Prediction of chaotic time series using hybrid neural network and attention mechanism

Chaotic time series forecasting has been widely used in various domains, and the accurate predicting of the chaotic time series plays a critical role in many public events. Recently, various deep learning algorithms have been used to forecast chaotic time series and achieved good prediction performance. In order to improve the prediction accuracy of chaotic time series, a prediction model (Att-CNN-LSTM) is proposed based on hybrid neural network and attention mechanism. In this paper, the convolutional neural network (CNN) and long short-term memory (LSTM) are used to form a hybrid neural network. In addition, a attention model with <i>softmax</i> activation function is designed to extract the key features. Firstly, phase space reconstruction and data normalization are performed on a chaotic time series, then convolutional neural network (CNN) is used to extract the spatial features of the reconstructed phase space, then the features extracted by CNN are combined with the original chaotic time series, and in the long short-term memory network (LSTM) the combined vector is used to extract the temporal features. And then attention mechanism captures the key spatial-temporal features of chaotic time series. Finally, the prediction results are computed by using spatial-temporal features. To verify the prediction performance of the proposed hybrid model, it is used to predict the Logistic, Lorenz and sunspot chaotic time series. Four kinds of error criteria and model running times are used to evaluate the performance of predictive model. The proposed model is compared with hybrid CNN-LSTM model, the single CNN and LSTM network model and least squares support vector machine(LSSVM), and the experimental results show that the proposed hybrid model has a higher prediction accuracy.