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Graph Navier Stokes Networks

arXiv 2605.21247 ↗First posted 20 May 2026cs.LGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 52 of its 99 references that are in the map. First posted on arXiv 20 May 2026.

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52 of 99 references.

References · 52

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2017Inductive Representation Learning on Large Graphscited by 6,284
  4. 2018Neural Ordinary Differential Equationscited by 3,733
  5. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  6. 2016Convolutional Neural Networks on Graphs with Fast Localized Spectral Filteringcited by 2,085
  7. 2019Simplifying Graph Convolutional Networkscited by 1,470
  8. 2018Pitfalls of Graph Neural Network Evaluationcited by 994
  9. 2018Predict then Propagate: Graph Neural Networks meet Personalized PageRankcited by 987
  10. 2016Revisiting Semi-Supervised Learning with Graph Embeddingscited by 970
  11. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 875
  12. 2020Simple and Deep Graph Convolutional Networkscited by 857
38 more
  1. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 821
  2. 2019Graph WaveNet for Deep Spatial-Temporal Graph Modelingcited by 820
  3. 2017Poincar'e Embeddings for Learning Hierarchical Representationscited by 674
  4. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 592
  5. 2019Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological Viewcited by 544
  6. 2019Multi-scale Attributed Node Embeddingcited by 543
  7. 2020Graph Neural Networks in Recommender Systems: A Surveycited by 493
  8. 2019MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixingcited by 442
  9. 2019Diffusion Improves Graph Learningcited by 414
  10. 2019Hyperbolic Graph Convolutional Neural Networkscited by 400
  11. 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 361
  12. 2021Large Scale Learning on Non-Homophilous Graphs: New Benchmarks and Strong Simple Methodscited by 309
  13. 2019PairNorm: Tackling Oversmoothing in GNNscited by 297
  14. 2021Graph Neural Network for Traffic Forecasting: A Surveycited by 260
  15. 2021Spatial-Temporal Graph ODE Networks for Traffic Flow Forecastingcited by 209
  16. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 208
  17. 2020Graph Neural Networks with Heterophilycited by 202
  18. 2021BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximationcited by 195
  19. 2022Finding Global Homophily in Graph Neural Networks When Meeting Heterophilycited by 179
  20. 2019Graph Neural Ordinary Differential Equationscited by 153
  21. 2021A Survey of Graph Neural Networks for Recommender Systems: Challenges, Methods, and Directionscited by 144
  22. 2018Contextual Stochastic Block Modelscited by 134
  23. 2019Multi-relational Poincar'e Graph Embeddingscited by 126
  24. 2019Continuous Graph Neural Networkscited by 114
  25. 2022Not too little, not too much: a theoretical analysis of graph (over)smoothingcited by 106
  26. 2021Dirichlet Energy Constrained Learning for Deep Graph Neural Networkscited by 97
  27. 2021Breaking the Limit of Graph Neural Networks by Improving the Assortativity of Graphs with Local Mixing Patternscited by 95
  28. 2022Convolutional Neural Networks on Graphs with Chebyshev Approximation, Revisitedcited by 87
  29. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  30. 2022GREAD: Graph Neural Reaction-Diffusion Networkscited by 54
  31. 2023Graph Neural Networks with Learnable and Optimal Polynomial Basescited by 36
  32. 2023Graph Neural Convection-Diffusion with Heterophilycited by 26
  33. 2024How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashingcited by 24
  34. 2022FlowX: Towards Explainable Graph Neural Networks via Message Flowscited by 20
  35. 2024Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FRONDcited by 16
  36. 2025Depth-Adaptive Graph Neural Networks via Learnable Bakry-'Emery Curvaturecited by 8
  37. 2024Graph Neural Networks Do Not Always Oversmoothcited by 7
  38. 2025Beyond Fixed Depth: Adaptive Graph Neural Networks for Node Classification Under Varying Homophilycited by 5

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