AlMomani Abd AlRahman R, Sun Jie, Bollt Erik
Electrical and Computer Engineering, Clarkson University, Potsdam, New York 13699, USA.
Theory Lab, Hong Kong Research Centre of Huawei Tech, Hong Kong 852, China.
Chaos. 2020 Jan;30(1):013107. doi: 10.1063/1.5133386.
In this work, we developed a nonlinear System Identification (SID) method that we called Entropic Regression. Our method adopts an information-theoretic measure for the data-driven discovery of the underlying dynamics. Our method shows robustness toward noise and outliers, and it outperforms many of the current state-of-the-art methods. Moreover, the method of Entropic Regression overcomes many of the major limitations of the current methods such as sloppy parameters, diverse scale, and SID in high-dimensional systems such as complex networks. The use of information-theoretic measures in entropic regression has unique advantages, due to the Asymptotic Equipartition Property of probability distributions, that outliers and other low-occurrence events are conveniently and intrinsically de-emphasized as not-typical, by definition. We provide a numerical comparison with the current state-of-the-art methods in sparse regression, and we apply the methods to different chaotic systems such as the Lorenz System, the Kuramoto-Sivashinsky equations, and the Double-Well Potential.
在这项工作中，我们开发了一种非线性系统识别（SID）方法，我们称之为熵回归。我们的方法采用一种信息论度量来通过数据驱动发现潜在动力学。我们的方法对噪声和异常值具有鲁棒性，并且优于许多当前的先进方法。此外，熵回归方法克服了当前方法的许多主要局限性，如参数不精确、尺度多样以及在复杂网络等高维系统中的系统识别问题。由于概率分布的渐近均分性质，在熵回归中使用信息论度量具有独特优势，即从定义上讲，异常值和其他低发生事件被方便且内在地视为非典型情况而被弱化。我们与稀疏回归中的当前先进方法进行了数值比较，并将这些方法应用于不同的混沌系统，如洛伦兹系统、Kuramoto - Sivashinsky方程和双势阱。
