Graph Navier Stokes Networks
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914621351264256 |
|---|---|
| author | Zhao, Zexing Shi, Guangsi Gong, Yu Wang, Tianyu Pan, Shirui Cheng, Hongye Li, Yuxiao |
| author_facet | Zhao, Zexing Shi, Guangsi Gong, Yu Wang, Tianyu Pan, Shirui Cheng, Hongye Li, Yuxiao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21247 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Graph Navier Stokes Networks Zhao, Zexing Shi, Guangsi Gong, Yu Wang, Tianyu Pan, Shirui Cheng, Hongye Li, Yuxiao Machine Learning 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. |
| title | Graph Navier Stokes Networks |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.21247 |