Modeling and prediction of chaotic systems with artificial neural networks
This study of chaotic systems and their prediction is motivated by the fact that many phenomena, both natural and man-made, are of a chaotic nature. Such phenomena include but are not limited to earthquakes, laser systems, epileptic seizures, combustion, and weather patterns. These phenomena have previously been thought to be unpredictable. However, it is indeed possible to predict time series generated by chaotic systems. The primary objective of this study is to develop a system that would train the artificial neural network (ANN) and then predict the future data of the process. In the present application, the chosen chaotic data set was obtained by solving Lorenz's equations. To predict the future data, the concept of a multilayer feed-forward ANN with nonlinear auto-regressive moving averages with exogenous input is used. A Backpropagation algorithm is used to train the network for the chaotic data. The final updated weights from the trained network were then used for the prediction of the future values of the system. Lyapunov exponents, phase diagrams and statistical analyses were used to evaluate the neural network output. A correlation of 94% and a negative Lyapunov exponent indicate that the results obtained from ANN are in good agreement with the actual values. Copyright (C) 2009 John Wiley & Sons, Ltd.
chaotic system artificial neural networks backpropagation lyapunov exponent multi-layered neural network narmax method