Understanding and Enhancing Graph Neural Networks From the Perspective of Partial Differential Equations

Guangdong Feng

Abstract


We understand graph neural networks from the perspective of partial diff erential equations. Firstly, based on the relationship
between the partial diff erential equation and the propagation equation of graph neural networks, the topology and node features are treated
as independent variables of the wave function to better combine the topological structure information of the graph with the node feature
information. Secondly, the theoretical framework of the graph neural network model PGNN is established by the variable separation
operation of the partial diff erential equation, which makes some existing models have diff erent degrees of PGNN approximation. Finally,
experiments show that the model in this paper achieves good results on commonly used citation datasets.

Keywords


Graph Neural Networks; Partial Diff erential Equations; Separation of Variables.

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References


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DOI: https://doi.org/10.18686/esta.v10i1.307

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