Seeking optimal parameters for achieving a lightweight reservoir computing: A computational endeavor

Reservoir computing (RC) is a promising approach for model-free prediction of complex nonlinear dynamical systems. Here, we reveal that the randomness in the parameter configurations of the RC has little influence on its short-term prediction accuracy of chaotic systems. This thus motivates us to articulate a new reservoir structure, called homogeneous reservoir computing (HRC). To further gain the optimal input scaling and spectral radius, we investigate the forecasting ability of the HRC with different parameters and find that there is an ellipse-like optimal region in the parameter space, which is completely beyond the area where the spectral radius is smaller than unity. Surprisingly, we find that this optimal region with better long-term forecasting ability can be accurately reflected by the contours of the $l_2$-norm of the output matrix, which enables us to judge the quality of the parameter selection more directly and efficiently.