mlsanityData to 7 Oct 2026

MultiScale MeshGraphNets

arXiv 2210.00612 ↗First posted 2 Oct 2022cs.LG cs.CEcited by 94

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Abstract (arXiv)

In recent years, there has been a growing interest in using machine learning to overcome the high cost of numerical simulation, with some learned models achieving impressive speed-ups over classical solvers whilst maintaining accuracy. However, these methods are usually tested at low-resolution settings, and it remains to be seen whether they can scale to the costly high-resolution simulations that we ultimately want to tackle. In this work, we propose two complementary approaches to improve the framework from MeshGraphNets, which demonstrated accurate predictions in a broad range of physical systems. MeshGraphNets relies on a message passing graph neural network to propagate information, and this structure becomes a limiting factor for high-resolution simulations, as equally distant points in space become further apart in graph space. First, we demonstrate that it is possible to learn accurate surrogate dynamics of a high-resolution system on a much coarser mesh, both removing the message passing bottleneck and improving performance; and second, we introduce a hierarchical approach (MultiScale MeshGraphNets) which passes messages on two different resolutions (fine and coarse), significantly improving the accuracy of MeshGraphNets while requiring less computational resources.

Key facts. Cited by 94 papers in the map (data through 7 Oct 2026). Builds on 21 of its 30 references that are in the map. First posted on arXiv 2 Oct 2022.

Builds on

21 of 30 references.

References · 21

  1. 2017Neural Message Passing for Quantum Chemistrycited by 3,460
  2. 2018Relational inductive biases, deep learning, and graph networkscited by 1,341
  3. 2015Multi-Scale Context Aggregation by Dilated Convolutionscited by 1,128
  4. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,099
  5. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  6. 2020Learning Mesh-Based Simulation with Graph Networkscited by 840
  7. 2018Hierarchical Graph Representation Learning with Differentiable Poolingcited by 786
  8. 2019Measuring and Relieving the Over-smoothing Problem for Graph Neural Networks from the Topological Viewcited by 544
  9. 2021Machine learning accelerated computational fluid dynamicscited by 461
  10. 2022Forecasting Global Weather with Graph Neural Networkscited by 165
  11. 2018Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flowscited by 147
  12. 2020Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Predictioncited by 137
9 more
  1. 2018Flexible Neural Representation for Physics Predictioncited by 91
  2. 2021Learned Coarse Models for Efficient Turbulence Simulationcited by 90
  3. 2022Predicting Physics in Mesh-reduced Space with Temporal Attentioncited by 82
  4. 2018Propagation Networks for Model-Based Control Under Partial Observationcited by 64
  5. 2020Learning Algebraic Multigrid Using Graph Neural Networkscited by 54
  6. 2021Simulating Continuum Mechanics with Multi-Scale Graph Neural Networkscited by 39
  7. 2022Physical Design using Differentiable Learned Simulatorscited by 37
  8. 2020Graph Networks with Spectral Message Passingcited by 17
  9. 2021Learning ground states of quantum Hamiltonians with graph networkscited by 12

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 5; 2023: 19; 2024: 18; 2025: 33; 2026: 19.

94 papers.

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  1. 2022GraphCast: Learning skillful medium-range global weather forecastingcited by 261
  2. 2022HOOD: Hierarchical Graphs for Generalized Modelling of Clothing Dynamicscited by 77
  3. 2023A graph convolutional autoencoder approach to model order reduction for parametrized PDEscited by 44
  4. 2022Efficient Learning of Mesh-Based Physical Simulation with BSMS-GNNcited by 43
  5. 2025OneForecast: A Universal Framework for Global and Regional Weather Forecastingcited by 30
  6. 2024Recent Advances on Machine Learning for Computational Fluid Dynamics: A Surveycited by 27
  7. 2023LagrangeBench: A Lagrangian Fluid Mechanics Benchmarking Suitecited by 26
  8. 2024Aero-Nef: Neural Fields for Rapid Aircraft Aerodynamics Simulationscited by 24
  9. 2025Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networkscited by 24
  10. 2023Graph-based Neural Weather Prediction for Limited Area Modelingcited by 22
  11. 2025GeoTransolver: Learning Physics on Irregular Domains Using Multi-scale Geometry Aware Physics Attention Transformercited by 20
  12. 2023Multiscale Graph Neural Network Autoencoders for Interpretable Scientific Machine Learningcited by 18
38 more
  1. 2023Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformercited by 18
  2. 2023Swarm Reinforcement Learning For Adaptive Mesh Refinementcited by 16
  3. 2024A Manifold Perspective on the Statistical Generalization of Graph Neural Networkscited by 16
  4. 2023Grounding Graph Network Simulators using Physical Sensor Observationscited by 15
  5. 2023MMGP: a Mesh Morphing Gaussian Process-based machine learning method for regression of physical problems under non-parameterized geometrical variabilitycited by 15
  6. 2022A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulationscited by 14
  7. 2024AhmedML: High-Fidelity Computational Fluid Dynamics Dataset for Incompressible, Low-Speed Bluff Body Aerodynamicscited by 13
  8. 2023MG-GNN: Multigrid Graph Neural Networks for Learning Multilevel Domain Decomposition Methodscited by 12
  9. 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11
  10. 2023GNN-based physics solver for time-independent PDEscited by 10
  11. 2024Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networkscited by 10
  12. 2025Diffusion-Based Hierarchical Graph Neural Networks for Simulating Nonlinear Solid Mechanicscited by 10
  13. 2025Automotive Crash Dynamics Modeling Accelerated with Machine Learningcited by 10
  14. 2024Multi-Grid Graph Neural Networks with Self-Attention for Computational Mechanicscited by 9
  15. 2023Physics-guided Shape-from-Template: Monocular Video Perception through Neural Surrogate Modelscited by 8
  16. 2025MeshMask: Physics-Based Simulations with Masked Graph Neural Networkscited by 8
  17. 2025End-to-End Probabilistic Framework for Learning with Hard Constraintscited by 8
  18. 2024A Microstructure-based Graph Neural Network for Accelerating Multiscale Simulationscited by 7
  19. 2025HEIST: A Graph Foundation Model for Spatial Transcriptomics and Proteomics Datacited by 7
  20. 2023Interpretable A-posteriori Error Indication for Graph Neural Network Surrogate Modelscited by 6
  21. 2023PhysGraph: Physics-Based Integration Using Graph Neural Networkscited by 5
  22. 2025PIORF: Physics-Informed Ollivier-Ricci Flow for Long-Range Interactions in Mesh Graph Neural Networkscited by 5
  23. 2025Geometry aware inference of steady state PDEs using Equivariant Neural Fields representationscited by 5
  24. 2023Multi-GPU Approach for Training of Graph ML Models on large CFD Meshescited by 4
  25. 2024EvoMesh: Adaptive Physical Simulation with Hierarchical Graph Evolutionscited by 4
  26. 2025A graph neural network surrogate model for mesh-based crashworthiness prediction of vehicle panel componentscited by 4
  27. 2025FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulationcited by 4
  28. 2025Training Transformers for Mesh-Based Simulationscited by 4
  29. 2024Object Dynamics Modeling with Hierarchical Point Cloud-based Representationscited by 3
  30. 2024Generalization capabilities of MeshGraphNets to unseen geometries for fluid dynamicscited by 3
  31. 2024Structure-Preserving Operator Learningcited by 3
  32. 2026Learning, Solving and Optimizing PDEs with TensorGalerkin: an efficient high-performance Galerkin assembly algorithmcited by 3
  33. 2023Learning Self-Prior for Mesh Inpainting Using Self-Supervised Graph Convolutional Networkscited by 2
  34. 2023Learning Efficient Surrogate Dynamic Models with Graph Spline Networkscited by 2
  35. 2024Learning Lagrangian Interaction Dynamics with Sampling-Based Model Order Reductioncited by 2
  36. 2024Scalable and Consistent Graph Neural Networks for Distributed Mesh-based Data-driven Modelingcited by 2
  37. 2025Hierarchical-embedding autoencoder with a predictor (HEAP) as efficient architecture for learning long-term evolution of complex multi-scale physical systemscited by 2
  38. 2025FIGNN: Feature-Specific Interpretability for Graph Neural Network Surrogate Modelscited by 2

50 most cited of 94 All 94 (JSON)