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The prediction of complex nonlinear dynamical systems with the help ofmachine learning techniques has become increasingly popular. In particular,reservoir computing turned out to be a very promising approach especially forthe reproduction of the long-term properties of a nonlinear system. Yet, athorough statistical analysis of the forecast results is missing. Using theLorenz and R\"ossler system we statistically analyze the quality of predictionfor different parametrizations - both the exact short-term prediction as wellas the reproduction of the long-term properties (the "climate") of the systemas estimated by the correlation dimension and largest Lyapunov exponent. Wefind that both short and longterm predictions vary significantly among therealizations. Thus special care must be taken in selecting the good predictionsas predictions which deliver better short-term prediction also tend to betterresemble the long-term climate of the system. Instead of only using purelyrandom Erd\"os-Renyi networks we also investigate the benefit of alternativenetwork topologies such as small world or scale-free networks and show whicheffect they have on the prediction quality. Our results suggest that theoverall performance with respect to the reproduction of the climate of both theLorenz and R\"ossler system is worst for scale-free networks. For the Lorenzsystem there seems to be a slight benefit of using small world networks whilefor the R\"ossler system small world and Erd\"os -Renyi networks performedequivalently well. In general the observation is that reservoir computing worksfor all network topologies investigated here.

Good and bad predictions: Assessing and improving the replication of chaotic attractors by means of reservoir computing