Deep Hybrid Neural Network and Improved Differential Neuroevolution for Chaotic Time Series Prediction

Chaos is widespread in non-linear systems such as finance, energy, and weather. In the chaos system, a variable changing with time generates a chaotic time series, which contains a wealth of information about the non-linear system, and it is helpful for us to analyze and understand chaos systems. Traditional hybrid models for chaotic time series prediction based on neural networks have problems such as low prediction accuracy and difficulty in determining the network topologies. In recent years, the chaotic time series prediction has attached the attention of researchers in the area of deep learning. In this paper, we use a deep hybrid neural network (DHNN) based on convolutional neural network (CNN), gated recurrent unit (GRU) network, and attention mechanism to predict chaotic time series. Besides, we use the idea of neuroevolution to optimize the topologies of the DHNN. In the DHNN, we use CNN to capture spatial features from phase space reconstruction of chaotic time series. Then, we combine spatial features with the original chaotic time series. GRU extracts the spatio-temporal features from the combined sequence, and an attention mechanism with a non-linear activation function is designed to capture critical spatio-temporal features. Besides, we propose an improved differential evolution (IDE) algorithm to optimize the topologies of the DHNN, including the filter sizes of CNN and the number of hidden neurons of GRU. We develop the IDE with an adaptive mutation operator and dynamic chaos crossover operator, which can improve convergence speed and reduce optimization time. In this paper, we use the theoretical Lorenz datasets, monthly mean total sunspot datasets, and the actual coal-mine gas concentration datasets to verify the prediction accuracy of the proposed prediction model. Experimental results have shown that the proposed prediction model performs well in chaotic time series forecasting.