Broad fractional-order echo state network with slime mould algorithm for multivariate time series prediction

In this paper, considering the infinite memory capability of fractional-order differential equations and the advantages of broad echo state network, a broad fractional-order echo state network (BFO-ESN) is proposed to build the multivariate time series prediction model. Firstly, the Pearson correlation coefficient method is utilized to filter the input data set and the output data set, which can clearly determine the number of reservoirs through the correlation between the two data sets. Secondly, the idea of fractional order is introduced into the broad echo state network, and then the internal characteristics of different learning tasks can be fully reflected. Thirdly, the reservoir parameters of BFO-ESN are optimized by using the slime mould algorithm (SMA). Finally, three numerical examples and a photovoltaic (PV) system are used to illustrate the effectiveness of BFO-ESN with SMA, and then some different optimization algorithms in the PV system are given to illustrate the advantage of SMA. •A broad fractional-order echo state network (BFO-ESN) is proposed.•Based on the LMI method, the stability criterion for the BFO-ESN is given.•The slime mould algorithm is given to optimize the reservoir parameters of BFO-ESN.•The three different time series are used to illustrate the effectiveness of BFO-ESN.•Some different optimization algorithms are given to illustrate the advantages of SMA.