提出新型图网络，让物理系统仿真更快更准。
Up-sampling-only and Adaptive Mesh-based GNN for Simulating Physical Systems
- 仅用上采样和自适应消息传播构建层级网格图网络
- 在梁模拟数据上误差降低40.99%，参数减少43.48%
- 适合需要高效高精度仿真的工程与科学计算场景
复杂机械系统的传统仿真依赖偏微分方程（PDE）的数值求解器，如有限元法（FEM），但常面临计算成本高、运行时间长的问题。近年来基于图神经网络（GNN）的仿真模型虽提升了运行速度且保持可接受精度，但仍难以适配复杂机械系统，存在表征无效、消息传播效率低等缺陷。为此，本文提出仅上采样与自适应消息传播技术，构建新型分层网格图网络UA-MGN，实现高效且有效的机械系统仿真。在两个合成数据集和一个真实数据集上的评估表明，该方法具有显著优势。例如，在Beam数据集上，相比当前最优的MS-MGN，UA-MGN误差降低40.99%，所用网络参数减少43.48%，浮点运算量（FLOPs）减少4.49%。
原文摘要 · Abstract (English)
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).
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