Graph Neural Networks (GNNs) based accelerated numerical simulation

Abstract

Finite element method (FEM) based high-fidelity simulation can be computationally demanding and time-consuming as engineering problems become more complicated. It is thus necessary to develop a surrogate model that only requires a small amount of computational time but retains sufficient accuracy. A graph neural network (GNN) based framework is proposed as a general surrogate model for FEM to simulate the Von Mises stress distribution. The mesh body is embedded to a graph and a novel global attribute representation is introduced to capture the geometry and boundary conditions while overcoming the common problem of over smoothing in graph deep learning. The challenge to deal with varying geometry and boundary conditions is overcome by the proposed model and thus it outperforms existing methods such as proper orthogonal decomposition (POD) and greedy algorithm in terms of generalization. Numerical experiments are given to demonstrate the capability of the model developed and the results show that the proposed model not only accurately predicts the stress distribution but also speed-ups hundreds of times faster compared to a FEM-based simulator, enabling real-time structural response analysis for the application of digital twin and structural health monitoring. It is indicated that GNNs can be a powerful tool for resolving complex physical problems, thereby assisting in advancing science and enhancing engineering productivity.