Deep Echo State Network With Multiple Adaptive Reservoirs for Time Series Prediction

In this article, considering the plasticity of reservoir, a deep echo state network with multiple adaptive reservoirs in series configuration, called MAR-DESN, is proposed for time series prediction. First, according to the characteristics of input signals and reservoir states, the number of reservoirs of MAR-DESN and each reservoir size can be automatically determined by using the principal component analysis. Second, a parameter optimization method based on Broyden–Fletcher–Goldfarb–Shanno quasi-Newton algorithm is given to optimize the reservoir parameters of MAR-DESN. Third, a sufficient condition for the uniform echo state property of MAR-DESN is given, such that the MAR-DESN can be stably applied in different applications. Finally, three examples are used to verify the effectiveness of MAR-DESN.