mlsanityData to 7 Oct 2026

Learning Symmetries of Classical Integrable Systems

arXiv 1906.04645 ↗First posted 11 Jun 2019physics.comp-ph cs.LGcited by 15

Not on the map. Why?

Abstract (arXiv)

The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel network architectures that parametrize symplectic transformations. We demonstrate the utility of these architectures by learning the structure of integrable models. Our work exemplifies the adaptation of neural transformations to a family constrained by more than the condition of invertibility, which we expect to be a common feature of applications of these methods.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Jun 2019.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 1; 2023: 2; 2024: 3; 2025: 4; 2026: 1.

15 papers.

Sort:

  1. 2021The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learningcited by 9
  2. 2021Locally-symplectic neural networks for learning volume-preserving dynamicscited by 9
  3. 2024Generalized Lagrangian Neural Networkscited by 9
  4. 2021Hamiltonian latent operators for content and motion disentanglement in image sequencescited by 5
  5. 2023The R-mAtrIx Netcited by 4
  6. 2024Noether's razor: Learning Conserved Quantitiescited by 4
  7. 2024Data-Driven Discovery of Conservation Laws from Trajectories via Neural Deflationcited by 3
  8. 2021KAM Theory Meets Statistical Learning Theory: Hamiltonian Neural Networks with Non-Zero Training Losscited by 2
  9. 2022Learning Integrable Dynamics with Action-Angle Networkscited by 2
  10. 2025Learning finite symmetry groups of dynamical systems via equivariance detectioncited by 2
  11. 2025Discovering Symmetries of ODEs by Symbolic Regressioncited by 1
  12. 2025Uncertainties in Physics-informed Inverse Problems: The Hidden Risk in Scientific AIcited by 1
3 more
  1. 2023A charge-preserving method for solving graph neural diffusion networkscited by 0
  2. 2025Deep Learning based discovery of Integrable Systemscited by 0
  3. 2026Attention-based optimizer for symmetry findingcited by 0