mlsanityData to 7 Oct 2026

Learning Hamiltonian neural Koopman operator and simultaneously sustaining and discovering conservation law

arXiv 2406.02154 ↗First posted 4 Jun 2024math-ph cs.LG math.MPcited by 7

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Abstract (arXiv)

Accurately finding and predicting dynamics based on the observational data with noise perturbations is of paramount significance but still a major challenge presently. Here, for the Hamiltonian mechanics, we propose the Hamiltonian Neural Koopman Operator (HNKO), integrating the knowledge of mathematical physics in learning the Koopman operator, and making it automatically sustain and even discover the conservation laws. We demonstrate the outperformance of the HNKO and its extension using a number of representative physical systems even with hundreds or thousands of freedoms. Our results suggest that feeding the prior knowledge of the underlying system and the mathematical theory appropriately to the learning framework can reinforce the capability of machine learning in solving physical problems.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 28 of its 60 references that are in the map. First posted on arXiv 4 Jun 2024.

Builds on

28 of 60 references.

References · 28

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2019Hamiltonian Neural Networkscited by 702
  3. 2017Deep learning for universal linear embeddings of nonlinear dynamicscited by 491
  4. 2021Physics-informed neural networks (PINNs) for fluid mechanics: A reviewcited by 470
  5. 2020Lagrangian Neural Networkscited by 388
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  7. 2021Physics-informed neural networks with hard constraints for inverse designcited by 277
  8. 2021Modern Koopman Theory for Dynamical Systemscited by 269
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  10. 2019Symplectic ODE-Net: Learning Hamiltonian Dynamics with Controlcited by 183
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16 more
  1. 2018Discovering physical concepts with neural networkscited by 117
  2. 2019Hamiltonian Graph Networks with ODE Integratorscited by 107
  3. 2019Physics-Informed Neural Networks for Power Systemscited by 80
  4. 2019Trivializations for Gradient-Based Optimization on Manifoldscited by 78
  5. 2020AI Poincar'e: Machine Learning Conservation Laws from Trajectoriescited by 77
  6. 2021Stiff Neural Ordinary Differential Equationscited by 77
  7. 2021Physics-informed neural networks for solving Reynolds-averaged Navierunicodex2013Stokes equationscited by 68
  8. 2020STEER: Simple Temporal Regularization For Neural ODEscited by 58
  9. 2021HyperPINN: Learning parameterized differential equations with physics-informed hypernetworkscited by 38
  10. 2021Neural Delay Differential Equationscited by 26
  11. 2021Adaptable Hamiltonian neural networkscited by 21
  12. 2017Machine Learning Topological Invariants with Neural Networkscited by 19
  13. 2018Discovering conservation laws from data for controlcited by 14
  14. 2022Discovering Conservation Laws using Optimal Transport and Manifold Learningcited by 12
  15. 2022Neural Stochastic Controlcited by 8
  16. 2022Neural Piecewise-Constant Delay Differential Equationscited by 4

Built on by

Cited by year (2026 to 7 Oct)

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

7 papers.

  1. 2025Interpretable Machine Learning in Physics: A Reviewcited by 11
  2. 2024Governing equation discovery of a complex system from snapshotscited by 6
  3. 2025Augmented Invertible Koopman Autoencoder for long-term time series forecastingcited by 3
  4. 2025Learning Hamiltonian Dynamics at Scale: A Differential-Geometric Approachcited by 2
  5. 2025Invertible Koopman neural operator for data-driven modeling of partial differential equationscited by 1
  6. 2026K-U-KAN: Koopman-Enhanced U-KAN for 3D Dental Reconstruction from a Single Panoramic X-ray Radiographcited by 0
  7. 2026Variational Augmented Invertible Koopman Autoencoder for probabilistic time series forecastingcited by 0