Fig. 8

Parameter-error task parameter sweeps evaluating the hybrid RC’s prediction of NLON trajectories with parameter error in its expert ODE model. Mean NMSE in the prediction of the hybrid RC (red), standard RC (blue), and the base ODE model (black) across the three dynamical regimes. Column: Dynamical regime, synchronous (a, d), asynchronous (b, e), multi-frequency (c, f). Row: Parameter varied, spectral radius (a–c), input scaling (d–f). Individual dots are individual reservoir/ODE instantiations, each representing the mean NMSE across 60 forecasts (20 for each realization of a ground truth regime). Solid lines are the mean of the mean NMSE across the reservoir/ODE instantiations. Shaded regions are one standard deviation across reservoir/ODE instantiations. The hybrid RC consistently outperforms the standard RC and the base ODE model. In the synchronous regime, a spectral radius above 1.0 causes a degradation in standard RC performance. This is present for the hybrid RC but it recovers as spectral radius increases further. Increasing input scaling improves standard RC performance on both the asynchronous and multi-frequency regimes. At high input scaling on the multi-frequency regime, the standard RC matches the hybrid RC performance.