Adaptive Levenberg-Marquardt Algorithm Based Echo State Network for Chaotic Time Series Prediction

摘要: Echo state networks (ESNs) have wide applications in chaotic time series prediction. In the ESN, if smallest singular value of reservoir matrix is infinitesimal, ill-posed problem might occur during training process. To overcome this problem, an adaptive Levenberg–Marquardt (LM) algorithm-based echo network (ALM-ESN) developed. developed ALM-ESN, a new damping term introduced into LM algorithm. The factor amended by trust region technique, furthermore, convergence analysis, and stability analysis are performed. Moreover, to make inputs fall within active activation function improve learning speed, weight initialization method using linear algebra deployed determine appropriate input weights weights. Simulations demonstrate that ALM-ESN can problem. Furthermore, it exhibits better performance robustness for prediction than some other existing methods.