Deep Multiphysics Fields Solver Established on Operator Learning Transformer and Finite Element Method

Abstract

The accurate acquisition of unknown multiphysics fields in specified regions is vital for industrial production. Traditional computational approaches often require dense mesh generation to achieve precise numerical results, leading to substantial computational resource consumption and extended processing times. However, recent advancements in deep learning (DL) have introduced alternative solutions to computational physics problems. This paper presents a novel multiphysics field solver that integrates operator learning with classical finite element methods (FEM). The overall structure of the framework is a Transformer based on the attention mechanism, with a loss function incorporating physical constraints. The network takes the result of a coarse grid finite element calculation as input, while the output target is the value of a dense grid computation. Compared to traditional DL frameworks, the proposed architecture consistently maintains low error rates across a range of input resolutions. Additionally, the high efficiency of graphics processing units (GPUs) enables fully trained networks to generate solutions in quasi-real time, demonstrating significant potential for practical applications.