将图拓扑信息融入神经控制微分方程，提升图上动态系统预测精度。
Spatial Shortcuts in Graph Neural Controlled Differential Equations
- 在隐状态与控制信号之间引入图拓扑信息，结构更优。
- 参数更少，预测平均绝对误差更低，优于无图信息的方法。
- 适合需要高效建模图结构动态系统的研究人员。
我们将先验图拓扑信息融入神经控制微分方程（NCDE），用于预测定义在图上的动力系统未来状态。该方法在已知因果图的图边上模拟对流数据，仅在训练时观测顶点数据。我们探索了模型架构中不同位置引入图信息的效果，发现位于隐状态与控制信号之间的外层位置在理论上和实验上均表现更优。所提出的知情NCDE相比未融合图拓扑信息的先前方法，在参数更少的情况下实现了更低的平均绝对误差（MAE）。
原文摘要 · Abstract (English)
We incorporate prior graph topology information into a Neural Controlled Differential Equation (NCDE) to predict the future states of a dynamical system defined on a graph. The informed NCDE infers the future dynamics at the vertices of simulated advection data on graph edges with a known causal graph, observed only at vertices during training. We investigate different positions in the model architecture to inform the NCDE with graph information and identify an outer position between hidden state and control as theoretically and empirically favorable. Our such informed NCDE requires fewer parameters to reach a lower Mean Absolute Error (MAE) compared to previous methods that do not incorporate additional graph topology information.
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