Time Series Prediction of ESN Based on Chebyshev Mapping and Strongly Connected Topology

Abstract This paper introduces a novel approach called Chebyshev mapping and strongly connected topology for optimization of echo state network (ESN). To enhance the predictive performance of ESNs for time series data, Chebyshev mapping is employed to optimize the irregular input weight matrix. And the reservoir of the ESN is also replaced using an adjacency matrix derived from a digital chaotic system, resulting in a reservoir with strong connectivity properties. Numerical experiments are conducted on various time series datasets, including the Mackey–Glass time series, Lorenz time series and solar sunspot numbers, validating the effectiveness of the proposed optimization methods. Compared with the traditional ESNs, the optimization method proposed in this paper has higher predictive performance, and effectively reduce the reservoir’s size and model complexity.