Aside from the observations here that RC-ESN significantly outperforms RNN-LSTM for short-term predictions, the problem of reservoir size can be tackled in at least two ways. First, Pathak *et al*.  [@pathak2018model] have proposed, and shown the effectiveness of, using a set of parallelized reservoirs, which allowed for easily dealing with high-dimensional chaotic toy models. Second, Figure \[res\_scaling\] shows that $E$ rapidly declines by a factor of around $3$ as $D$ is increased from $500$ to $5000$, decreases slightly as $D$ is further doubled to $10000$, and then barely changes as $D$ is doubled again to $20000$. Training the RC-ESN with $D=20000$ versus $D=5000$ comes with a higher computational cost ($16$ GB memory and $\approx 6$ CPU hours for $D=5000$ and $64$ GB memory and $\approx 18$ CPU hours for $D=20000$), while little improvement in accuracy is gained. Thus, concepts from inexact computing can be used to choose $D$ such that precision is traded for large savings in computational resources, which can be then reinvested into more simulations, higher resolutions for critical processes etc. [@palem2014inexactness; @palmer2014climate; @duben2014benchmark; @leyffer2016doing; @thornes2017use].

![For RC-ESN: scaling of average prediction error between $0-0.5$ MTU ($E$, Eq. (\[eq:E\])) with reservoir size $D$. $N=500000$ is used.[]{data-label="res_scaling"}](res_scaling.eps){width="50.00000%"}

Long-term statistics: 