Fig. 5: Reservoir-computing based long-term dynamics prediction.

a An illustration of hybrid transformer/reservoir-computing framework. The time series reconstructed by the transformer is used to train the reservoir computer that generates time series of the target system of arbitrary length, leading to a reconstructed attractor that agrees with the ground truth. b RMSE and DV versus the sparsity parameter. Shaded areas represent the standard deviation. c Color-coded ensemble-averaged DV in the reservoir-computing hyperparameter plane (Tl, Ns) for Sr = 0.93 (Sm = 0.8). d DV versus training length Tl for Ns = 500 and versus reservoir network size Ns for Tl = 105. In all cases, 50 independent realizations are used.