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Hamiltonian Graph Networks with ODE Integrators

arXiv 1909.12790 ↗First posted 27 Sep 2019cs.LG physics.comp-phcited by 108

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Abstract (arXiv)

We introduce an approach for imposing physically informed inductive biases in learned simulation models. We combine graph networks with a differentiable ordinary differential equation integrator as a mechanism for predicting future states, and a Hamiltonian as an internal representation. We find that our approach outperforms baselines without these biases in terms of predictive accuracy, energy accuracy, and zero-shot generalization to time-step sizes and integrator orders not experienced during training. This advances the state-of-the-art of learned simulation, and in principle is applicable beyond physical domains.

Key facts. Cited by 108 papers in the map (data through 14 Oct 2026). First posted on arXiv 27 Sep 2019.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 29; 2022: 28; 2023: 21; 2024: 15; 2025: 9; 2026: 6.

108 papers.

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  1. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  2. 2022GraphCast: Learning skillful medium-range global weather forecastingcited by 267
  3. 2021GRAND: Graph Neural Diffusioncited by 258
  4. 2023A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detectioncited by 145
  5. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  6. 2021gradSim: Differentiable simulation for system identification and visuomotor controlcited by 100
  7. 2023EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoningcited by 97
  8. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 92
  9. 2021Beltrami Flow and Neural Diffusion on Graphscited by 84
  10. 2022Lie Point Symmetry Data Augmentation for Neural PDE Solverscited by 77
  11. 2022Equivariant Graph Mechanics Networks with Constraintscited by 68
  12. 2021Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systemscited by 67
38 more
  1. 2022Geometrically Equivariant Graph Neural Networks: A Surveycited by 56
  2. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 52
  3. 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
  4. 2022Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separatelycited by 47
  5. 2021MALI: A memory efficient and reverse accurate integrator for Neural ODEscited by 42
  6. 2021Simulating Continuum Mechanics with Multi-Scale Graph Neural Networkscited by 40
  7. 2022Learning Physical Dynamics with Subequivariant Graph Neural Networkscited by 39
  8. 2024Equivariant Graph Neural Operator for Modeling 3D Dynamicscited by 38
  9. 2022Thermodynamics-informed graph neural networkscited by 33
  10. 2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 31
  11. 2022ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networkscited by 31
  12. 2022Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamicscited by 30
  13. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  14. 2024A Survey of Geometric Graph Neural Networks: Data Structures, Models and Applicationscited by 28
  15. 2021Constraint-based graph network simulatorcited by 27
  16. 2023SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biasescited by 27
  17. 2021Which priors matter? Benchmarking models for learning latent dynamicscited by 26
  18. 2023Reversible and irreversible bracket-based dynamics for deep graph neural networkscited by 26
  19. 2021An Extensible Benchmark Suite for Learning to Simulate Physical Systemscited by 24
  20. 2022Equivariant Graph Hierarchy-Based Neural Networkscited by 24
  21. 2022Learning Articulated Rigid Body Dynamics with Lagrangian Graph Neural Networkcited by 23
  22. 2022Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systemscited by 23
  23. 2021Adaptable Hamiltonian neural networkscited by 21
  24. 2021Combining Physics and Deep Learning to learn Continuous-Time Dynamics Modelscited by 20
  25. 2022Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systemscited by 20
  26. 2022Dimensionless machine learning: Imposing exact units equivariancecited by 17
  27. 2021Group Equivariant Conditional Neural Processescited by 16
  28. 2022Exact conservation laws for neural network integrators of dynamical systemscited by 15
  29. 2023Feature Transportation Improves Graph Neural Networkscited by 15
  30. 2025Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networkscited by 14
  31. 2021HamNet: Conformation-Guided Molecular Representation with Hamiltonian Neural Networkscited by 13
  32. 2021Reasoning-Modulated Representationscited by 13
  33. 2022Machine learning and invariant theorycited by 13
  34. 2022Learning the Dynamics of Particle-based Systems with Lagrangian Graph Neural Networkscited by 12
  35. 2023Node Embedding from Neural Hamiltonian Orbits in Graph Neural Networkscited by 12
  36. 2022Towards Fast Simulation of Environmental Fluid Mechanics with Multi-Scale Graph Neural Networkscited by 11
  37. 2022Constants of motion networkcited by 10
  38. 2023Towards fully covariant machine learningcited by 10

50 most cited of 108 All 108 (JSON)