  Turbulent flows consist of a wide range of interacting scales. Since the
scale range increases as some power of the flow Reynolds number, a faithful
simulation of the entire scale range is prohibitively expensive at high
Reynolds numbers. The most expensive aspect concerns the small scale motions;
thus, major emphasis is placed on understanding and modeling them, taking
advantage of their putative universality. In this work, using physics-informed
deep learning methods, we present a modeling framework to capture and predict
the small scale dynamics of turbulence, via the velocity gradient tensor. The
model is based on obtaining functional closures for the pressure Hessian and
viscous Laplacian contributions as functions of velocity gradient tensor. This
task is accomplished using deep neural networks that are consistent with
physical constraints and incorporate Reynolds number dependence explicitly to
account for small-scale intermittency. We then utilize a massive direct
numerical simulation database, spanning two orders of magnitude in the
large-scale Reynolds number, for training and validation. The model learns from
low to moderate Reynolds numbers, and successfully predicts velocity gradient
statistics at both seen and higher (unseen) Reynolds numbers. The success of
our present approach demonstrates the viability of deep learning over
traditional modeling approaches in capturing and predicting small scale
features of turbulence.
