Identification of nonlinear dynamical systems has been popularized by sparse identification of the nonlinear dynamics (SINDy) via the sequentially thresholded least squares (STLS) algorithm. Many extensions SINDy have emerged in the literature to deal with experimental data which are finite in length and noisy. Recently, the computationally intensive method of ensembling bootstrapped SINDy models (E-SINDy) was proposed for model identification, handling finite, highly noisy data. While the extensions of SINDy are numerous, their sparsity-promoting estimators occasionally provide sparse approximations of the dynamics as opposed to exact recovery. Furthermore, these estimators suffer under multicollinearity, e.g. the irrepresentable condition for the Lasso. In this paper, we demonstrate that the Trimmed Lasso for robust identification of models (TRIM) can provide exact recovery under more severe noise, finite data, and multicollinearity as opposed to E-SINDy. Additionally, the computational cost of TRIM is asymptotically equal to STLS since the sparsity parameter of the TRIM can be solved efficiently by convex solvers. We compare these methodologies on challenging nonlinear systems, specifically the Lorenz 63 system, the Bouc Wen oscillator from the nonlinear dynamics benchmark of No\"el and Schoukens, 2016, and a time delay system describing tool cutting dynamics. This study emphasizes the comparisons between STLS, reweighted $\ell_1$ minimization, and Trimmed Lasso in identification with respect to problems faced by practitioners: the problem of finite and noisy data, the performance of the sparse regression of when the library grows in dimension (multicollinearity), and automatic methods for choice of regularization parameters.

该研究介绍了对非线性动力系统进行识别的方法，包括稀疏识别非线性动力学（SINDy）、顺序阈值最小二乘（STLS）算法、基于模型集成的SINDy模型（E-SINDy）、用于鲁棒模型识别的修剪Lasso（TRIM）等方面的研究。通过对Lorenz 63系统、Bouc Wen振荡器和描述刀具切割动力学的时间延迟系统的比较，突出了STLS、修剪Lasso等在面对实践中遇到的问题（例如有限且带噪声的数据、当库增大时的稀疏回归性能以及正则化参数的自动选择方法）方面的优劣。

通过修剪Lasso精确识别非线性动力系统