让神经网络看清有向图的细微流动差异
Topology-aware Neural Flux Prediction Guided by Physics
- 用显式差分矩阵捕捉方向梯度，增强对高频信号的感知
- 引入物理约束使消息传递符合自然规律，提升建模精度
- 适合研究水流、交通等复杂流动系统的科研人员
图神经网络（GNN）在处理有向图时，常无法保留节点信号中的高频成分，导致难以区分正向与反向拓扑结构。本文提出一种新框架，结合显式差分矩阵以建模方向梯度，以及隐式物理约束，确保GNN的消息传递过程符合自然规律。在真实世界有向图数据集——水力流量网络和城市交通流量网络上的实验表明，该方法能有效捕捉拓扑细节差异，显著提升对流动态的建模能力。
原文摘要 · Abstract (English)
Graph Neural Networks (GNNs) often struggle in preserving high-frequency components of nodal signals when dealing with directed graphs. Such components are crucial for modeling flow dynamics, without which a traditional GNN tends to treat a graph with forward and reverse topologies equal.To make GNNs sensitive to those high-frequency components thereby being capable to capture detailed topological differences, this paper proposes a novel framework that combines 1) explicit difference matrices that model directional gradients and 2) implicit physical constraints that enforce messages passing within GNNs to be consistent with natural laws. Evaluations on two real-world directed graph data, namely, water flux network and urban traffic flow network, demonstrate the effectiveness of our proposal.
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