Fig. 10
From: Modeling nonlinear oscillator networks using physics-informed hybrid reservoir computing

Mean valid time, \(t^*\), achieved by individual hybrid (red) and standard (blue) RCs across 20 test forecasts in the grid search. Columns: parameter sets corresponding to each corner of the grid search cube are labeled (A)–(H) (Fig. 7). Rows: dynamical regimes. Top row: synchronous, middle row: heteroclinic cycles, bottom row: partial synchrony. Horizontal lines: the mean of the mean valid time across reservoirs. Shaded regions: one standard deviation across reservoirs. On the synchronous regime, Hybrid RCs achieve near perfect performance for all parameter sets. The standard RC also performs well on the synchronous regime, however high regularization and spectral radius significantly reduce performance. On the heteroclinic cycles regime, hybrid RCs consistently outperform standard RCs. High spectral radius again reduces the performance of the standard RC. Low regularization increases the variance in the hybrid RC performance. Maximum valid time on the heteroclinic cycles regime is \(45.8\%\) higher for the hybrid RC than the standard RC. On the partial synchrony regime, both models perform poorly, however the hybrid RC is more consistent across parameter sets. High spectral radius severely reduces the standard RC performance again. The hybrid RC does not show an improvement in maximum valid time over the standard RC on the partial synchrony regime.