Physics-informed deep neural networks applied to scalar subgrid flux modeling in a mixed DNS/LES framework

The application of artificial neural networks (ANNs) to turbulence closure has been an emergent and active area of research in recent years due to the success of such data-driven methods in fields of computer vision, natural language processing, and other industrial and scientific disciplines. In this research, we apply ANNs to spacio-temporal dynamic modeling of the subgrid passive scalar flux as it relates to large-eddy simulations (LESs). By training on direct numerical simulations (DNSs) of homogeneous isotropic turbulence coupled to a passive scalar, we optimize ANNs to predict the subgrid scalar flux as a function of resolved-scale features. Trained models are then implemented in simulation and evaluated with \textit{a-posteriori} analysis. In these simulations, filtered scalar advection is coupled to explicitly filtered and statistically-stationary turbulence such that scalar dynamics have no dependence on potentially inaccurate subgrid stress models. By analysis with single- and multi-point statistics, we demonstrate that the data-driven models compete, and often out-perform, properly optimized canonical models. We suggest that this simulation framework may serve as a simplified closure testbed for the investigation and evaluation of data-driven turbulence closures.