Dai Min, Gao Ting, Lu Yubin, Zheng Yayun, Duan Jinqiao
School of Mathematics and Statistics and Center for Mathematical Science, Huazhong University of Science and Technology, Wuhan 430074, China.
Twitter, 1335 Market St. #900, San Francisco, California 94103, USA.
Chaos. 2020 Nov;30(11):113124. doi: 10.1063/5.0012858.
In recent years, data-driven methods for discovering complex dynamical systems in various fields have attracted widespread attention. These methods make full use of data and have become powerful tools to study complex phenomena. In this work, we propose a framework for detecting dynamical behaviors, such as the maximum likelihood transition path, of stochastic dynamical systems from data. For a stochastic dynamical system, we use the Kramers-Moyal formula to link the sample path data with coefficients in the system, then use the extended sparse identification of nonlinear dynamics method to obtain these coefficients, and finally calculate the maximum likelihood transition path. With two examples of stochastic dynamical systems with additive or multiplicative Gaussian noise, we demonstrate the validity of our framework by reproducing the known dynamical system behavior.
近年来，用于在各个领域发现复杂动力系统的数据驱动方法受到了广泛关注。这些方法充分利用数据，已成为研究复杂现象的有力工具。在这项工作中，我们提出了一个从数据中检测随机动力系统的动力学行为（如最大似然转移路径）的框架。对于一个随机动力系统，我们使用克莱默斯 - 莫亚尔公式将样本路径数据与系统中的系数联系起来，然后使用扩展的非线性动力学稀疏识别方法来获得这些系数，最后计算最大似然转移路径。通过具有加性或乘性高斯噪声的随机动力系统的两个例子，我们通过重现已知的动力系统行为来证明我们框架的有效性。
