让图神经网络满足电流守恒定律，提升电路与电网建模效果
Flow-Attentional Graph Neural Networks
- 引入流注意力机制，强制满足基尔霍夫第一定律
- 在电路与电网数据上，分类与回归任务性能显著提升
- 能区分普通注意力无法分辨的非同构图，适合物理系统建模
图神经网络已成为图结构数据学习的核心工具。然而，现有GNN未考虑图中物理资源流动（如电网中的电流或交通网络中的车流）所遵循的守恒定律，可能导致模型性能下降。为此，本文提出流注意力机制，将原有图注意力机制改造为满足基尔霍夫第一定律的形式。进一步分析表明，该修改提升了模型表达能力，并识别出一组普通注意力无法区分但流注意力可区分的非同构图。在电子电路和电力网络两个流图数据集上的大量实验表明，流注意力显著增强了基于注意力的GNN在图级分类与回归任务上的表现。
原文摘要 · Abstract (English)
Graph Neural Networks (GNNs) have become essential for learning from graph-structured data. However, existing GNNs do not consider the conservation law inherent in graphs associated with a flow of physical resources, such as electrical current in power grids or traffic in transportation networks, which can lead to reduced model performance. To address this, we propose flow attention, which adapts existing graph attention mechanisms to satisfy Kirchhoff$\text{'}$s first law. Furthermore, we discuss how this modification influences the expressivity and identify sets of non-isomorphic graphs that can be discriminated by flow attention but not by standard attention. Through extensive experiments on two flow graph datasets (electronic circuits and power grids) we demonstrate that flow attention enhances the performance of attention-based GNNs on both graph-level classification and regression tasks.
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