用自注意力增强图神经网络，提升流体力学模拟精度与效率
Multi-Grid Graph Neural Networks with Self-Attention for Computational Mechanics
- 结合自注意力与消息传递机制，直接处理网格数据
- 在圆柱绕流基准测试中RMSE降低15%，自监督训练再降25%
- 提出动态网格剪枝技术，适用于大规模复杂仿真问题
有限元方法的进步在多个领域至关重要，尤其在计算流体动力学（CFD）中推动了精度与效率的提升。尽管卷积神经网络（CNN）通过将网格映射为图像在CFD中取得成功，但近年来研究逐渐转向利用图神经网络（GNN）进行直接网格处理。本文提出一种融合自注意力与消息传递的新型模型，在著名的圆柱绕流基准测试中实现RMSE降低15%。此外，提出基于自注意力的动态网格剪枝技术，构建出稳健的基于GNN的多网格方法，同样使RMSE减少15%。同时，提出一种基于BERT的自监督训练方法，实现25%的RMSE下降。论文包含消融实验，并在多个挑战性数据集上超越现有最先进模型，展现出类似自然语言与图像处理领域的进展潜力。最后，引入一个规模比现有数据集大至少一个数量级的新型网格数据集。代码与数据集将发布于https://github.com/DonsetPG/multigrid-gnn。
原文摘要 · Abstract (English)
Advancement in finite element methods have become essential in various disciplines, and in particular for Computational Fluid Dynamics (CFD), driving research efforts for improved precision and efficiency. While Convolutional Neural Networks (CNNs) have found success in CFD by mapping meshes into images, recent attention has turned to leveraging Graph Neural Networks (GNNs) for direct mesh processing. This paper introduces a novel model merging Self-Attention with Message Passing in GNNs, achieving a 15\% reduction in RMSE on the well known flow past a cylinder benchmark. Furthermore, a dynamic mesh pruning technique based on Self-Attention is proposed, that leads to a robust GNN-based multigrid approach, also reducing RMSE by 15\%. Additionally, a new self-supervised training method based on BERT is presented, resulting in a 25\% RMSE reduction. The paper includes an ablation study and outperforms state-of-the-art models on several challenging datasets, promising advancements similar to those recently achieved in natural language and image processing. Finally, the paper introduces a dataset with meshes larger than existing ones by at least an order of magnitude. Code and Datasets will be released at https://github.com/DonsetPG/multigrid-gnn.
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