mlsanityData to 14 Oct 2026

Learning Neural Hamiltonian Dynamics: A Methodological Overview

arXiv 2203.00128 ↗First posted 28 Feb 2022cs.LGcited by 8

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Abstract (arXiv)

The past few years have witnessed an increased interest in learning Hamiltonian dynamics in deep learning frameworks. As an inductive bias based on physical laws, Hamiltonian dynamics endow neural networks with accurate long-term prediction, interpretability, and data-efficient learning. However, Hamiltonian dynamics also bring energy conservation or dissipation assumptions on the input data and additional computational overhead. In this paper, we systematically survey recently proposed Hamiltonian neural network models, with a special emphasis on methodologies. In general, we discuss the major contributions of these models, and compare them in four overlapping directions: 1) generalized Hamiltonian system; 2) symplectic integration, 3) generalized input form, and 4) extended problem settings. We also provide an outlook of the fundamental challenges and emerging opportunities in this area.

Key facts. Cited by 8 papers in the map (data through 14 Oct 2026). Builds on 29 of its 56 references that are in the map. First posted on arXiv 28 Feb 2022.

Builds on

29 of 56 references.

References · 29

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,908
  3. 2016OpenAI Gymcited by 1,736
  4. 2019Hamiltonian Neural Networkscited by 712
  5. 2017The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problemscited by 583
  6. 2017Solving high-dimensional partial differential equations using deep learningcited by 556
  7. 2016Input Convex Neural Networkscited by 414
  8. 2021Neural Operator: Learning Maps Between Function Spacescited by 414
  9. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 212
  10. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 184
  11. 2019Symplectic Recurrent Neural Networkscited by 150
  12. 2019Hamiltonian Generative Networkscited by 137
17 more
  1. 2019Hamiltonian Graph Networks with ODE Integratorscited by 108
  2. 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 105
  3. 2021Machine learning structure preserving brackets for forecasting irreversible processescited by 52
  4. 2022Dissipative Hamiltonian Neural Networks: Learning Dissipative and Conservative Dynamics Separatelycited by 47
  5. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 44
  6. 2019Differentiable Game Mechanicscited by 43
  7. 2021Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Mapscited by 41
  8. 2020Benchmarking Energy-Conserving Neural Networks for Learning Dynamics from Datacited by 40
  9. 2019Variational Integrator Networks for Physically Structured Embeddingscited by 36
  10. 2020Sparse Symplectically Integrated Neural Networkscited by 20
  11. 2022Learning Hamiltonians of constrained mechanical systemscited by 14
  12. 2021HamNet: Conformation-Guided Molecular Representation with Hamiltonian Neural Networkscited by 13
  13. 2021Symplectic Adjoint Method for Exact Gradient of Neural ODE with Minimal Memorycited by 11
  14. 2021Identifying Physical Law of Hamiltonian Systems via Meta-Learningcited by 8
  15. 2021Weak Form Generalized Hamiltonian Learningcited by 8
  16. 2021Active Learning of Quantum System Hamiltonians yields Query Advantagecited by 3
  17. 2021Neural Symplectic Integrator with Hamiltonian Inductive Bias for the Gravitational N-body Problemcited by 2

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Cited by year

Citing papers per year: 2022: 2; 2023: 3; 2024: 2; 2025: 1.

8 papers.

  1. 2023Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraintscited by 15
  2. 2022Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systemscited by 11
  3. 2022Thermodynamics of learning physical phenomenacited by 10
  4. 2023Physics-Informed Learning Using Hamiltonian Neural Networks with Output Error Noise Modelscited by 5
  5. 2025SlotPi: Physics-informed Object-centric Reasoning Modelscited by 5
  6. 2023Separable Hamiltonian Neural Networkscited by 1
  7. 2024Phase autoencoder for limit-cycle oscillatorscited by 0
  8. 2024Neural Hamilton: Can A.I. Understand Hamiltonian Mechanics?cited by 0