标题： 基于学习的复杂机械系统的有限元方法建模 显示英文标题

标题： Learning-Based Finite Element Methods Modeling for Complex Mechanical Systems

摘要： 复杂机械系统仿真在许多实际应用中非常重要。 目前基于有限元法（FEM）的实际数值求解器由于计算开销巨大而面临挑战。 尽管在减少计算时间和保证可接受精度方面取得了许多进展，但最近基于CNN或GNN的仿真模型仍然难以有效表示由距离网格节点的长程空间依赖性以及独立学习局部和全局表示所导致的复杂机械仿真。 本文提出了一种新颖的两级网格图网络。 该网络的关键在于交织开发的图块和注意力块，以便更好地学习即使对于长程空间依赖性的机械交互。 在三个合成数据集和一个真实数据集上的评估证明了我们工作的优越性。 例如，在梁数据集上，我们的工作使预测误差降低了54.3%，可学习网络参数减少了9.87%。 显示英文摘要

摘要： 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.