Graph Neural Convection-Diffusion with Heterophily
This addresses the issue for researchers and practitioners working with heterophilic graphs, where traditional GNNs often fail, though it appears incremental as it builds on existing GNN frameworks.
The paper tackles the problem of poor performance of graph neural networks (GNNs) on heterophilic graphs by proposing a novel GNN that models information flow using the convection-diffusion equation, achieving competitive performance on node classification tasks compared to state-of-the-art methods.
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}.