Title: Graph Navier Stokes Networks

Abstract: Graph Neural Networks (GNNs) have become a fundamental pillar of deep learning, with the majority of current methodologies relying on graph signal processing and diffusion equations to facilitate message passing. Nevertheless, these techniques are prone to the oversmoothing issue, a phenomenon wherein node features lose their distinctiveness as the depth of the network grows. Drawing inspiration from the Navier Stokes equations, we propose Graph Navier Stokes Networks (GNSN), an innovative framework that moves beyond traditional diffusion-centric message passing by integrating convection into graph structures. GNSN establishes a dynamic velocity field on the graph to manage convection, thereby allowing for more streamlined and direct message propagation. Through an adaptive equilibrium between convection and diffusion, GNSN effectively manages datasets exhibiting diverse degrees of homophily. Comprehensive testing on twelve real-world datasets reveals that GNSN consistently surpasses state-of-the-art baselines in classification performance. Furthermore, experimental findings highlight the model’s capability to mitigate the oversmoothing challenge.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC