Data-driven discovery of linear dynamical systems from noisy data

Wang, YaSen; Yuan, Ye; Fang, HuaZhen; Ding, Han

doi:10.1007/s11431-023-2520-6

Cited by 2 publications

(1 citation statement)

References 41 publications

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“…Recent advances in measurement and information technologies have improved the quantity and quality of available data. Owing to these improvements, data-driven approaches have attracted attention as a method to extract the system structure and features from data [1][2][3]. Notably, the extraction of dynamical systems from time-series data is challenging in various fields, encompassing natural sciences, such as earth science [4,5] and neuroscience [6,7], and engineering domains, such as fluid engineering [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Sparse Estimation for Hamiltonian Mechanics

Note,

Watanabe,

Yoshimura

et al. 2024

Mathematics

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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.

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