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In this paper, the performance of three deep learning methods for predictingshort-term evolution and for reproducing the long-term statistics of amulti-scale spatio-temporal Lorenz 96 system is examined. The methods are: echostate network (a type of reservoir computing, RC-ESN), deep feed-forwardartificial neural network (ANN), and recurrent neural network with longshort-term memory (RNN-LSTM). This Lorenz 96 system has three tiers ofnonlinearly interacting variables representing slow/large-scale ($X$),intermediate ($Y$), and fast/small-scale ($Z$) processes. For training ortesting, only $X$ is available; $Y$ and $Z$ are never known or used. We showthat RC-ESN substantially outperforms ANN and RNN-LSTM for short-termprediction, e.g., accurately forecasting the chaotic trajectories for hundredsof numerical solver's time steps, equivalent to several Lyapunov timescales.The RNN-LSTM and ANN show some prediction skills as well; RNN-LSTM bests ANN.Furthermore, even after losing the trajectory, data predicted by RC-ESN andRNN-LSTM have probability density functions (PDFs) that closely match the truePDF, even at the tails. The PDF of the data predicted using ANN, however,deviates from the true PDF. Implications, caveats, and applications todata-driven and data-assisted surrogate modeling of complex nonlinear dynamicalsystems such as weather/climate are discussed.

Data-driven prediction of a multi-scale Lorenz 96 chaotic system using deep learning methods: Reservoir computing, ANN, and RNN-LSTM