mlsanityData to 7 Oct 2026

Identifying Physical Law of Hamiltonian Systems via Meta-Learning

arXiv 2102.11544 ↗First posted 23 Feb 2021cs.LG physics.comp-phcited by 8

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Abstract (arXiv)

Hamiltonian mechanics is an effective tool to represent many physical processes with concise yet well-generalized mathematical expressions. A well-modeled Hamiltonian makes it easy for researchers to analyze and forecast many related phenomena that are governed by the same physical law. However, in general, identifying a functional or shared expression of the Hamiltonian is very difficult. It requires carefully designed experiments and the researcher's insight that comes from years of experience. We propose that meta-learning algorithms can be potentially powerful data-driven tools for identifying the physical law governing Hamiltonian systems without any mathematical assumptions on the representation, but with observations from a set of systems governed by the same physical law. We show that a well meta-trained learner can identify the shared representation of the Hamiltonian by evaluating our method on several types of physical systems with various experimental settings.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 34 of its 51 references that are in the map. First posted on arXiv 23 Feb 2021.

Builds on

34 of 51 references.

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22 more
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Cited by year

Citing papers per year: 2021: 2; 2022: 4; 2023: 1; 2024: 0; 2025: 1.

8 papers.

  1. 2021Physics-Guided Deep Learning for Dynamical Systems: A Surveycited by 43
  2. 2021LEADS: Learning Dynamical Systems that Generalize Across Environmentscited by 39
  3. 2022Enhancing the Inductive Biases of Graph Neural ODE for Modeling Dynamical Systemscited by 20
  4. 2022Learning Neural Hamiltonian Dynamics: A Methodological Overviewcited by 8
  5. 2022Learning Trajectories of Hamiltonian Systems with Neural Networkscited by 4
  6. 2022Towards Cross Domain Generalization of Hamiltonian Representation via Meta Learningcited by 3
  7. 2023Graph Neural Stochastic Differential Equations for Learning Brownian Dynamicscited by 2
  8. 2025Meta-learning Structure-Preserving Dynamicscited by 2