Adaptive Graph Rewiring to Mitigate Over-Squashing in Mesh-Based GNNs for Fluid Dynamics Simulations
Sangwoo Seo, Hyunsung Kim, Jiwan Kim, Chanyoung Park
TL;DR
AdaMeshNet tackles over-squashing in mesh-based GNNs by introducing adaptive graph rewiring that activates new edges during message passing to reflect the gradual propagation of physical interactions. Bottleneck nodes are identified via Ollivier–Ricci curvature, and a rewiring delay score combining shortest-path distance and velocity differences determines the layer at which new connections are formed, enabling layer-wise, time-delayed information flow. Empirical results on CylinderFlow and Airfoil show AdaMeshNet consistently outperforms static rewiring baselines in velocity and pressure RMSE and yields more accurate velocity contour propagation, validating the effectiveness of temporally aware rewiring. The approach offers a physically grounded, scalable strategy to improve long-range interaction modeling in mesh-based CFD simulations with potential broader applicability to other dynamic graph domains.
Abstract
Mesh-based simulation using Graph Neural Networks (GNNs) has been recognized as a promising approach for modeling fluid dynamics. However, the mesh refinement techniques which allocate finer resolution to regions with steep gradients can induce the over-squashing problem in mesh-based GNNs, which prevents the capture of long-range physical interactions. Conventional graph rewiring methods attempt to alleviate this issue by adding new edges, but they typically complete all rewiring operations before applying them to the GNN. These approaches are physically unrealistic, as they assume instantaneous interactions between distant nodes and disregard the distance information between particles. To address these limitations, we propose a novel framework, called Adaptive Graph Rewiring in Mesh-Based Graph Neural Networks (AdaMeshNet), that introduces an adaptive rewiring process into the message-passing procedure to model the gradual propagation of physical interactions. Our method computes a rewiring delay score for bottleneck nodes in the mesh graph, based on the shortest-path distance and the velocity difference. Using this score, it dynamically selects the message-passing layer at which new edges are rewired, which can lead to adaptive rewiring in a mesh graph. Extensive experiments on mesh-based fluid simulations demonstrate that AdaMeshNet outperforms conventional rewiring methods, effectively modeling the sequential nature of physical interactions and enabling more accurate predictions.