Using Artificial Neural Networks and Support Vector Regression to Model the Lyapunov Exponent

Finding the salient patterns in chaotic data has been the holy grail of Chaos Theory. Examples of chaotic data include the fluctuations of the stock market, weather, and many other natural systems. Real world data has proven to be extremely difficult to predict due to it high dimensionality and the potential for noise. It has been shown that artificial neural networks have been able to accurately calculate the Lyapunov Exponent, a feature that determines the divergence of two initially close trajectories and thus chaos. A variation of the support vector machine called support vector regression is used in function approximation and applying this tool to chaotic data may yield another model that can also be used in the prediction of the Lyapunov Exponent. Since support vector machines have been found to arrive at a prediction much faster than the artificial neural network, it may prove to be the model to use in time sensitive applications.