# Forecasting Hamiltonian dynamics without canonical coordinates

arXiv: https://arxiv.org/abs/2010.15201 · HTML: https://mlsanity.com/paper/2010.15201/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2020.

## Built on by (most cited first, 17 of 17)

- [Which priors matter? Benchmarking models for learning latent dynamics](https://mlsanity.com/paper/2111.05458/) (2021)
- [Adaptable Hamiltonian neural networks](https://mlsanity.com/paper/2102.13235/) (2021)
- [Stable Port-Hamiltonian Neural Networks](https://mlsanity.com/paper/2502.02480/) (2025)
- [Machine-Learning Non-Conservative Dynamics for New-Physics Detection](https://mlsanity.com/paper/2106.00026/) (2021)
- [Data-Driven Identification of Quadratic Representations for Nonlinear Hamiltonian Systems using Weakly Symplectic Liftings](https://mlsanity.com/paper/2308.01084/) (2023)
- [Efficient PINNs via Multi-Head Unimodular Regularization of the Solutions Space](https://mlsanity.com/paper/2501.12116/) (2025)
- [SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Vision](https://mlsanity.com/paper/2111.05986/) (2021)
- [Learning Trajectories of Hamiltonian Systems with Neural Networks](https://mlsanity.com/paper/2204.05077/) (2022)
- [Learning Hamiltonian dynamics by reservoir computer](https://mlsanity.com/paper/2104.14474/) (2021)
- [Learning unidirectional coupling using echo-state network](https://mlsanity.com/paper/2303.13562/) (2023)
- [Unified Spatiotemporal Physics-Informed Learning (USPIL): A Framework for Modeling Complex Predator-Prey Dynamics](https://mlsanity.com/paper/2509.13425/) (2025)
- [Machine Learning Hamiltonian Dynamical Systems with Sparse and Noisy Data](https://mlsanity.com/paper/2604.17470/) (2026)
- [Neuronal diversity can improve machine learning for physics and beyond](https://mlsanity.com/paper/2204.04348/) (2022)
- [Generating extreme quantum scattering in graphene with machine learning](https://mlsanity.com/paper/2212.06929/) (2022)
- [Unsupervised Learning of Hybrid Latent Dynamics: A Learn-to-Identify Framework](https://mlsanity.com/paper/2403.08194/) (2024)
- [Recovering Sharp Conductivity Features in the Finite-Data Calder'on Problem with Physics-Informed Neural Networks](https://mlsanity.com/paper/2606.28158/) (2026)
- [Gravitational Duals from Equations of State II: Large Hierarchies and False Vacua](https://mlsanity.com/paper/2606.30117/) (2026)

## 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.