Recognizing Chaos by Deep Learning and Transfer Learning on Recurrence Plots

Abstract

Chaos recognition is necessary to determine the prediction possibility for specific time series. In this paper, we attempt to seek a novel chaos recognition method based on the recurrent plot (RP) and the convolutional neural network (CNN). The RP can transform the time series into a two-dimensional image, which intuitively reflects the inherent nature of the time series. On the other hand, the CNN is powerful in pattern classification. In this way, the existing chaos recognition results can be unified in a general framework to form accumulated knowledge, which can be used to recognize novel dynamics. First, three major time series classes, namely chaotic, periodic and random ones generated from the classical dynamics, are represented by the RPs respectively. Then, these RPs are used as the dataset to train the residual neural network (ResNet). In this process, the transfer learning is used to speed up convergence. The chaos recognition precision can be up to 97.6%. Finally, different encoding methods and classification networks are used for comparative experiments, and the resultant ResNet is applied to the time series from a supercavitating vehicle motion and two hyperchaotic systems. The experimental results demonstrate the effectiveness of the proposed method.