Robust Dynamic Mode Decomposition
Robust Dynamic Mode Decomposition
复制标题
鲁棒动态模式分解
作者：
Amir Hossein Abolmasoumi;M. Netto;L. Mili
本文提出了一种具有统计和数值鲁棒性的鲁棒动态模态分解（RDMD）方法。统计鲁棒性确保在高斯和非高斯概率分布（包括重尾分布）下的估计效率。建议的RDMD是统计稳健的，因为在数据集中的离群值通过投影统计标记和抑制使用Schweppe型Huber广义最大似然估计，最大限度地减少凸Huber成本函数。后者使用迭代重加权最小二乘算法求解，该算法具有比牛顿算法更好的收敛性和数值稳定性。利用动力系统的正则模型进行的数值模拟表明了所提出的RDMD方法的优良性能。结果表明，它优于文献中提出的其他几种方法。
This paper develops a robust dynamic mode decomposition (RDMD) method endowed with statistical and numerical robustness. Statistical robustness ensures estimation efficiency at the Gaussian and non-Gaussian probability distributions, including heavy-tailed distributions. The proposed RDMD is statistically robust because the outliers in the data set are flagged via projection statistics and suppressed using a Schweppe-type Huber generalized maximum-likelihood estimator that minimizes a convex Huber cost function. The latter is solved using the iteratively reweighted least-squares algorithm that is known to exhibit an excellent convergence property and numerical stability than the Newton algorithms. Several numerical simulations using canonical models of dynamical systems demonstrate the excellent performance of the proposed RDMD method. The results reveal that it outperforms several other methods proposed in the literature.
影响因子：
2.1
作者：
Azencot, Omri;Yin, Wotao;Bertozzi, Andrea
通讯作者：
Bertozzi, Andrea