mlsanityData to 7 Oct 2026

Learning Mesh-Based Simulation with Graph Networks

arXiv 2010.03409 ↗First posted 7 Oct 2020cs.LG cs.CEcited by 840

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Cited by 25 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike favorable trade-offs between accuracy and efficiency. However, high-dimensional scientific simulations are very expensive to run, and solvers and parameters must often be tuned individually to each system studied. Here we introduce MeshGraphNets, a framework for learning mesh-based simulations using graph neural networks. Our model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation. Our results show it can accurately predict the dynamics of a wide range of physical systems, including aerodynamics, structural mechanics, and cloth. The model's adaptivity supports learning resolution-independent dynamics and can scale to more complex state spaces at test time. Our method is also highly efficient, running 1-2 orders of magnitude faster than the simulation on which it is trained. Our approach broadens the range of problems on which neural network simulators can operate and promises to improve the efficiency of complex, scientific modeling tasks.

Key facts. Cited by 840 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Oct 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 58; 2022: 102; 2023: 125; 2024: 149; 2025: 184; 2026: 222.

840 papers.

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  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  2. 2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 416
  3. 2021Neural Operator: Learning Maps Between Function Spacescited by 413
  4. 2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 299
  5. 2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
  6. 2022Transformer for Partial Differential Equations' Operator Learningcited by 270
  7. 2021Combinatorial optimization and reasoning with graph neural networkscited by 267
  8. 2022GraphCast: Learning skillful medium-range global weather forecastingcited by 261
  9. 2023WeatherBench 2: A benchmark for the next generation of data-driven global weather modelscited by 227
  10. 2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225
  11. 2023MeshDiffusion: Score-based Generative 3D Mesh Modelingcited by 198
  12. 2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 190
38 more
  1. 2024Poseidon: Efficient Foundation Models for PDEscited by 186
  2. 2022Forecasting Global Weather with Graph Neural Networkscited by 165
  3. 2023Towards Better Dynamic Graph Learning: New Architecture and Unified Librarycited by 154
  4. 2022A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstructioncited by 150
  5. 2022Pre-training via Denoising for Molecular Property Predictioncited by 124
  6. 2023Scalable Transformer for PDE Surrogate Modelingcited by 123
  7. 2021Geometric Deep Learning on Molecular Representationscited by 113
  8. 2021Deep Generative Models in Engineering Design: A Reviewcited by 103
  9. 2021PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEscited by 97
  10. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  11. 2022MultiScale MeshGraphNetscited by 94
  12. 2022Clifford Neural Layers for PDE Modelingcited by 91
  13. 2021Learned Coarse Models for Efficient Turbulence Simulationcited by 90
  14. 2023Multiple Physics Pretraining for Physical Surrogate Modelscited by 90
  15. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  16. 2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equationscited by 87
  17. 2022Predicting Physics in Mesh-reduced Space with Temporal Attentioncited by 82
  18. 2021Scaling Up Graph Neural Networks Via Graph Coarseningcited by 80
  19. 2023Operator Learning with Neural Fields: Tackling PDEs on General Geometriescited by 80
  20. 2025PhysTwin: Physics-Informed Reconstruction and Simulation of Deformable Objects from Videoscited by 78
  21. 2022HOOD: Hierarchical Graphs for Generalized Modelling of Clothing Dynamicscited by 77
  22. 2022AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutionscited by 77
  23. 2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 74
  24. 2026PointWorld: Scaling 3D World Models for In-The-Wild Robotic Manipulationcited by 74
  25. 2022Rediscovering orbital mechanics with machine learningcited by 71
  26. 2022Continuous PDE Dynamics Forecasting with Implicit Neural Representationscited by 71
  27. 2022Equivariant Graph Mechanics Networks with Constraintscited by 67
  28. 2023Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulationcited by 65
  29. 2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 64
  30. 2022Learning Multi-Object Dynamics with Compositional Neural Radiance Fieldscited by 63
  31. 2021Learning Visible Connectivity Dynamics for Cloth Smoothingcited by 61
  32. 2021Encoding physics to learn reaction-diffusion processescited by 61
  33. 2023Graph Neural Networks for temporal graphs: State of the art, open challenges, and opportunitiescited by 60
  34. 2023Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamicscited by 56
  35. 2025FourCastNet 3: A geometric approach to probabilistic machine-learning weather forecasting at scalecited by 56
  36. 2023Eagle: Large-Scale Learning of Turbulent Fluid Dynamics with Mesh Transformerscited by 54
  37. 2022Blending Neural Operators and Relaxation Methods in PDE Numerical Solverscited by 53
  38. 2024AdaptiGraph: Material-Adaptive Graph-Based Neural Dynamics for Robotic Manipulationcited by 52

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