Optimal reservoir computers for forecasting systems of nonlinear dynamics

Prediction and analysis of systems of nonlinear dynamics is crucial in many applications. Here, we study characteristics and optimization of reservoir computing, a machine learning technique that has gained attention as a suitable method for this task. By systematically applying Bayesian optimization on reservoirs we show that reservoirs of low connectivity perform better than or as well as those of high connectivity in forecasting noiseless Lorenz and coupled Wilson-Cowan systems. We also show that, unexpectedly, computationally effective reservoirs of unconnected nodes (RUN) outperform reservoirs of linked network topologies in predicting these systems. In the presence of noise, reservoirs of linked nodes perform only slightly better than RUNs. In contrast to previously reported results, we find that the topology of linked reservoirs has no significance in the performance of system prediction. Based on our findings, we give a procedure for designing optimal reservoir computers (RC) for forecasting dynamical systems. This work paves way for computationally effective RCs applicable to real-time prediction of signals measured on systems of nonlinear dynamics such as EEG or MEG signals measured on a brain.