Coupled multiphysics solver for irregular regions based on graph neural network

Abstract

Multiphysics analysis, involving the coupled phenomena of various physics fields, such as electro-mechanical, thermofluidic, thermoelectric, and thermo-hygric phenomena, plays a critical role in advancing technology and engineering disciplines. Conventional numerical algorithms are generally time-consuming and resource-demanding. Thanks to the rapid development in deep learning (DL), data-driven, physics-informed, and operator learning methods have been proposed to accelerate the calculation process. However, existing DL methods, encompassing convolutional neural network (CNN) and graph neural network (GNN) based approaches, exhibit limitations in effectively handling irregular regions and addressing the challenges posed by multiphysics tasks. To tackle these problems, we propose a DL framework based on GNN with a coupled solver. In the solving process of the proposed framework, a graph is generated according to the given region, and then a graph coupled-field solving network (GCFSN) is adopted. We have conducted three experiments using GCFSN to solve the coupled-field and the mean relative error is about 5%. The experimental results have verified the superior performance and generalization ability of the GCFSN method in solving the thermal-coupled physics problems on an irregular region.

Keywords

• Coupled multiphysics field
• Finite element method
• Partial differential equation
• Irregular region
• Deep learning
• Graph neural network