Proper choice of hyperparameters in reservoir computing of chaotic maps

Abstract

Reservoir computing (RC) are powerful to learn and predict dynamical behaviors. However, it has been found that both the reservoir size and the hyperparameters can greatly affect the learning ability of RC on dynamical systems, the mechanism of which still remains unclear. This paper discusses the influence of hyperparameters of RC with different sizes of reservoir on learning typical chaotic maps. An analytic method is purposed to obtain the hyperparameters that can exhibit better learning ability of RC by analyzing high order derivatives of the error loss function. In the case of RC with one or two nodes, the well-performing hyperparameters are analytically obtained for learning the logistic map, which are consistent with numerical results. The analytic method also shows its ability in RC with multiple nodes to learn singer and sine chaotic maps. This work provides deeper insight in learning and predicting behaviors of RC as well as presents guidance for the selection of hyperparameters of RC to learn chaotic systems.