Graph Navier Stokes Networks

TL;DR

Graph Navier Stokes Networks (GNSN) introduce a convection-based message passing mechanism inspired by fluid dynamics to improve graph neural network performance and mitigate oversmoothing.

Contribution

The paper proposes GNSN, a novel GNN architecture that incorporates convection inspired by Navier Stokes equations, surpassing diffusion-based methods in accuracy and oversmoothing mitigation.

Findings

GNSN outperforms state-of-the-art models on twelve datasets.

GNSN effectively alleviates the oversmoothing problem.

GNSN adapts to datasets with different homophily levels.

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.