Convolutional neural networks for heat conduction

Abstract

This paper presents a data-driven approach to solve heat conduction problems, in particular 2D heat conduction problems. The physical laws which govern such problems are modeled by partial differential equations. We examine temperature distributions of conductors that have square geometry subjected to various boundary conditions, both Dirichlet and Neumann. The data consists of images of these distributions in a semi-continuous form. Conventionally, such problems may be solved analytically or using numerical methods which can be computationally expensive. We attempt to use Image-Based Deep Learning algorithms such as encoder-decoders and variational auto-encoders which do not involve the physical laws of the problem. We also study the efficacy of deterministic models against probabilistic models and the feasibility of using image-based deep-learning methods for engineering applications.