Solving Inverse Heat Transfer Problems Without Surrogate Models: A Fast, Data-Sparse, Physics Informed Neural Network Approach

Abstract

Physics informed neural networks have been recently gaining attention for effectively solving a wide variety of partial differential equations. Unlike the traditional machine learning techniques that require experimental or computational databases for training surrogate models, physics informed neural network avoids the excessive dependence on prior data by injecting the governing physical laws as regularizing constraints into the underlying neural network model. Although one can find several successful applications of physics informed neural network in the literature, a systematic study that compares the merits and demerits of this method with conventional machine learning methods is not well explored. In this study, we aim to investigate the effectiveness of this approach in solving inverse problems by comparing and contrasting its performance with conventional machine learning methods while solving four inverse test cases in heat transfer. We show that physics informed neural network is able to solve inverse heat transfer problems in a data-sparse manner by avoiding surrogate models altogether. This study is expected to contribute toward a more robust and effective solution for inverse heat transfer problems. We intend to sensitize researchers in inverse methods to this emerging approach and provide a preliminary analysis of its advantages and disadvantages.