  Reservoir computing is a very promising approach for the prediction of
complex nonlinear dynamical systems. Besides capturing the exact short-term
trajectories of nonlinear systems, it has also proved to reproduce its
characteristic long-term properties very accurately. However, predictions do
not always work equivalently well. It has been shown that both short- and
long-term predictions vary significantly among different random realizations of
the reservoir. In order to gain an understanding on when reservoir computing
works best, we investigate some differential properties of the respective
realization of the reservoir in a systematic way. We find that removing nodes
that correspond to the largest weights in the output regression matrix reduces
outliers and improves overall prediction quality. Moreover, this allows to
effectively reduce the network size and, therefore, increase computational
efficiency. In addition, we use a nonlinear scaling factor in the hyperbolic
tangent of the activation function. This adjusts the response of the activation
function to the range of values of the input variables of the nodes. As a
consequence, this reduces the number of outliers significantly and increases
both the short- and long-term prediction quality for the nonlinear systems
investigated in this study. Our results demonstrate that a large optimization
potential lies in the systematical refinement of the differential reservoir
properties for a given dataset.
