Graph Navier-Stokes Networks

Graph Neural Networks (GNNs) have emerged as a cornerstone of deep learning, with most existing methods rooted in graph signal processing and diffusion equations to model message passing. However, these approaches inherently suffer from the oversmoothing problem, where node features become indistinguishable as the network depth increases. Inspired by the Navier-Stokes equations, we introduce Graph Navier-Stokes Networks (GNSN), a novel architecture that transcends conventional diffusion-based message passing by incorporating convection into graph structures. GNSN defines a dynamic velocity field on the graph to govern convection, enabling more efficient and direct message propagation. By adaptively balancing convection and diffusion, GNSN effectively handles datasets with varying levels of homophily. And our analysis reveals, for the first time, a systematic inverse correlation between graph homophily and the strength of convection during message passing. Extensive evaluations across real-world datasets demonstrate that GNSN consistently outperforms state-of-the-art baselines in classification accuracy. Moreover, experimental results further emphasize its effectiveness in alleviating the oversmoothing problem. 1 2 * Work done while the author was an undergraduate student at Northwest A&F University. He is currently with Georgia Institute of Technology.