chaotic system, when only the slow/large-scale variables are known (during training) and are of interest (to predict during testing)?* We emphasize that unlike many other studies, our focus is not on reproducing long-term statistics of the underlying dynamical system (although that will be examined too), but on predicting the short-term trajectory from a given initial condition. Furthermore, we emphasize that, following the problem formulation introduced by [@dueben2018challenges], the system’s state-vector is only partially known and the fast/small-scale variables are unknown even during training.

Our objective is more clearly demonstrated using the canonical chaotic system that we will use as a testbed for the data-driven methods: A multi-scale Lorenz 96 system: $$\begin{aligned}
\label{lorenz}
\frac{dX_k}{dt}=X_{k-1}\left(X_{k+1}-X_{k-2}\right)+F-\frac{hc}{b}\Sigma_jY_{j,k} \label{eq:L1} \\ 
\frac{dY_{j,k}}{dt}=-cbY_{j+1,k}\left(Y_{j+2,k}-Y_{j-1,k}\right)-cY_{j,k}+  \frac{hc}{b}X_k -\frac{he}{d}\Sigma_iZ_{i,j,k} \label{eq:L2}\\
\frac{dZ_{i,j,k}}{dt}=edZ_{i-1,j,k}\left(Z_{i+1,j,k}-Z_{i-2,j,k}\right)- geZ_{i,j,k}+  \frac{he}{d}Y_{j,k} \label{eq:L3}\end{aligned}$$ This set of coupled nonlinear ODEs is a 3-tier extension of Lorenz’s original model [@lorenz1996predictability] and has been proposed by Thornes *et al*.  [@thornes2017use] as a fitting prototype for multi-scale chaotic variability of the weather/climate system and a useful testbed for novel methods. In these equations, $F=20$ is a large-scale forcing that makes the system highly chaotic; $b=c=e=d=g=10$ and $h=1$ are tuned to produce appropriate spatio-temporal variability in the three variables (see below). The indices $i, j, 