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

• URL: http://arxiv.org/abs/2504.04052v1
• Date: Sat, 05 Apr 2025 04:14:05 GMT
• Title: PIORF: Physics-Informed Ollivier-Ricci Flow for Long-Range Interactions in Mesh Graph Neural Networks
• Authors: Youn-Yeol Yu, Jeongwhan Choi, Jaehyeon Park, Kookjin Lee, Noseong Park,
• Abstract summary: We propose Physics-Informed Ollivier-Ricci Flow (PIORF), a novel rewiring method that combines physical correlations with graph topology.<n>We show that PIORF consistently outperforms baseline models and existing rewiring methods, achieving up to 26.2 improvement.
• Score: 23.97389618896843
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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