MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi'an 710072, China.
Chaos. 2023 Jan;33(1):013103. doi: 10.1063/5.0130526.
This work develops a regularized least absolute deviation-based sparse identification of dynamics (RLAD-SID) method to address outlier problems in the classical metric-based loss function and the sparsity constraint framework. Our method uses absolute derivation loss as a substitute of Euclidean loss. Moreover, a corresponding computationally efficient optimization algorithm is derived on the basis of the alternating direction method of multipliers due to the non-smoothness of both the new proposed loss function and the regularization term. Numerical experiments are performed to evaluate the effectiveness of RLAD-SID using several exemplary nonlinear dynamical systems, such as the van der Pol equation, the Lorenz system, and the 1D discrete logistic map. Furthermore, detailed numerical comparisons are provided with other existing methods in metric-based sparse regression. Numerical results demonstrate that (1) RLAD-SID shows significant robustness toward a large outlier and (2) RLAD-SID can be seen as a particular metric-based sparse regression strategy that exhibits the effectiveness of the metric-based sparse regression framework for solving outlier problems in a dynamical system identification.
本工作提出了一种基于正则化最小绝对值偏差的稀疏动态辨识（RLAD-SID）方法，以解决经典基于度量的损失函数和稀疏约束框架中的异常值问题。我们的方法使用绝对值导数损失代替欧几里得损失。此外，由于新提出的损失函数和正则化项的非光滑性，基于乘子交替方向法推导出了相应的计算高效的优化算法。使用几个典型的非线性动力系统，如范德波尔方程、洛伦兹系统和 1D 离散 logistic 映射，进行数值实验来评估 RLAD-SID 的有效性。此外，还与基于度量的稀疏回归中的其他现有方法进行了详细的数值比较。数值结果表明：(1) RLAD-SID 对大异常值具有显著的鲁棒性；(2) RLAD-SID 可以看作是一种基于度量的稀疏回归策略，它展示了基于度量的稀疏回归框架在解决动力系统辨识中异常值问题的有效性。
