FIG. 1: Countour Plot for one run of the Imperfect model with a recursive rollout for1000 timesteps from t= 500,000. Performance crosses our f = 0.4 threshold at a valid time of τ = 334

FIG. 2: NRMSE for Imperfect Model prediction from t= 500,000 for 1000 timestes.

FIG. 3: Mean NRMSE plot averaged over 10 different initial conditions of the imperfectmodel forecast for 1000 timesteps. Mean valid time for the imperfect model forecast isτ = 356

FIG. 4: Countour Plot for one run of the ESN model with a recursive rollout for 1000timesteps from t = 501,000. Performance crosses our f = 0.4 threshold at a valid timeof τ = 115 for this specific run.

FIG. 5: Mean NRMSE plot averaged over 10 different initial conditions of the ESN modelforecast for 1000 timesteps. Mean valid time for the imperfect model forecast is τ = 195

FIG. 6: Forecast performance of the Hybrid ESN with X-only prediction and partialcoupling. The ESN predicts only the X variables, which are fed into the imperfect modelto evolve Y(t).

FIG. 7: Forecast performance of the Hybrid ESN with X-only prediction and no coupling.The imperfect model and ESN evolve independently after initialization.

FIG. 8: Forecast performance of the fully coupled Hybrid ESN with joint (X,Y) predic-tion. Predictions are used to evolve both the reservoir and the imperfect model.

Refrencese

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Results

Refrencese