Graph Neural Convection-Diffusion with Heterophily

Abstract: Graph neural networks (GNNs) have shown promising results across various graph learning tasks, but they often assume homophily, which can result in poor performance on heterophilic graphs. The connected nodes are likely to be from different classes or have dissimilar features on heterophilic graphs. In this paper, we propose a novel GNN that incorporates the principle of heterophily by modeling the flow of information on nodes using the convection-diffusion equation (CDE). This allows the CDE to take into account both the diffusion of information due to homophily and the ``convection'' of information due to heterophily. We conduct extensive experiments, which suggest that our framework can achieve competitive performance on node classification tasks for heterophilic graphs, compared to the state-of-the-art methods. The code is available at \url{https://github.com/zknus/Graph-Diffusion-CDE}.