Leaky echo state network based on methane topology applied to time series prediction

In this paper, a proposed echo state network (ESN) model called F‐ESN is based on methane topology. Due to the neurons in the reservoir of the ESN model being random and sparsely connected, the stability of the system structure could be better, and the prediction accuracy could be higher. To solve this issue, the reservoir's neuronal connectivity is modified to a certain methane structure. A master neuron governs each little unit and communicates with the others to pass information. In addition, MFO optimized by adaptive dynamic operators is used to optimize the three parameters of ESN : leakage rate (a)$ (a)$, spectral radius of the connection weight matrix (ρ)$ (\rho )$, and input scale factor (sin)$ (s^{in})$. To verify the effectiveness of the proposed method, low‐frequency sin time series, high‐frequency SIN time series, and MG time series are simulated. The experimental results show that the methane topology can further improve the prediction accuracy of leakage echo state networks. The ESN of methane topology improves the stability and robustness of the system. The MFO algorithm is used to optimize the parameters of the system and further improve the prediction performance of the system.