  The success of recurrent neural networks (RNNs) has been demonstrated in many
applications related to turbulence, including flow control, optimization,
turbulent features reproduction as well as turbulence prediction and modeling.
With this study we aim to assess the capability of these networks to reproduce
the temporal evolution of a minimal turbulent channel flow. We first obtain a
data-driven model based on a modal decomposition in the Fourier domain (which
we denote as FFT-POD) of the time series sampled from the flow. This particular
case of turbulent flow allows us to accurately simulate the most relevant
coherent structures close to the wall. Long-short-term-memory (LSTM) networks
and a Koopman-based framework (KNF) are trained to predict the temporal
dynamics of the minimal-channel-flow modes. Tests with different configurations
highlight the limits of the KNF method compared to the LSTM, given the
complexity of the flow under study. Long-term prediction for LSTM show
excellent agreement from the statistical point of view, with errors below 2%
for the best models with respect to the reference. Furthermore, the analysis of
the chaotic behaviour through the use of the Lyapunov exponents and of the
dynamic behaviour through Poincar\'e maps emphasizes the ability of the LSTM to
reproduce the temporal dynamics of turbulence. Alternative reduced-order models
(ROMs), based on the identification of different turbulent structures, are
explored and they continue to show a good potential in predicting the temporal
dynamics of the minimal channel.
