Graph neural network structural limitation for thermal simulation and architecture optimization through rating system

Abstract

Graph neural networks are well suited for physics based simulation. Among other features, graphs can accurately represent thermal effects, with energy conservation operating on the nodes (vertices) and heat flow coursing through edges. Moreover, graph neural networks incorporate the data topology and allow simulation on a wide variety of geometries. In this paper, various graph neural networks are trained using analytical solutions to the transient heat equation. Several architectures and hyper-parameters are compared to empirically identify good practices when using a graph neural network for numerical simulation. In addition, a novel method to optimize the network architecture is proposed. It is based on rating systems used to evaluate players’ skill level in competitive games. The results show that graph neural network-based simulation shares mutual restrictions with classical discretizations techniques (such as the Von Neumann stability criterion) and also that graph neural networks can be a potent generalization tool for heat transfer problems.