective allows for the preservation of complex temporal profiles without the typical staircase distortions of total variation (TV) priors or the excessive blurring of Gaussian models. A key feature of our framework is the hierarchical implementation, which yields an automated, data-driven selection of hyperparameters. The results demonstrate that while PH-based inference yields competitive accuracy compared to TV regularization, it offers superior performance in preserving the multiscale characteristics of the Robin coefficient, providing a robust alternative for convective heat transfer diagnostics

翻译：时间相关Robin系数的重构是一个具有挑战性的逆热传导问题，其本质上的不适定性导致求解困难。本文引入一种结合持续同调先验的分层贝叶斯方法，用于实现鲁棒的系数估计。通过量化拓扑特征的生成与消亡，基于持续同调的先验提供了超越局部导数惩罚的全局结构约束。数值实验表明，这种拓扑视角能够保留复杂的时间轮廓，既避免了总变分先验中典型的阶梯状畸变，也消除了高斯模型中的过度模糊效应。本方法的关键特征在于分层实现，能够自动实现数据驱动的超参数选择。结果表明，尽管基于持续同调的推理与总变分正则化在精度上具有竞争力，但在保留Robin系数多尺度特征方面表现更为优越，为对流传热诊断提供了一种稳健的替代方案。