The Bayesian Framework for Inverse Problems in Heat Transfer

Abstract

The aim of this paper is to provide researchers dealing with inverse heat transfer problems a review of the Bayesian approach to inverse problems, the related modeling issues, and the methods that are used to carry out inference. In Bayesian inversion, the aim is not only to obtain a single point estimate for the unknown, but rather to characterize uncertainties in estimates, or predictions. Before any measurements are available, we have some uncertainty in the unknown. After carrying out measurements, the uncertainty has been reduced, and the task is to quantify this uncertainty, and in addition to give plausible suggestions for answers to questions of interest. The focus of this review is on the modeling-related topics in inverse problems in general, and the methods that are used to compute answers to questions. In particular, we build a scene of how to handle and model the unavoidable uncertainties that arise with real physical measurements. In addition to giving a brief review of existing Bayesian treatments of inverse heat transfer problems, we also describe approaches that might be successful with inverse heat transfer problems.