mlsanityData to 7 Oct 2026

PIORF: Physics-Informed Ollivier-Ricci Flow for Long-Range Interactions in Mesh Graph Neural Networks

arXiv 2504.04052 ↗First posted 5 Apr 2025cs.LG cs.AIcited by 5

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Abstract (arXiv)

Recently, data-driven simulators based on graph neural networks have gained attention in modeling physical systems on unstructured meshes. However, they struggle with long-range dependencies in fluid flows, particularly in refined mesh regions. This challenge, known as the 'over-squashing' problem, hinders information propagation. While existing graph rewiring methods address this issue to some extent, they only consider graph topology, overlooking the underlying physical phenomena. We propose Physics-Informed Ollivier-Ricci Flow (PIORF), a novel rewiring method that combines physical correlations with graph topology. PIORF uses Ollivier-Ricci curvature (ORC) to identify bottleneck regions and connects these areas with nodes in high-velocity gradient nodes, enabling long-range interactions and mitigating over-squashing. Our approach is computationally efficient in rewiring edges and can scale to larger simulations. Experimental results on 3 fluid dynamics benchmark datasets show that PIORF consistently outperforms baseline models and existing rewiring methods, achieving up to 26.2 improvement.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 28 of its 57 references that are in the map. First posted on arXiv 5 Apr 2025.

Builds on

28 of 57 references.

References · 28

  1. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
  2. 2021E(n) Equivariant Graph Neural Networkscited by 951
  3. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  4. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  5. 2020A Generalization of Transformer Networks to Graphscited by 653
  6. 2020On the Bottleneck of Graph Neural Networks and its Practical Implicationscited by 624
  7. 2021Understanding over-squashing and bottlenecks on graphs via curvaturecited by 471
  8. 2019Diffusion Improves Graph Learningcited by 414
  9. 2018Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluidscited by 219
  10. 2020Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Predictioncited by 137
  11. 2022FoSR: First-order spectral rewiring for addressing oversquashing in GNNscited by 104
  12. 2022Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvaturecited by 96
16 more
  1. 2022MultiScale MeshGraphNetscited by 94
  2. 2023Understanding Oversquashing in GNNs through the Lens of Effective Resistancecited by 94
  3. 2018Flexible Neural Representation for Physics Predictioncited by 91
  4. 2022DiffWire: Inductive Graph Rewiring via the Lov'asz Boundcited by 79
  5. 2018Propagation Networks for Model-Based Control Under Partial Observationcited by 64
  6. 2019Community Detection on Networks with Ricci Flowcited by 62
  7. 2023Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformerscited by 54
  8. 2022Oversquashing in GNNs through the lens of information contraction and graph expansioncited by 52
  9. 2022Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNNcited by 43
  10. 2023Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvaturecited by 39
  11. 2023Cooperative Graph Neural Networkscited by 35
  12. 2023Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networkscited by 32
  13. 2023Adaptive Message Passing: A General Framework to Mitigate Oversmoothing, Oversquashing, and Underreachingcited by 23
  14. 2023Exposition on over-squashing problem on GNNs: Current Methods, Benchmarks and Challengescited by 22
  15. 2023Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformercited by 18
  16. 2024PANDA: Expanded Width-Aware Message Passing Beyond Rewiringcited by 10

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 4; 2026: 1.

5 papers.

  1. 2025Improving Long-Range Interactions in Graph Neural Simulators via Hamiltonian Dynamicscited by 6
  2. 2025Rapid training of Hamiltonian graph networks using random featurescited by 2
  3. 2025Adaptive Graph Rewiring to Mitigate Over-Squashing in Mesh-Based GNNs for Fluid Dynamics Simulationscited by 1
  4. 2025MicroRicci: A Greedy and Local Ricci Flow Solver for Self-Tuning Mesh Smoothingcited by 0
  5. 2026HI-MeshGraphNets: Efficient and Accurate Mesh-based Physics Learning with Hierarchical Multi-scale Graph Neural Networkscited by 0