mlsanityData to 7 Oct 2026

Learning Trajectories of Hamiltonian Systems with Neural Networks

arXiv 2204.05077 ↗First posted 11 Apr 2022cs.AI stat.MLcited by 4

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Abstract (arXiv)

Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's equations of motion. Many recent works focus on improving the integration schemes used when training HNNs. In this work, we propose to enhance HNNs with an estimation of a continuous-time trajectory of the modeled system using an additional neural network, called a deep hidden physics model in the literature. We demonstrate that the proposed integration scheme works well for HNNs, especially with low sampling rates, noisy and irregular observations.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 24 of its 32 references that are in the map. First posted on arXiv 11 Apr 2022.

Builds on

24 of 32 references.

References · 24

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12 more
  1. 2021Symplectic Learning for Hamiltonian Neural Networkscited by 35
  2. 2020Nonseparable Symplectic Neural Networkscited by 31
  3. 2022Deconstructing the Inductive Biases of Hamiltonian Neural Networkscited by 31
  4. 2021Which priors matter? Benchmarking models for learning latent dynamicscited by 26
  5. 2020Symplectic Neural Networks in Taylor Series Form for Hamiltonian Systemscited by 24
  6. 2020Sparse Symplectically Integrated Neural Networkscited by 20
  7. 2019Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Datacited by 18
  8. 2020Forecasting Hamiltonian dynamics without canonical coordinatescited by 17
  9. 2021MC-LSTM: Mass-Conserving LSTMcited by 17
  10. 2021HamNet: Conformation-Guided Molecular Representation with Hamiltonian Neural Networkscited by 13
  11. 2021Learning Contact Dynamics using Physically Structured Neural Networkscited by 10
  12. 2021Identifying Physical Law of Hamiltonian Systems via Meta-Learningcited by 8

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Cited by year

Citing papers per year: 2022: 1; 2023: 1; 2024: 2.

4 papers.

  1. 2022Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systemscited by 23
  2. 2024Symplectic Neural Flows for Modeling and Discoverycited by 4
  3. 2024Data-Driven Discovery of Conservation Laws from Trajectories via Neural Deflationcited by 3
  4. 2023Separable Hamiltonian Neural Networkscited by 1