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- Title
Extracting parametric dynamics from time-series data.
- Authors
Ma, Huimei; Lu, Xiaofan; Zhang, Linan
- Abstract
In this paper, we present a data-driven regression approach to identify parametric governing equations from time-series data. Iterative computations are performed for each time stamp to first determine if the governing equations to be recovered are time dependent. The results are then used as input data to extract the parametric equations. A combination of the constrained ℓ 1 and ℓ 0 + ℓ 2 optimization problems are used to ensure parsimonious representation of the learned dynamics in the form of parametric differential equations. The method is demonstrated on three canonical dynamics. We show that the proposed method outperforms other sparse-promoting algorithms in identifying parametric differential equations in the low-noise regime in the aspect of accuracy and computation time.
- Subjects
PARAMETRIC equations; DIFFERENTIAL forms; DIFFERENTIAL equations; TIMESTAMPS; TIME series analysis
- Publication
Nonlinear Dynamics, 2023, Vol 111, Issue 16, p15177
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-023-08643-z