Up-sampling-only and Adaptive Mesh-based GNN for Simulating Physical Systems
Fu Lin, Jiasheng Shi, Shijie Luo, Qinpei Zhao, Weixiong Rao, Lei Chen
TL;DR
UA-MGN addresses the high computational cost of FEM-based mechanical simulations by introducing an up-sampling-only, adaptive hierarchical GNN on multi-level mesh graphs. The method propagates information from coarse to fine meshes to capture global context early and uses adaptive, direction-aware MP to mitigate over-smoothing and infinite loops. Empirical results on Beam, SteeringWheel, and CylinderFlow show substantial accuracy gains (e.g., 40.99% RMSE reduction on Beam) with smaller parameter counts (≈43% fewer) and lower FLOPs (≈4.5% fewer) than state-of-the-art baselines, while delivering fast inference times. The work advances efficient physics-informed learning for irregular meshes and provides a scalable blueprint for multi-level mesh learning and adaptive MP in GNN-based PDE solvers.
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).