Analysis and Prediction of Chaotic Time Series Based on Deep Learning Neural Networks

Abstract

In this paper, we propose a Differencing Long Short-Term Memory (D-LSTM) architecture as an extension of recurrent neural networks. The differencing is the latter value minus the previous value, which can reduce the noise of the original data to make it smooth and improve the prediction accuracy. We design a 3D nonlinear chaotic system and analyze its properties and dynamic behaviors by phase portraits, equilibrium points, Lyapunov exponents, spectral entropy. We study prediction result by change the initial value and the coefficient for our chaotic system. We compare D-LSTM with Adaptive Neuro Fuzzy Inference system (ANFIS) and original Long Short-Term Memory (LSTM), using Root Mean Square Error (RMSE) to measure their performance. The result shows that our model is almost better than others.