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.

通过机器学习方法和非线性时间序列分析，我们利用循环度量对时间序列产生的各种动力学状态进行分类，并使用逻辑回归、随机森林和支持向量机这三种机器学习算法进行研究。我们的输入特征来自非线性时间序列的循环量化和相应循环网络的特征度量。通过从标准非线性动力学系统生成合成数据以进行训练和测试，我们评估了机器学习算法在将时间序列分类为周期性、混沌、超混沌或噪声分类中的效率和性能。此外，我们探索了分类方案中输入特征的重要性，并发现量化循环点密度的特征最相关。此外，我们还展示了经过训练的算法如何成功预测两颗变量星 SX Her 和 AC Her 的动力学状态，使用它们的光曲线数据。