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
This paper introduces AdaMeshNet, an adaptive graph rewiring framework for mesh-based GNNs in fluid dynamics, which models gradual physical interactions and improves prediction accuracy over traditional methods.
Contribution
The paper proposes a novel adaptive rewiring approach that dynamically determines when to add edges based on physical interaction delays, addressing over-squashing in mesh-based GNNs.
Findings
AdaMeshNet outperforms conventional rewiring methods in fluid simulations.
The adaptive rewiring captures the sequential nature of physical interactions.
Improved accuracy in modeling long-range physical effects.
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…
Peer Reviews
Decision·ICLR 2026 Conference Withdrawn Submission
* physically consistent rewiring: introduces an adaptive rewiring mechanism that reflects real-world gradual propagation of information in fluids and considers both curvature and velocity/distance * theoretical grounding: provides a mathematical analysis of over-squashing in MGN, supported by some Jacobian-based derivation * dynamic adaptation * ablation studies are present
* the computational efficiency is not clear * the provided code is just a placeholder (message "File not found" appears when trying to see it) * looking to Tables 1 and 2 I observe the stds of metrics comparable to the metrics values, what means unstable training * ablation studies could be better if errors of the obtained metrics would have also plotted
1. The paper tackles the important and challenging problem of over-squashing in mesh-based GNNs for physics simulations. 2. The empirical results in Tables 1 and 2 consistently show that AdaMeshNet achieves a lower RMSE than the baselines, including PIORF, across both datasets. 3. The ablation study effectively demonstrates that both the distance and velocity components of the heuristic score (Eq. 8) are necessary to achieve the reported performance.
1. The paper presents its physics-informed selection strategy as novel. However, the entire logic—(1) identify topological bottlenecks using node-level ORC, and select a rewiring target $v_{i^*}$ that maximizes the velocity difference $||v_i - v_j||$—is identical to the strategy proposed in the PIORF paper[1]; The *only* novel contribution of this work is the calculation of $s_{delay}$ to decide *when* to add this pre-selected edge, which is an incremental modification, not a "novel framework".
- The paper introduces a layer-wise, physically grounded rewiring approach, addressing the unrealistic assumption of instantaneous interactions in static methods. - Experiment results demonstrate that the proposed method has superior performance.
- Experiments are confined to two datasets; broader validation would strengthen generality claims. - Adaptive rewiring during training increases computational overhead. It would be better if the authors could add some runtime or scalability analysis. - Performance depends notably on $\alpha$ (rewiring ratio) and $\beta$ (distance–velocity weighting), but the tuning process may not generalize easily to new settings. - Lemma 1 formalizes information decay but does not quantify how adaptive rewirin
1. The proposed AdaMeshNet introduces dynamic, layer-dependent rewiring via a rewiring delay score based on velocity difference and graph distance. This adaptive process is conceptually distinct from static rewiring methods, and better reflects gradual physical propagation. 2. The visualization and analysis (e.g., Cylinder Flow velocity contour comparisons) provide intuitive physical explanations of how adaptive rewiring reduces unrealistic instantaneous information transfer.
1. The evaluation is restricted to two fluid datasets (CylinderFlow and Airfoil). Broader validation on non-fluid domains (e.g., deformable solids, elastic plates, cloth dynamics) would better demonstrate generality. 2. The key rewiring criterion — connecting nodes with large velocity differences — is directly inherited from PIORF (Yu et al., 2025), potentially diminishing the novelty of the contribution. I suggest investigating other physical quantities (e.g., pressure, density, or vorticity) t
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Taxonomy
TopicsModel Reduction and Neural Networks · Lattice Boltzmann Simulation Studies · Advanced Graph Neural Networks