A Bayesian approach with persistent homology prior for Robin coefficient identification in a parabolic problem

TL;DR

This paper presents a hierarchical Bayesian method with a persistent homology prior for robustly reconstructing time-dependent Robin coefficients in inverse heat transfer problems, capturing complex temporal features effectively.

Contribution

It introduces a novel topological prior based on persistent homology within a hierarchical Bayesian framework for inverse heat transfer coefficient estimation.

Findings

PH prior preserves complex temporal profiles better than TV and Gaussian priors.

Hierarchical implementation enables automatic hyperparameter selection.

Method achieves accuracy comparable to TV regularization with improved multiscale feature preservation.

Abstract

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