Graph Navier Stokes Networks

2026-05-20

AI Summary

This work addresses the challenges of over-smoothing in deep graph neural networks and inefficient message passing on heterogeneous graphs. Inspired by the Navier–Stokes equations, it introduces—for the first time—the convection–diffusion mechanism from fluid dynamics into graph neural networks, proposing a convection–diffusion message passing framework integrated with a dynamic velocity field. By adaptively balancing convection and diffusion processes, the method enables more efficient and directional information propagation, thereby overcoming the limitations of conventional purely diffusive paradigms. Extensive experiments on twelve real-world datasets demonstrate that the proposed model substantially mitigates over-smoothing and consistently outperforms state-of-the-art approaches across node classification tasks.

Abstract

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 is able to efficiently handle datasets with varying levels of homophily. Extensive evaluations across twelve 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.

Problem

• oversmoothing
• Graph Neural Networks
• message passing
• diffusion equations
• homophily

Innovation

• Graph Neural Networks
• Navier-Stokes Equations
• Convection-Diffusion
• Oversmoothing
• Message Passing