mlsanityData to 7 Oct 2026

Hamiltonian Neural Networks

arXiv 1906.01563 ↗First posted 4 Jun 2019cs.NEcited by 702

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Cited by 21 in World models, but placed by its own abstract, which didn’t fit.

Abstract (arXiv)

Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models that learn and respect exact conservation laws in an unsupervised manner. We evaluate our models on problems where conservation of energy is important, including the two-body problem and pixel observations of a pendulum. Our model trains faster and generalizes better than a regular neural network. An interesting side effect is that our model is perfectly reversible in time.

Key facts. Cited by 702 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Jun 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2020: 2; 2021: 112; 2022: 103; 2023: 91; 2024: 95; 2025: 118; 2026: 181.

702 papers.

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  1. 2021Characterizing possible failure modes in physics-informed neural networkscited by 632
  2. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 185
  3. 2021DC3: A learning method for optimization with hard constraintscited by 181
  4. 2021Scalars are universal: Equivariant machine learning, structured like classical physicscited by 127
  5. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 116
  6. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 103
  7. 2021gradSim: Differentiable simulation for system identification and visuomotor controlcited by 100
  8. 2022Approximately Equivariant Networks for Imperfectly Symmetric Dynamicscited by 95
  9. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  10. 2021Chaos as an interpretable benchmark for forecasting and data-driven modellingcited by 87
  11. 2024ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEscited by 78
  12. 2022Lie Point Symmetry Data Augmentation for Neural PDE Solverscited by 76
38 more
  1. 2021Residual Pathway Priors for Soft Equivariance Constraintscited by 74
  2. 2021Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systemscited by 66
  3. 2021Geometric Deep Learning and Equivariant Neural Networkscited by 64
  4. 2022When Physics Meets Machine Learning: A Survey of Physics-Informed Machine Learningcited by 64
  5. 2021Scientific Machine Learning Benchmarkscited by 60
  6. 2021Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modelingcited by 59
  7. 2021A Dynamical System Perspective for Lipschitz Neural Networkscited by 59
  8. 2021UnICORNN: A recurrent model for learning very long time dependenciescited by 56
  9. 2021Robot Learning from Randomized Simulations: A Reviewcited by 56
  10. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 51
  11. 2021One-Shot Transfer Learning of Physics-Informed Neural Networkscited by 49
  12. 2022Generalizing to New Physical Systems via Context-Informed Dynamics Modelcited by 49
  13. 2021Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progressioncited by 48
  14. 2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 48
  15. 2025Physics-Constrained Flow Matching: Sampling Generative Models with Hard Constraintscited by 46
  16. 2023Parallelizing non-linear sequential models over the sequence lengthcited by 45
  17. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
  18. 2021Noisy Recurrent Neural Networkscited by 42
  19. 2021Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Mapscited by 41
  20. 2021Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modelingcited by 40
  21. 2023Generative Adversarial Symmetry Discoverycited by 40
  22. 2025NewtonGen: Physics-Consistent and Controllable Text-to-Video Generation via Neural Newtonian Dynamicscited by 40
  23. 2021Continuous-Time Model-Based Reinforcement Learningcited by 39
  24. 2021Meta-Learning Dynamics Forecasting Using Task Inferencecited by 37
  25. 2021Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learningcited by 37
  26. 2021Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Controlcited by 37
  27. 2023Geometric Clifford Algebra Networkscited by 37
  28. 2021Symplectic Learning for Hamiltonian Neural Networkscited by 35
  29. 2024Parameterized Physics-informed Neural Networks for Parameterized PDEscited by 35
  30. 2022Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systemscited by 34
  31. 2021Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Modelscited by 33
  32. 2021Graph Neural Networks Accelerated Molecular Dynamicscited by 33
  33. 2021Enforcing Policy Feasibility Constraints through Differentiable Projection for Energy Optimizationcited by 31
  34. 2022Deconstructing the Inductive Biases of Hamiltonian Neural Networkscited by 31
  35. 2022Thermodynamics-informed graph neural networkscited by 31
  36. 2024Neural Material Adaptor for Visual Grounding of Intrinsic Dynamicscited by 30
  37. 2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 29
  38. 2022Learning continuous models for continuous physicscited by 28

50 most cited of 702 All 702 (JSON)