  We describe tests validating progress made toward acceleration and automation
of hydrodynamic codes in the regime of developed turbulence by three Deep
Learning (DL) Neural Network (NN) schemes trained on Direct Numerical
Simulations of turbulence. Even the bare DL solutions, which do not take into
account any physics of turbulence explicitly, are impressively good overall
when it comes to qualitative description of important features of turbulence.
However, the early tests have also uncovered some caveats of the DL approaches.
We observe that the static DL scheme, implementing Convolutional GAN and
trained on spatial snapshots of turbulence, fails to reproduce intermittency of
turbulent fluctuations at small scales and details of the turbulence geometry
at large scales. We show that the dynamic NN schemes, namely LAT-NET and
Compressed Convolutional LSTM, trained on a temporal sequence of turbulence
snapshots are capable to correct for the caveats of the static NN. We suggest a
path forward towards improving reproducibility of the large-scale geometry of
turbulence with NN.
