CNN-LSTM based incremental attention mechanism enabled phase-space reconstruction for chaotic time series prediction

Abstract

To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network, we propose a convolutional neural network (CNN)-long short-term memory (LSTM) prediction model based on the incremental attention mechanism. Firstly, a traversal search is conducted through the traversal layer for finite parameters in the phase space. Then, an incremental attention layer is utilized for parameter judgment based on the dimension weight criteria (DWC). The phase space parameters that best meet DWC are selected and fed into the input layer. Finally, the constructed CNN-LSTM network extracts spatiotemporal features and provides the final prediction results. The model is verified using Logistic, Lorenz, and sunspot chaotic time series, and the performance is compared from the two dimensions of prediction accuracy and network phase space structure. Additionally, the CNN-LSTM network based on incremental attention is compared with LSTM, CNN, recurrent neural network (RNN), and support vector regression (SVR) for prediction accuracy. The experiment results indicate that the proposed composite network model possesses enhanced capability in extracting temporal features and achieves higher prediction accuracy. Also, the algorithm to estimate the phase space parameter is compared with the traditional CAO, false nearest neighbor, and C–C, three typical methods for determining the chaotic phase space parameters. The experiments reveal that the phase space parameter estimation algorithm based on the incremental attention mechanism is superior in prediction accuracy compared with the traditional phase space reconstruction method in five networks, including CNN-LSTM, LSTM, CNN, RNN, and SVR.

Keywords

• Chaotic time series
• Incremental attention mechanism
• Phase-space reconstruction