From Deep to Physics-Informed Learning of Turbulence: Diagnostics*

We describe tests which allow to validate the progress made toward acceleration and automation of hydro-codes. We aim to verify whether various statistical properties, constraints, and relations not enforced explicitly within the Deep Learning (DL) training hold. To do this, we compare results extracted from the training data and from the generated/synthetic data. Through the tests we verify physical laws and intuition about turbulence. Three DL schemes, GANS of [1],  LAT-NET of [2] and LSTM of [3] are juxtaposed within the setting of the homogeneous, isotropic, stationary 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, we also uncovered some significant caveats of the DL approaches and describe the next steps  aimed at making corrections to the respective DL schemes through reinforcement of the special feature of turbulence that the current DL scheme fails to extract.

[1] http://meetings.aps.org/Meeting/DFD17/Session/A31.8

[2] https://arxiv.org/abs/1705.09036

[3] https://arxiv.org/abs/1804.09269