Modeling and Prediction of Chaotic System with Artificial Neural Network
Jonathan W. Woolley, Praveen K. Agarwal, and John Baker
International Journal of Numerical Methods in Fluids
Status: Accepted and In Revision, revision submitted April 16, 2009
ABSTRACT
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 which would train the Artificial Neural Network and then
predict the future data of the process. In the present application, the chosen
data set which is chaotic in nature was obtained by solving Lorenz’s fluid
equations. To predict the future data,
the concept of a multilayer feed-forward Artificial Neural Network (ANN) with Non-linear
Auto-Regressive Moving Averages eXogenous input (NARMAX) is used. Back-Propagation algorithm is used to train
the chaotic data. Once the ANN is trained with error accuracy of 0.0001or less,
the final updated weights from the trained network were then used to predict
the future values of the system. The Lyapunov
exponent, phase diagrams and statistical analysis were used for verification
and validation. A correlation of 94% and a negative Lyapunov exponent indicate
that the results obtained from Artificial Neural Networks are in good agreement
with the actual values.
