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Sparse Estimation for Hamiltonian Mechanics

Author

Listed:
  • Yuya Note

    (Department of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan)

  • Masahito Watanabe

    (Department of Aerospace Engineering, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan)

  • Hiroaki Yoshimura

    (Department of Applied Mechanics and Aerospace Engineering, School of Fundamental Science and Engineering, Waseda University, Okubo, Shinjuku-ku, Tokyo 169-8555, Japan)

  • Takaharu Yaguchi

    (Department of Mathematics, Graduate School of Science, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan)

  • Toshiaki Omori

    (Department of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan
    Center for Mathematical and Data Sciences, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan)

Abstract

Estimating governing equations from observed time-series data is crucial for understanding dynamical systems. From the perspective of system comprehension, the demand for accurate estimation and interpretable results has been particularly emphasized. Herein, we propose a novel data-driven method for estimating the governing equations of dynamical systems based on machine learning with high accuracy and interpretability. The proposed method enhances the estimation accuracy for dynamical systems using sparse modeling by incorporating physical constraints derived from Hamiltonian mechanics. Unlike conventional approaches used for estimating governing equations for dynamical systems, we employ a sparse representation of Hamiltonian, allowing for the estimation. Using noisy observational data, the proposed method demonstrates a capability to achieve accurate parameter estimation and extraction of essential nonlinear terms. In addition, it is shown that estimations based on energy conservation principles exhibit superior accuracy in long-term predictions. These results collectively indicate that the proposed method accurately estimates dynamical systems while maintaining interpretability.

Suggested Citation

  • Yuya Note & Masahito Watanabe & Hiroaki Yoshimura & Takaharu Yaguchi & Toshiaki Omori, 2024. "Sparse Estimation for Hamiltonian Mechanics," Mathematics, MDPI, vol. 12(7), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:974-:d:1363550
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    References listed on IDEAS

    as
    1. Kevin Course & Prasanth B. Nair, 2023. "State estimation of a physical system with unknown governing equations," Nature, Nature, vol. 622(7982), pages 261-267, October.
    2. Ryosuke X. Oyanagi & Tatsu Kuwatani & Toshiaki Omori, 2021. "Exploration of nonlinear parallel heterogeneous reaction pathways through Bayesian variable selection," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 94(2), pages 1-12, February.
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