as discussed in Thornes *et al*.  [@thornes2017use], 1 MTU in this system corresponds to $\approx 3.75$ Earth days in the real atmosphere.

### Training and testing datasets

To build the training and testing datasets from the numerical solution, we have sampled $X \in \Re^{8}$ at every $\Delta t$ and then standardized the data by subtracting the mean and dividing by the standard deviation. We then construct a training set consisting of $N$ sequential samples and a testing consisting of the next $2000$ sequential samples from point $N+1$ to $N+2000$. We have randomly chosen $100$ such training/testing sets, each of length $(N+2000)\Delta t$ starting from a random point and separated from the next training/testing set by at least $2000 \Delta t$. There is never any overlap between the training and the testing sequences in any of the $100$ training/testing sets.

Reservoir computing-echo state network (RC-ESN)
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### Architecture

The RC-ESN [@jaeger2004harnessing; @Jaeger2007] is an RNN that has a reservoir with $D$ neurons, which are sparsely connected in an Erdős-Rényi graph configuration (see Figure \[esn\_demo\]). The connectivity of the reservoir neurons is represented by the adjacency matrix $\mathbf{A}$ of size $D\times D$ whose values are drawn from a uniform random distribution on 