提出新型图神经网络模型，提升多图数据处理中的高频信息保留与传播效率。
Second-Order Tensorial Partial Differential Equations on Graphs
- 基于二阶张量微分方程构建连续图神经网络框架
- 在交通预测任务中优于现有方法，保持高频特征不衰减
- 理论分析确保模型稳定且抗图扰动，适合复杂网络建模
多交互图上的数据处理对诸多应用至关重要，但现有方法多依赖离散滤波或一阶连续模型，导致高频信息衰减和信息传播缓慢。本文提出图上的二阶张量偏微分方程（SoTPDEG），并建立首个理论完备的二阶连续乘积图神经网络（GNN）框架。方法利用笛卡尔积图上余弦核的可分离性，实现高效谱分解，同时保留高频成分。进一步提供关于过平滑性和图扰动下的稳定性严格分析，奠定坚实理论基础。在时空交通预测实验中，性能优于对比方法。
原文摘要 · Abstract (English)
Processing data on multiple interacting graphs is crucial for many applications, but existing approaches rely mostly on discrete filtering or first-order continuous models, dampening high frequencies and slow information propagation. In this paper, we introduce second-order tensorial partial differential equations on graphs (SoTPDEG) and propose the first theoretically grounded framework for second-order continuous product graph neural networks (GNNs). Our method exploits the separability of cosine kernels in Cartesian product graphs to enable efficient spectral decomposition while preserving high-frequency components. We further provide rigorous over-smoothing and stability analysis under graph perturbations, establishing a solid theoretical foundation. Experimental results on spatiotemporal traffic forecasting illustrate the superiority over the compared methods.
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