Evaluating the Training Performance of Artificial Neural Network Using Small Time Series Segments of The Lorenz Chaotic System
Lei Zhang · 2018
Nonlinear Auto-Regressive (NAR) model can be designed by training Artificial Neural Network (ANN) to generate and predict time series outputs of chaotic systems. This is ben-eficial for the simulation and analysis of Electroencephalogram (EEG) time series signals in the study of brain dynamics. This paper evaluates the ANN training performance using small time series segments of the Lorenz chaotic system as training data, which are generated using the Lorenz system equations and the forward Euler method. Ten small contiguous segments are used for ANN training. Each segment is further divided into three contiguous blocks for training, validation and testing. The mean squared error (MSE) is used to measure the training performance. The MSEs of different ANN architecture are normalized based on the computational cost. The standard deviation (S) of the testing performance is used to measure and compare the generalization of the ANN for the ten training segments. The training segments are generated with equivalent length, which is the product of the step size (dt) and the number of samples (n). The step size is used to generate training samples with various precision. The evaluation results show that both the ANN training performance and generalization can be improved by optimizing the ANN architecture and increasing the precision of the training samples.