We integrate machine learning approaches with nonlinear time series analysis, specifically utilizing recurrence measures to classify various dynamical states emerging from time series. We implement three machine learning algorithms Logistic Regression, Random Forest, and Support Vector Machine for this study. The input features are derived from the recurrence quantification of nonlinear time series and characteristic measures of the corresponding recurrence networks. For training and testing we generate synthetic data from standard nonlinear dynamical systems and evaluate the efficiency and performance of the machine learning algorithms in classifying time series into periodic, chaotic, hyper-chaotic, or noisy categories. Additionally, we explore the significance of input features in the classification scheme and find that the features quantifying the density of recurrence points are the most relevant. Furthermore, we illustrate how the trained algorithms can successfully predict the dynamical states of two variable stars, SX Her and AC Her from the data of their light curves.

翻译：我们将机器学习方法与非线性时间序列分析相结合，具体利用递归度量对时间序列中出现的各种动力学状态进行分类。本研究实施了三种机器学习算法：逻辑回归、随机森林和支持向量机。输入特征来源于非线性时间序列的递归量化分析以及相应递归网络的特征度量。为进行训练和测试，我们生成了标准非线性动力学系统的合成数据，并评估了机器学习算法在将时间序列分类为周期、混沌、超混沌或噪声类别时的效率和性能。此外，我们探讨了输入特征在分类方案中的重要性，发现量化递归点密度的特征最为关键。进一步地，我们展示了训练后的算法如何成功根据两颗变星（SX Her和AC Her）的光变曲线数据预测其动力学状态。