mlsanityData to 7 Oct 2026

Learning Energy Conserving Dynamics Efficiently with Hamiltonian Gaussian Processes

arXiv 2303.01925 ↗First posted 3 Mar 2023stat.ML cs.LGcited by 6

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Abstract (arXiv)

Hamiltonian mechanics is one of the cornerstones of natural sciences. Recently there has been significant interest in learning Hamiltonian systems in a free-form way directly from trajectory data. Previous methods have tackled the problem of learning from many short, low-noise trajectories, but learning from a small number of long, noisy trajectories, whilst accounting for model uncertainty has not been addressed. In this work, we present a Gaussian process model for Hamiltonian systems with efficient decoupled parameterisation, and introduce an energy-conserving shooting method that allows robust inference from both short and long trajectories. We demonstrate the method's success in learning Hamiltonian systems in various data settings.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 26 of its 51 references that are in the map. First posted on arXiv 3 Mar 2023.

Builds on

26 of 51 references.

References · 26

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14 more
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Cited by year (2026 to 7 Oct)

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

6 papers.

  1. 2024Noether's razor: Learning Conserved Quantitiescited by 4
  2. 2025Data-efficient Kernel Methods for Learning Hamiltonian Systemscited by 2
  3. 2025Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Datacited by 1
  4. 2025Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processescited by 1
  5. 2026Structure-Preserving Gaussian Processes Via Discrete Euler-Lagrange Equationscited by 0
  6. 2026Structure-preserving uncertainty quantification for GENERIC dynamicscited by 0