Chaotic Time Series Recognition: A Deep Learning Model Inspired by Complex Systems Characteristics

A deep learning method is developed for chaotic time series classification. We investigate the chaotic state of a dynamical system, based on the output of the system. One of the main obstacles in time series classification is mapping a high-dimensional vector into a scalar value. To reduce the dimensions, it is common to use an average pooling layer block after feature extraction block. This blind process results in models with high computational complexity and potent to overfitting. One alternative is to extract the features manually, then apply shallow learning models to classify the time series. In fact, since complexity lies between the chaos and order, it is a sound idea to refer to complex systems characteristics to explore the chaotic region entrance. Therefore, chaotic state of a dynamical system can be recognized solely based on these characteristics. Inspired by this concept, we conclude that there is a feature space in which the output vector can be sparsified. Thus, we propose a deep learning method which the feature space dimensions successively are reduced in the feature extraction process. Specifically, we employ a fully convolutional network and add on two maximum pooling layers to the relevant feature extraction block. To validate the proposed model, the Lorenz system is employed which exhibits chaotic/non-chaotic states. We generate a labeled dataset containing 10000 samples each with 20000 features of the output of Lorenz system. The proposed model achieves 99.45 percent accuracy over 2000 unseen samples, higher than all the other competitor methods.