Adaptive Graph Rewiring to Mitigate Over-Squashing in Mesh-Based GNNs for Fluid Dynamics Simulations

2025-11-16

AI Summary

Grid-based graph neural networks (GNNs) for fluid simulation suffer from “over-compression” under mesh refinement—i.e., excessive spatial coarsening impedes modeling of long-range physical interactions. Method: We propose AdaMeshNet, an adaptive graph rewiring framework that embeds delay-aware dynamic rewiring into the message-passing layers. Unlike static rewiring assuming instantaneous long-range interactions, AdaMeshNet computes a delay score for bottleneck nodes based on shortest-path distances and velocity differences, triggering edge updates adaptively across propagation layers. This explicitly models the gradual propagation of physical perturbations while preserving inter-particle distances and temporal dynamics. Contribution/Results: Experiments demonstrate that AdaMeshNet significantly outperforms baselines across diverse meshed fluid simulation tasks. It effectively alleviates over-compression, enhances modeling of long-range dependencies, and improves accuracy in flow field prediction.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Multiagent Systems: Adversarial Agents

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Mitigating over-squashing in mesh-based GNNs for fluid dynamics
• Capturing long-range physical interactions in refined meshes
• Modeling gradual propagation of interactions with adaptive rewiring

Innovation

• Adaptive graph rewiring during message-passing
• Rewiring delay score using distance and velocity
• Dynamic edge insertion at specific GNN layers