Barrio Roberto, Lozano Álvaro, Mayora-Cebollero Ana, Mayora-Cebollero Carmen, Miguel Antonio, Ortega Alfonso, Serrano Sergio, Vigara Rubén
Departamento de Matemática Aplicada and IUMA, Computational Dynamics group, Universidad de Zaragoza, Zaragoza E-50009, Spain.
Departamento de Matemáticas and IUMA, Computational Dynamics group, Universidad de Zaragoza, Zaragoza E-50009, Spain.
Chaos. 2023 Jul 1;33(7). doi: 10.1063/5.0143876.
In this article, we study how a chaos detection problem can be solved using Deep Learning techniques. We consider two classical test examples: the Logistic map as a discrete dynamical system and the Lorenz system as a continuous dynamical system. We train three types of artificial neural networks (multi-layer perceptron, convolutional neural network, and long short-term memory cell) to classify time series from the mentioned systems into regular or chaotic. This approach allows us to study biparametric and triparametric regions in the Lorenz system due to their low computational cost compared to traditional techniques.
在本文中，我们研究如何使用深度学习技术解决混沌检测问题。我们考虑两个经典的测试示例：作为离散动力系统的逻辑斯谛映射和作为连续动力系统的洛伦兹系统。我们训练三种类型的人工神经网络（多层感知器、卷积神经网络和长短期记忆单元），以将来自上述系统的时间序列分类为规则或混沌。与传统技术相比，这种方法由于其较低的计算成本，使我们能够研究洛伦兹系统中的双参数和三参数区域。
