Mangiarotti Sylvain, Huc Mireille
Centre d'Études Spatiales de la Biosphère, UPS-CNRS-CNES-INRA-IRD, Observatoire Midi-Pyrénées, 18 avenue Édouard Belin, 31401 Toulouse, France.
Chaos. 2019 Feb;29(2):023133. doi: 10.1063/1.5081448.
The aim of the present work is to investigate the possibility to retrieve the original sets of dynamical equations directly from observational time series when all the system variables are observed. Time series are generated from chosen dynamical systems, and the global modeling technique is applied to obtain optimal models of parsimonious structure from these time series. The obtained models are then compared to the original equations to investigate if the original equations can be retrieved. Twenty-seven systems are considered in the study. The Rössler system is first used to illustrate the procedure and then to test the robustness of the approach under various conditions, varying the initial conditions, time series length, dynamical regimes, subsampling (and resampling), measurement noise, and dynamical perturbations. The other 26 systems (four rational ones included) of various algebraic structures, sizes, and dimensions are then considered to investigate the generality of the approach.
本研究的目的是探讨当所有系统变量都可观测时，直接从观测时间序列中恢复原始动力学方程组的可能性。时间序列由选定的动力系统生成，并应用全局建模技术从这些时间序列中获得具有简约结构的最优模型。然后将得到的模型与原始方程进行比较，以研究是否能够恢复原始方程。本研究考虑了27个系统。首先使用罗塞尔系统来说明该过程，然后在各种条件下测试该方法的稳健性，包括改变初始条件、时间序列长度、动力学状态、子采样（和重采样）、测量噪声和动力学扰动。接着考虑其他26个具有不同代数结构、规模和维度的系统（包括4个有理系统），以研究该方法的通用性。
