Lorenz Chaotic System Artificial Neural Network Training with Single Time Series Input and Multiple Time Series Outputs for EEG Prediction

Abstract

The goal of this research is to develop an efficient artificial neural network (ANN) architecture to predict three chaotic time series outputs for Lorenz system using single time series input. The training performances are evaluated and compared for different ANN architectures with multiple hidden layers, as well as for input data with different combination of time series, including the first and second order differences of the time series. It is found that given the same ANN architecture, the training results of multiple time series outputs using single time series (x) input are much worse than those using multiple time series inputs. However, the training results can be improved significantly by increasing the number of ANN hidden layers up to 3; and marginally improved by adding the first and second order differences of the x time series, as well as adding steps for calculating the first and second order differences of the input time series.