mlsanityData to 7 Oct 2026

Hamiltonian Neural Networks with Automatic Symmetry Detection

arXiv 2301.07928 ↗First posted 19 Jan 2023cs.LG math.DScited by 6

Not on the map. Why?

Abstract (arXiv)

Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite the data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we enhance HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach allows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples, a pendulum on a cart and a two-body problem from astrodynamics are considered.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 15 of its 40 references that are in the map. First posted on arXiv 19 Jan 2023.

Builds on

15 of 40 references.

References · 15

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2019Hamiltonian Neural Networkscited by 702
  4. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 536
  5. 2020Lagrangian Neural Networkscited by 388
  6. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  7. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 183
  8. 2019Symplectic Recurrent Neural Networkscited by 148
  9. 2021Automatic Symmetry Discovery with Lie Algebra Convolutional Networkcited by 82
  10. 2021Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Mapscited by 41
  11. 2020Symplectic Gaussian Process Regression of Hamiltonian Flow Mapscited by 17
  12. 2020Learning ODE Models with Qualitative Structure Using Gaussian Processescited by 9
3 more
  1. 2022Discrete Lagrangian Neural Networks with Automatic Symmetry Discoverycited by 5
  2. 2022Learning Interpretable Dynamics from Images of a Freely Rotating 3D Rigid Bodycited by 4
  3. 2022Data-driven discovery of non-Newtonian astronomy via learning non-Euclidean Hamiltoniancited by 1

Built on by

Cited by year (2026 to 7 Oct)

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

6 papers.

  1. 2023Symmetry Preservation in Hamiltonian Systems: Simulation and Learningcited by 6
  2. 2024Symplectic Neural Flows for Modeling and Discoverycited by 4
  3. 2024Training Hamiltonian neural networks without backpropagationcited by 2
  4. 2025Rapid training of Hamiltonian graph networks using random featurescited by 2
  5. 2025Data-efficient Kernel Methods for Learning Hamiltonian Systemscited by 2
  6. 2026DreamSAC: Learning Hamiltonian World Models via Symmetry Explorationcited by 1