The optimal reservoir computer for nonlinear dynamics

Analysis and prediction of real-world complex systems of nonlinear dynamics relies largely on surrogate models. Reservoir computers (RC) have proven useful in replicating the climate of chaotic dynamics. The quality of surrogate models based on RCs is crucially dependent on judiciously determined optimal implementation that involves selecting optimal reservoir topology and hyperparameters. By systematically applying Bayesian hyperparameter optimization and using ensembles of reservoirs of various topology we show that the topology of linked reservoirs has no significance in forecasting dynamics of the chaotic Lorenz system. By simulations we show that simple reservoirs of unconnected nodes outperform reservoirs of linked reservoirs as surrogate models for the Lorenz system in different regimes. We give a derivation for why reservoirs of unconnected nodes have the maximum entropy and hence are optimal. We conclude that the performance of an RC is based on mere functional transformation, not in its dynamical properties as has been generally presumed. Hence, RC could be improved by including information on dynamics more strongly in the model.