Prediction of nonlinear dynamical system output with multilayer perceptron and radial basis function neural networks

The ability of multilayer perceptron (MLP) and radial basis function (RBF) neural networks to predict the future output of chaotic and non-chaotic nonlinear dynamical systems (NDS) is analyzed. Static (i.e., feedforward) MLP and RBF neural nets (NN) are trained using a NDS with a stable attractor. The capabilities and limitations of each net architecture in terms of prediction accuracy are discussed. Emphasis is also placed on identifying the training problems for each net structure and relating these to their inherent capabilities and limitations. Static and locally recurrent RBF NN are also trained on a NDS with a chaotic attractor (i.e., the Lorenz attractor). The prediction ability of a static net structure for NDS with stable attractors and for NDS with a chaotic attractor are compared. The impact of adding feedback to the RBF neurons in terms of prediction ability is also analyzed. Training problems for each net structure are also discussed