An echo state network model with the protein structure for time series prediction

From the perspective of bionics of biological structure, this paper proposes a new reservoir topology structure with an α-helix form of the secondary protein, named S-ESN. This network model has some advantages compared with the standard leaky-echo state network (Leaky-ESN) model. Because the neurons in the traditional reservoir are randomly and sparsely connected, the stability of the echo state network (ESN) will be reduced, and the prediction accuracy will also be decreased. The S-ESN model proposed greatly improves the internal stability of the reservoir, the dynamic activity of neurons and the prediction accuracy of the ESN. At the same time, the improved moth-flame optimization algorithm (MFO) with the probability of jump disturbance is used to optimize the three parameters: the leakage rate (a), the spectral radius (ρ), and the input scaling factor (sin), which can further improve the stability and predictability of the S-ESN. In order to verify the performance of S-ESN, three virtual time series Sin time series with low frequency, Sin time series with high frequency, Mackey-Glass time series (MG) and one practical Sunspot are selected as experimental data. The experimental results show that the S-ESN model has better prediction accuracy.