mlsanityData to 14 Oct 2026

Multi-Grid Graph Neural Networks with Self-Attention for Computational Mechanics

arXiv 2409.11899 ↗First posted 18 Sep 2024cs.LG cs.CEcited by 9

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Abstract (arXiv)

Advancement in finite element methods have become essential in various disciplines, and in particular for Computational Fluid Dynamics (CFD), driving research efforts for improved precision and efficiency. While Convolutional Neural Networks (CNNs) have found success in CFD by mapping meshes into images, recent attention has turned to leveraging Graph Neural Networks (GNNs) for direct mesh processing. This paper introduces a novel model merging Self-Attention with Message Passing in GNNs, achieving a 15% reduction in RMSE on the well known flow past a cylinder benchmark. Furthermore, a dynamic mesh pruning technique based on Self-Attention is proposed, that leads to a robust GNN-based multigrid approach, also reducing RMSE by 15%. Additionally, a new self-supervised training method based on BERT is presented, resulting in a 25% RMSE reduction. The paper includes an ablation study and outperforms state-of-the-art models on several challenging datasets, promising advancements similar to those recently achieved in natural language and image processing. Finally, the paper introduces a dataset with meshes larger than existing ones by at least an order of magnitude. Code and Datasets will be released at https://github.com/DonsetPG/multigrid-gnn.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 28 of its 43 references that are in the map. First posted on arXiv 18 Sep 2024.

Builds on

28 of 43 references.

References · 28

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16 more
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  2. 2019Graph Transformer Networkscited by 523
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 3; 2026: 5.

9 papers.

  1. 2026MeshGraphNet-Transformer: Scalable Mesh-based Learned Simulation for Solid Mechanicscited by 10
  2. 2025MeshMask: Physics-Based Simulations with Masked Graph Neural Networkscited by 9
  3. 2024EvoMesh: Adaptive Physical Simulation with Hierarchical Graph Evolutionscited by 4
  4. 2025Curriculum Learning for Mesh-based simulationscited by 1
  5. 2026Mask-Morph Graph U-Net: A Generalisable Mesh-Based Surrogate for Crashworthiness Field Prediction under Large Geometric Variationcited by 1
  6. 2025Automated discovery of finite volume schemes using Graph Neural Networkscited by 0
  7. 2026Multi-fidelity graph-based neural networks architectures to learn Navier-Stokes solutions on non-parametrized 2D domainscited by 0
  8. 2026Mesh Based Simulations with Spatial and Temporal awarenesscited by 0
  9. 2026Physics-Informed Coarsening for Multigrid Graph Neural Surrogatescited by 0