mlsanityData to 7 Oct 2026

Learning Hamiltonians of constrained mechanical systems

arXiv 2201.13254 ↗First posted 31 Jan 2022math.NA cs.LG cs.NAcited by 14

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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.

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

Builds on

7 of 29 references.

References · 7

  1. 2019Hamiltonian Neural Networkscited by 702
  2. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 183
  3. 2019Symplectic Recurrent Neural Networkscited by 148
  4. 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 102
  5. 2021Symplectic Learning for Hamiltonian Neural Networkscited by 35
  6. 2021Equivariant neural networks for inverse problemscited by 29
  7. 2020Sparse Symplectically Integrated Neural Networkscited by 20

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 4; 2023: 4; 2024: 3; 2025: 1; 2026: 2.

14 papers.

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  1. 2022Pseudo-Hamiltonian Neural Networks with State-Dependent External Forcescited by 17
  2. 2022FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantitiescited by 12
  3. 2022Dynamical systems' based neural networkscited by 10
  4. 2023Pseudo-Hamiltonian neural networks for learning partial differential equationscited by 10
  5. 2022Learning Neural Hamiltonian Dynamics: A Methodological Overviewcited by 8
  6. 2024A Riemannian Framework for Learning Reduced-order Lagrangian Dynamicscited by 7
  7. 2025Learning mechanical systems from real-world data using discrete forced Lagrangian dynamicscited by 6
  8. 2023Fixed-kinetic Neural Hamiltonian Flows for enhanced interpretability and reduced complexitycited by 4
  9. 2023Learning Dynamical Systems from Noisy Data with Inverse-Explicit Integratorscited by 4
  10. 2024Symplectic Neural Networks Based on Dynamical Systemscited by 4
  11. 2024Symplectic Neural Flows for Modeling and Discoverycited by 4
  12. 2023Predictions Based on Pixel Data: Insights from PDEs and Finite Differencescited by 2
2 more
  1. 2026Hypothesis-driven construction of mesoscopic dynamicscited by 1
  2. 2026Learning piecewise-smooth dynamical systemscited by 0