Sparse Estimation for Hamiltonian Mechanics

HANDLE オープンアクセス

抄録

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.

収録刊行物

詳細情報 詳細情報について

  • CRID
    1050862931498149888
  • ISSN
    22277390
  • HANDLE
    20.500.14094/0100488748
  • 本文言語コード
    en
  • 資料種別
    journal article
  • データソース種別
    • IRDB

問題の指摘

ページトップへ