mlsanityData to 7 Oct 2026

MAgNET: A Graph U-Net Architecture for Mesh-Based Simulations

arXiv 2211.00713 ↗First posted 1 Nov 2022cs.LG cs.CEcited by 26

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Abstract (arXiv)

In many cutting-edge applications, high-fidelity computational models prove to be too slow for practical use and are therefore replaced by much faster surrogate models. Recently, deep learning techniques have increasingly been utilized to accelerate such predictions. To enable learning on large-dimensional and complex data, specific neural network architectures have been developed, including convolutional and graph neural networks. In this work, we present a novel encoder-decoder geometric deep learning framework called MAgNET, which extends the well-known convolutional neural networks to accommodate arbitrary graph-structured data. MAgNET consists of innovative Multichannel Aggregation (MAg) layers and graph pooling/unpooling layers, forming a graph U-Net architecture that is analogous to convolutional U-Nets. We demonstrate the predictive capabilities of MAgNET in surrogate modeling for non-linear finite element simulations in the mechanics of solids.

Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). Builds on 36 of its 84 references that are in the map. First posted on arXiv 1 Nov 2022.

Builds on

36 of 84 references.

References · 36

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24 more
  1. 2019Self-Attention Graph Poolingcited by 421
  2. 2019Semantic Graph Convolutional Networks for 3D Human Pose Regressioncited by 204
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  5. 2021Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problemscited by 100
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  10. 2021Deep Learning for Reduced Order Modelling and Efficient Temporal Evolution of Fluid Simulationscited by 36
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  12. 2021Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Datacited by 31
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 1; 2024: 9; 2025: 9; 2026: 6.

26 papers.

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  1. 2024A review of graph neural network applications in mechanics-related domainscited by 14
  2. 2024Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networkscited by 10
  3. 2023Interpretable A-posteriori Error Indication for Graph Neural Network Surrogate Modelscited by 6
  4. 2022Convolution, aggregation and attention based deep neural networks for accelerating simulations in mechanicscited by 5
  5. 2026Artificial Intelligence in Materials Science and Engineering: Current Landscape, Key Challenges, and Future Trajectoriecited by 5
  6. 2025A graph neural network surrogate model for mesh-based crashworthiness prediction of vehicle panel componentscited by 4
  7. 2024A hybrid numerical methodology coupling Reduced Order Modeling and Graph Neural Networks for non-parametric geometries: applications to structural dynamics problemscited by 3
  8. 2024LatticeGraphNet: A two-scale graph neural operator for simulating lattice structurescited by 2
  9. 2024Scalable and Consistent Graph Neural Networks for Distributed Mesh-based Data-driven Modelingcited by 2
  10. 2024Topology-Agnostic Graph U-Nets for Scalar Field Prediction on Unstructured Meshescited by 2
  11. 2025Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systemscited by 2
  12. 2025FIGNN: Feature-Specific Interpretability for Graph Neural Network Surrogate Modelscited by 2
14 more
  1. 2024Learning Nonlinear Finite Element Solution Operators using Multilayer Perceptrons and Energy Minimizationcited by 1
  2. 2025Recurrent U-Net-Based Graph Neural Network (RUGNN) for Accurate Deformation Predictions in Sheet Material Formingcited by 1
  3. 2025Multi-Stage Graph Neural Networks for Data-Driven Prediction of Natural Convection in Enclosed Cavitiescited by 1
  4. 2025Graph Network-based Structural Simulator: Graph Neural Networks for Structural Dynamicscited by 1
  5. 2024Learning-Based Finite Element Methods Modeling for Complex Mechanical Systemscited by 0
  6. 2024Predicting Wall Thickness Changes in Cold Forging Processes: An Integrated FEM and Neural Network approachcited by 0
  7. 2025Machine learning surrogate models of many-body dispersion interactions in polymer meltscited by 0
  8. 2025Learning Deformable Body Interactions With Adaptive Spatial Tokenizationcited by 0
  9. 2025Adaptive Fusion Graph Network for 3D Strain Field Prediction in Solid Rocket Motor Grainscited by 0
  10. 2026Deep Wave Network for Modeling Multi-Scale Physical Dynamicscited by 0
  11. 2026NSPOD: Accelerating Krylov solvers via DeepONet-learned POD subspacescited by 0
  12. 2026Mask-Morph Graph U-Net: A Generalisable Mesh-Based Surrogate for Crashworthiness Field Prediction under Large Geometric Variationcited by 0
  13. 2026HyperShape: Hyperelasticity Across Diverse Shapescited by 0
  14. 2026Generalizing Soft Tissue Deformation and Force Prediction Across Material Stiffness and Geometrycited by 0