Second-Order Tensorial Partial Differential Equations on Graphs
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Abstract (arXiv)
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.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 35 of its 46 references that are in the map. First posted on arXiv 2 Sep 2025.
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References · 35
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23 more
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