Up-sampling-only and Adaptive Mesh-based GNN for Simulating Physical Systems

TL;DR

This paper introduces UA-MGN, a hierarchical Mesh Graph Network with up-sampling and adaptive message passing, significantly improving efficiency and accuracy in mechanical system simulations compared to existing GNN models.

Contribution

The paper proposes a novel hierarchical GNN architecture with up-sampling and adaptive message passing for better mechanical system simulation.

Findings

40.99% lower errors on Beam dataset

43.48% fewer network parameters

4.49% fewer FLOPs

Abstract

Traditional simulation of complex mechanical systems relies on numerical solvers of Partial Differential Equations (PDEs), e.g., using the Finite Element Method (FEM). The FEM solvers frequently suffer from intensive computation cost and high running time. Recent graph neural network (GNN)-based simulation models can improve running time meanwhile with acceptable accuracy. Unfortunately, they are hard to tailor GNNs for complex mechanical systems, including such disadvantages as ineffective representation and inefficient message propagation (MP). To tackle these issues, in this paper, with the proposed Up-sampling-only and Adaptive MP techniques, we develop a novel hierarchical Mesh Graph Network, namely UA-MGN, for efficient and effective mechanical simulation. Evaluation on two synthetic and one real datasets demonstrates the superiority of the UA-MGN. For example, on the Beam dataset, compared to the state-of-the-art MS-MGN, UA-MGN leads to 40.99% lower errors but using only 43.48% fewer network parameters and 4.49% fewer floating point operations (FLOPs).