the employed multi-scale Lorenz 96 system are identical to that of [@dueben2018challenges], who reported their ANN to have some skills in data-driven prediction of the spatio-temporal evolution of $X$. Finally, Vlachas *et al*. [@vlachas2018data] found an RNN-LSTM to have skills (though limited) for predicting the short-term spatio-temporal evolution (item 1) of a number of chaotic toy models such as the original Lorenz 96 system.

Here we aim to build on these pioneering studies and examine, *side by side*, the performance of RC-ESN, ANN, and RNN-LSTM in achieving (1) and (2) for the chaotic multi-scale Lorenz 96 system. [We emphasize the need for such a side-by-side comparison that uses the exact same system as the testbed and metrics for assessing performance.]{}

The structure of the paper is as follows: in section \[sec\_method\], the multi-scale Lorenz 96 system and the three deep learning methods are discussed; results on how these methods predict the short-term spatio-temporal evolution of $X$ and reproduce the long-term statistics of $X$ are presented in section \[sec\_results\]; key findings and future work are discussed in section \[sec:discussion\].

![The conventional approach of solving the full governing equations numerically versus our data-driven approach for predicting the spatio-temporal evolution of the slow/large-scale 