Qiao Mu, Liang Yanchun, Tavares Adriano, Shi Xiaohu
School of Mathematics, Jilin University, Changchun 130021, China.
Department of Industrial Electronics, School of Engineering, University of Minho, 4800-058 Guimares, Portugal.
Entropy (Basel). 2023 Jun 24;25(7):973. doi: 10.3390/e25070973.
Chaotic time series are widely present in practice, but due to their characteristics-such as internal randomness, nonlinearity, and long-term unpredictability-it is difficult to achieve high-precision intermediate or long-term predictions. Multi-layer perceptron (MLP) networks are an effective tool for chaotic time series modeling. Focusing on chaotic time series modeling, this paper presents a generalized degree of freedom approximation method of MLP. We then obtain its Akachi information criterion, which is designed as the loss function for training, hence developing an overall framework for chaotic time series analysis, including phase space reconstruction, model training, and model selection. To verify the effectiveness of the proposed method, it is applied to two artificial chaotic time series and two real-world chaotic time series. The numerical results show that the proposed optimized method is effective to obtain the best model from a group of candidates. Moreover, the optimized models perform very well in multi-step prediction tasks.
混沌时间序列在实际中广泛存在，但由于其具有内部随机性、非线性和长期不可预测性等特点，难以实现高精度的中、长期预测。多层感知器（MLP）网络是混沌时间序列建模的有效工具。本文聚焦于混沌时间序列建模，提出了一种MLP的广义自由度近似方法。然后我们得到了其赤池信息准则，并将其设计为训练的损失函数，从而构建了一个混沌时间序列分析的整体框架，包括相空间重构、模型训练和模型选择。为验证所提方法的有效性，将其应用于两个人造混沌时间序列和两个实际混沌时间序列。数值结果表明，所提优化方法能有效地从一组候选模型中获得最佳模型。此外，优化后的模型在多步预测任务中表现良好。
