用双层图网络提升复杂机械系统仿真精度与效率
Learning-Based Finite Element Methods Modeling for Complex Mechanical Systems
- 设计图块与注意力块交织的双层网格图网络
- 在梁数据集上误差降低54.3%，参数减少9.87%
- 适合需要高精度物理仿真的工程建模场景
复杂机械系统仿真在诸多实际应用中至关重要。当前主流的有限元方法（FEM）计算开销大。尽管已有基于CNN或GNN的模型在降低计算时间与保持可接受精度方面取得进展，但面对远距离节点间的长程空间依赖，以及局部与全局表征独立学习的挑战，仍难以有效建模复杂机械系统。本文提出一种新型两层网格图网络，通过交织设计的图块与注意力块，更有效地学习机械相互作用，即使在长程空间依赖下也表现优异。在三个合成数据集和一个真实数据集上的评估表明，本方法具有显著优势。例如，在梁数据集上，预测误差降低54.3%，可学习参数减少9.87%。
原文摘要 · Abstract (English)
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.
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