Prediction of a Lorenz chaotic attractor using two-layer perceptron neural network

This paper investigates the prediction of a Lorenz chaotic attractor having relatively high values of Lypunov's exponents. The characteristic of this time series is its rich chaotic behavior. For such dynamic reconstruction problem, regularized radial basis function (RBF) neural network (NN) models have been widely employed in the literature. However, author recommends using a two-layer multi-layer perceptron (MLP) NN-based recurrent model. When none of the available linear models have been able to learn the dynamics of this attractor, it is shown that the proposed NN-based auto regressive (AR) and auto regressive moving average (ARMA) models with regularization have not only learned the true trajectory of this attractor, but also performed much better in multi-step-ahead predictions. However, equivalent linear models seem to fail miserably in learning the dynamics of the time series, despite the low values of Akaike's final prediction error (FPE) estimate. Author proposes to employ the recurrent NN-based ARMA model with regularization which clearly outperforms all other models and thus, it is possible to obtain good results for prediction and reconstruction of the dynamics of the chaotic time series with NN-based models.