Time Series Analysis and Prediction of Nonlinear Systems with Ensemble Learning Framework Applied to Deep Learning Neural Networks

Abstract In this paper, we design a framework to predict the value of time series for nonlinear systems. In order to achieve this goal, many studies of applications and plans for machine learning and even deep learning become currently popular. First, we select four nonlinear systems: including a proposed four-dimensional chaotic system, Lorenz system, Duffing oscillator, and Rossler attractor. The framework has three learning parts as Long Short-Term Memory (LSTM) based on Generate Performance Model (GPM), ensemble learning based on Restrict and Control Model (RCM), and one-dimensional convolution neural network (1-DCNN) of dirichlet distribution based on Overall Verification Model (OVM). Before learning steps, we exploit K-means method as pre-processing and hypothesis verification to improve the prediction accuracy. After learning steps, we construct four forecasting progresses as Point by Point Generated Method (PPGM), Sequence Full Generated Method (SFGM), Sequence Multiple Generated Method (SMGM), and Improvement with RCM and OVM (IPRO) to predict the value of the time steps. Finally, we use Mean Average Error (MAE) as the criterion of the prediction, and estimate the accuracy by comparing the error region of the average standard deviation.