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Forecasting Hamiltonian dynamics without canonical coordinates

arXiv 2010.15201 ↗First posted 28 Oct 2020cs.LG nlin.CDcited by 17

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Abstract (arXiv)

Conventional neural networks are universal function approximators, but because they are unaware of underlying symmetries or physical laws, they may need impractically many training data to approximate nonlinear dynamics. Recently introduced Hamiltonian neural networks can efficiently learn and forecast dynamical systems that conserve energy, but they require special inputs called canonical coordinates, which may be hard to infer from data. Here we significantly expand the scope of such networks by demonstrating a simple way to train them with any set of generalised coordinates, including easily observable ones.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Oct 2020.

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Citing papers per year: 2021: 5; 2022: 3; 2023: 2; 2024: 1; 2025: 3; 2026: 3.

17 papers.

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  1. 2021Which priors matter? Benchmarking models for learning latent dynamicscited by 26
  2. 2021Adaptable Hamiltonian neural networkscited by 21
  3. 2025Stable Port-Hamiltonian Neural Networkscited by 13
  4. 2021Machine-Learning Non-Conservative Dynamics for New-Physics Detectioncited by 10
  5. 2023Data-Driven Identification of Quadratic Representations for Nonlinear Hamiltonian Systems using Weakly Symplectic Liftingscited by 6
  6. 2025Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Spacecited by 6
  7. 2021SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Visioncited by 5
  8. 2022Learning Trajectories of Hamiltonian Systems with Neural Networkscited by 4
  9. 2021Learning Hamiltonian dynamics by reservoir computercited by 2
  10. 2023Learning unidirectional coupling using echo-state networkcited by 2
  11. 2025Unified Spatiotemporal Physics-Informed Learning (USPIL): A Framework for Modeling Complex Predator-Prey Dynamicscited by 1
  12. 2026Machine Learning Hamiltonian Dynamical Systems with Sparse and Noisy Datacited by 1
5 more
  1. 2022Neuronal diversity can improve machine learning for physics and beyondcited by 0
  2. 2022Generating extreme quantum scattering in graphene with machine learningcited by 0
  3. 2024Unsupervised Learning of Hybrid Latent Dynamics: A Learn-to-Identify Frameworkcited by 0
  4. 2026Recovering Sharp Conductivity Features in the Finite-Data Calder'on Problem with Physics-Informed Neural Networkscited by 0
  5. 2026Gravitational Duals from Equations of State II: Large Hierarchies and False Vacuacited by 0