Fig. 9

Residual physics task parameter sweeps evaluating the short-term forecast performance of the hybrid RC with missing non-linearities in its expert ODE model. Mean valid time, \(t^*\), achieved by the hybrid RC (red), standard RC (blue), and the base ODE model (black) across the four dynamical regimes, and four different parameter sweeps. Column: Dynamical regime, synchronous (a, e, i, m), asynchronous (b, f, j, n), heteroclinic cycles (c, g, k, o), partial synchrony (d, h, l, p). Row: Parameter varied, spectral radius (a–d), input scaling (e–h), regularization (i–l), reservoir size, \(D_r\) (m–p). Individual dots are individual reservoir/ODE instantiations, each representing the mean valid time across 20 forecasts. Solid lines are the mean of the mean valid time across the reservoir/ODE instantiations. Shaded regions are one standard deviation across reservoir/ODE instantiations. The hybrid RC generally outperforms the standard RC even on regimes out of its expert model’s domain. The spectral radius significantly affects performance, with the standard RC showing degradation above a spectral radius of 1.0. The hybrid RC behaves differently, showing recovery of performance when the spectral radius is above 1.0. Input scaling primarily affects the asynchronous, heteroclinic cycles and partial synchrony regimes, with optimum performance reached at minimal input scaling. Regularization strongly affects the performance of both the hybrid and standard RCs, with low regularization causing failure. Hybrid RCs have a broader range of viable regularization strength on the heteroclinic cycles and partial synchrony regimes. Reservoir size has little effect as long as a minimum of 100 nodes is available.