From Deep to Physics-Informed Learning of Turbulence: Diagnostics

We describe physical tests validating progress made toward acceleration and automation of hydrodynamic codes in the regime of developed turbulence by two {\bf Deep Learning} (DL) Neural Network (NN) schemes trained on {\bf 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 scheme, LAT-NET, trained on a temporal sequence of turbulence snapshots is capable to correct for the small-scale caveat of the static NN. We suggest a path forward towards improving reproducibility of the large-scale geometry of turbulence with NN.