Brugnago Eduardo L, Gallas Jason A C, Beims Marcus W
Departamento de Física, Universidade Federal do Paraná, 81531-990 Curitiba, Brazil.
Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany.
Chaos. 2020 Aug;30(8):083106. doi: 10.1063/5.0009765.
In this paper, the alignment of covariant Lyapunov vectors is used to train multi-layer perceptron ensembles in order to predict the duration of regimes in chaotic time series of Rikitake's geomagnetic dynamo model. The machine learning procedure reveals the relevance of the alignment of distinct covariant Lyapunov vectors for the predictions. To train multi-layer perceptron, we use a classification procedure that associates the number of maxima (or minima) inside regimes of motion with the duration of the corresponding regime. Remarkably accurate predictions are obtained, even for the longest regimes whose duration times are around 17.5 Lyapunov times. We also found long duration regimes with a distinctive statistical behavior, namely, the longest regimes are more likely to occur, a quite unusual behavior. In fact, we observed a largest regime above which no regimes were observed.
在本文中，协变李雅普诺夫向量的对齐被用于训练多层感知器集成，以便预测利吉塔克地磁发电机模型混沌时间序列中各状态的持续时间。机器学习过程揭示了不同协变李雅普诺夫向量的对齐对于预测的相关性。为了训练多层感知器，我们使用一种分类过程，该过程将运动状态内的极大值（或极小值）数量与相应状态的持续时间相关联。即使对于持续时间约为17.5个李雅普诺夫时间的最长状态，也能获得非常准确的预测。我们还发现了具有独特统计行为的长持续时间状态，即最长的状态更有可能出现，这是一种相当不寻常的行为。事实上，我们观察到一个最大的状态，在其之上没有观察到其他状态。
