Saved in:
Bibliographic Details
Main Authors: Yang, Xiaomei, Jia, Jiaying, Deng, Zhiliang
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2512.24046
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908989969661952
author Yang, Xiaomei
Jia, Jiaying
Deng, Zhiliang
author_facet Yang, Xiaomei
Jia, Jiaying
Deng, Zhiliang
contents 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
format Preprint
id arxiv_https___arxiv_org_abs_2512_24046
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Bayesian approach with persistent homology prior for Robin coefficient identification in a parabolic problem
Yang, Xiaomei
Jia, Jiaying
Deng, Zhiliang
Computation
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
title A Bayesian approach with persistent homology prior for Robin coefficient identification in a parabolic problem
topic Computation
url https://arxiv.org/abs/2512.24046