Learning-Based Finite Element Methods Modeling for Complex Mechanical Systems

TL;DR

This paper introduces a two-level mesh graph network that enhances the simulation of complex mechanical systems by effectively capturing long-range spatial dependencies, outperforming existing CNN and GNN models in accuracy and efficiency.

Contribution

A novel two-level mesh graph network combining Graph and Attention Blocks to improve long-range dependency modeling in mechanical system simulations.

Findings

54.3% lower prediction errors on Beam dataset

9.87% fewer learnable parameters

Superior performance on synthetic and real datasets

Abstract

Complex mechanic systems simulation is important in many real-world applications. The de-facto numeric solver using Finite Element Method (FEM) suffers from computationally intensive overhead. Though with many progress on the reduction of computational time and acceptable accuracy, the recent CNN or GNN-based simulation models still struggle to effectively represent complex mechanic simulation caused by the long-range spatial dependency of distance mesh nodes and independently learning local and global representation. In this paper, we propose a novel two-level mesh graph network. The key of the network is to interweave the developed Graph Block and Attention Block to better learn mechanic interactions even for long-rang spatial dependency. Evaluation on three synthetic and one real datasets demonstrates the superiority of our work. For example, on the Beam dataset, our work leads to 54.3\% lower prediction errors and 9.87\% fewer learnable network parameters.