Departamento de Física, Universidade Federal do Paraná, 81531-990 Curitiba, Brazil.
Departamento de Informática, Universidade Federal do Paraná, 81531-990 Curitiba, Brazil.
Chaos. 2020 May;30(5):053101. doi: 10.1063/5.0003892.
In this paper, we use machine learning strategies aiming to predict chaotic time series obtained from the Lorenz system. Such strategies prove to be successful in predicting the evolution of dynamical variables over a short period of time. Transitions between the regimes and their duration can be predicted with great accuracy by means of counting and classification strategies, for which we train multi-layer perceptron ensembles. Even for the longest regimes the occurrences and duration can be predicted. We also show the use of an echo state network to generate data of the time series with an accuracy of up to a few hundreds time steps. The ability of the classification technique to predict the regime duration of more than 11 oscillations corresponds to around 10 Lyapunov times.
在本文中，我们使用机器学习策略来预测来自洛伦兹系统的混沌时间序列。这些策略在短时间内预测动力学变量的演化被证明是成功的。通过计数和分类策略，可以非常准确地预测状态之间的转变及其持续时间，为此我们训练了多层感知机集合。即使对于最长的状态，也可以预测其发生和持续时间。我们还展示了使用回声状态网络生成时间序列数据的方法，其精度高达几百个时间步。分类技术预测超过 11 个振荡的状态持续时间的能力对应于大约 10 个李雅普诺夫时间。
