Multi-steps prediction of chaotic time series based on echo state network

Considering of the ill-posed problem in learning process of echo state network(ESN), a new learning algorithm of ESN is proposed based on regularization method. The regularization term provides a stable solution to function approximation with a tradeoff between accuracy and smoothness of the solutions. So the redundant weights of neural network are damped and converged to the zero state. The structure of neural network will become more compact with a particular accuracy. The neural network has good generalization. The simulation results show that the proposed algorithm has higher accuracy than the prediction model based on RBF network in multi-steps prediction by Lorenz and Chen mapping.