# Learning Hamiltonians of constrained mechanical systems

arXiv: https://arxiv.org/abs/2201.13254 · HTML: https://mlsanity.com/paper/2201.13254/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 31 Jan 2022.

## Builds on (most cited first, 7 of 7)

- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control](https://mlsanity.com/paper/1909.12077/) (2019)
- [Symplectic Recurrent Neural Networks](https://mlsanity.com/paper/1909.13334/) (2019)
- [Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints](https://mlsanity.com/paper/2010.13581/) (2020)
- [Symplectic Learning for Hamiltonian Neural Networks](https://mlsanity.com/paper/2106.11753/) (2021)
- [Equivariant neural networks for inverse problems](https://mlsanity.com/paper/2102.11504/) (2021)
- [Sparse Symplectically Integrated Neural Networks](https://mlsanity.com/paper/2006.12972/) (2020)

## Built on by (most cited first, 14 of 14)

- [Pseudo-Hamiltonian Neural Networks with State-Dependent External Forces](https://mlsanity.com/paper/2206.02660/) (2022)
- [FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantities](https://mlsanity.com/paper/2210.00272/) (2022)
- [Dynamical systems' based neural networks](https://mlsanity.com/paper/2210.02373/) (2022)
- [Pseudo-Hamiltonian neural networks for learning partial differential equations](https://mlsanity.com/paper/2304.14374/) (2023)
- [Learning Neural Hamiltonian Dynamics: A Methodological Overview](https://mlsanity.com/paper/2203.00128/) (2022)
- [A Riemannian Framework for Learning Reduced-order Lagrangian Dynamics](https://mlsanity.com/paper/2410.18868/) (2024)
- [Learning mechanical systems from real-world data using discrete forced Lagrangian dynamics](https://mlsanity.com/paper/2505.20370/) (2025)
- [Fixed-kinetic Neural Hamiltonian Flows for enhanced interpretability and reduced complexity](https://mlsanity.com/paper/2302.01955/) (2023)
- [Learning Dynamical Systems from Noisy Data with Inverse-Explicit Integrators](https://mlsanity.com/paper/2306.03548/) (2023)
- [Symplectic Neural Networks Based on Dynamical Systems](https://mlsanity.com/paper/2408.09821/) (2024)
- [Symplectic Neural Flows for Modeling and Discovery](https://mlsanity.com/paper/2412.16787/) (2024)
- [Predictions Based on Pixel Data: Insights from PDEs and Finite Differences](https://mlsanity.com/paper/2305.00723/) (2023)
- [Hypothesis-driven construction of mesoscopic dynamics](https://mlsanity.com/paper/2605.16211/) (2026)
- [Learning piecewise-smooth dynamical systems](https://mlsanity.com/paper/2608.19785/) (2026)

## Abstract (arXiv)

Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined by one scalar function, the Hamiltonian. The solution trajectories are often constrained to evolve on a submanifold of a linear vector space. In this work, we propose new approaches for the accurate approximation of the Hamiltonian function of constrained mechanical systems given sample data information of their solutions. We focus on the importance of the preservation of the constraints in the learning strategy by using both explicit Lie group integrators and other classical schemes.