Second-Order Tensorial Partial Differential Equations on Graphs

• URL: http://arxiv.org/abs/2509.02015v3
• Date: Tue, 16 Sep 2025 14:41:12 GMT
• Title: Second-Order Tensorial Partial Differential Equations on Graphs
• Authors: Aref Einizade, Fragkiskos D. Malliaros, Jhony H. Giraldo,
• Abstract summary: We introduce second-order tensorial partial differential equations on graphs (SoTPDEG)<n>We propose the first theoretically grounded framework for second-order continuous product graph neural networks (GNNs)
• Score: 13.421159402806675
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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