Table 1.

Performance metrics for the three algorithms (L96). There was one large training set D_tr, and then 100 smaller training sets D_te for each algorithm. For L96 tasks, the prediction is considered diverged when normalized testing error (SF) exceeds 0.3. Time until divergence is measured in model time units (MTU, 1MTU = 200Δt), a standardized timescale for L96. The HSR-ESN only worked on a subset of testing cases that were temporally distant from generated training data, while others instantly failed. For this and future tables, results are given as mean ± s.d. over 100 trials.

	training error	TF error	SF error	divergence time
LSR-ESN	1.80 × 10−4	$4.33\times {10}^{-2}\pm 1.75\times {10}^{-3^{\phantom{\int }}}$	1.16 ± 1.06 × 10−1	1.25 ± 4.85 × 10−1
HSR-ESN	7.10 × 10−5	4.08 × 10−1 ± 3.37 × 10−1	1.09 × 101 ± 8.62	4.53 × 10−1 ± 5.93 × 10−1
D2R2	2.24 × 10−4	2.28 × 10−4 ± 2.11 × 10−5	1.13 ± 1.06 × 10−1	1.60 ± 5.31 × 10−1