Data to 7 Oct 2026

Learning to Simulate Complex Physics with Graph Networks

arXiv 2002.09405 ↗First posted 21 Feb 2020cs.LG physics.comp-ph stat.MLcited by 867

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Cited by 33 in Diffusion models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our framework---which we term "Graph Network-based Simulators" (GNS)---represents the state of a physical system with particles, expressed as nodes in a graph, and computes dynamics via learned message-passing. Our results show that our model can generalize from single-timestep predictions with thousands of particles during training, to different initial conditions, thousands of timesteps, and at least an order of magnitude more particles at test time. Our model was robust to hyperparameter choices across various evaluation metrics: the main determinants of long-term performance were the number of message-passing steps, and mitigating the accumulation of error by corrupting the training data with noise. Our GNS framework advances the state-of-the-art in learned physical simulation, and holds promise for solving a wide range of complex forward and inverse problems.

Key facts. Cited by 867 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Feb 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2020: 1; 2021: 93; 2022: 143; 2023: 150; 2024: 146; 2025: 163; 2026: 171.

867 papers.

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2021Machine learning accelerated computational fluid dynamicscited by 461
2022Fourier Neural Operator with Learned Deformations for PDEs on General Geometriescited by 416
2022Message Passing Neural PDE Solverscited by 368
2021OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphscited by 328
2024Transolver: A Fast Transformer Solver for PDEs on General Geometriescited by 299
2023Geometry-Informed Neural Operator for Large-Scale 3D PDEscited by 293
2022Transformer for Partial Differential Equations' Operator Learningcited by 270
2021Combinatorial optimization and reasoning with graph neural networkscited by 267
2022GraphCast: Learning skillful medium-range global weather forecastingcited by 261
2022Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphscited by 258
2021Factorized Fourier Neural Operatorscited by 237
2021Geometric and Physical Quantities Improve E(3) Equivariant Message Passingcited by 225

38 more

2021Towards Causal Representation Learningcited by 207
2023NodeFormer: A Scalable Graph Structure Learning Transformer for Node Classificationcited by 207
2023EquiformerV2: Improved Equivariant Transformer for Scaling to Higher-Degree Representationscited by 201
2022Towards Multi-spatiotemporal-scale Generalized PDE Modelingcited by 190
2024Poseidon: Efficient Foundation Models for PDEscited by 186
2021Spherical Message Passing for 3D Graph Networkscited by 166
2024Understanding World or Predicting Future? A Comprehensive Survey of World Modelscited by 161
2023Towards Better Dynamic Graph Learning: New Architecture and Unified Librarycited by 154
2022A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstructioncited by 150
2021Physion: Evaluating Physical Prediction from Vision in Humans and Machinescited by 145
2023PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identificationcited by 145
2023SGFormer: Simplifying and Empowering Transformers for Large-Graph Representationscited by 131
2022Pre-training via Denoising for Molecular Property Predictioncited by 124
2023Scalable Transformer for PDE Surrogate Modelingcited by 123
2021DropGNN: Random Dropouts Increase the Expressiveness of Graph Neural Networkscited by 117
2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 116
2023DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecastingcited by 105
2023EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoningcited by 97
2022MultiScale MeshGraphNetscited by 94
2022Forces are not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulationscited by 92
2024Reconstruction and Simulation of Elastic Objects with Spring-Mass 3D Gaussianscited by 92
2022Clifford Neural Layers for PDE Modelingcited by 91
2021Learned Coarse Models for Efficient Turbulence Simulationcited by 90
2023On the Expressive Power of Geometric Graph Neural Networkscited by 89
2022Trustworthy Graph Neural Networks: Aspects, Methods and Trendscited by 88
2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
2021Long-time integration of parametric evolution equations with physics-informed DeepONetscited by 87
2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equationscited by 87
2022Tutorial on amortized optimizationcited by 83
2022Predicting Physics in Mesh-reduced Space with Temporal Attentioncited by 82
2021Generalization and Robustness Implications in Object-Centric Learningcited by 81
2025PhysTwin: Physics-Informed Reconstruction and Simulation of Deformable Objects from Videoscited by 78
2022One Transformer Can Understand Both 2D & 3D Molecular Datacited by 77
2022HOOD: Hierarchical Graphs for Generalized Modelling of Clothing Dynamicscited by 77
2021DIG: A Turnkey Library for Diving into Graph Deep Learning Researchcited by 76
2022Lie Point Symmetry Data Augmentation for Neural PDE Solverscited by 76
2023Machine learning with data assimilation and uncertainty quantification for dynamical systems: a reviewcited by 74
2026PointWorld: Scaling 3D World Models for In-The-Wild Robotic Manipulationcited by 74

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