Physical invariance in neural networks for subgrid-scale scalar flux modeling

In this paper we present a new strategy to model the subgrid-scale scalar flux in three-dimensional turbulent incompressible flow using physics-informed neural networks (NNs). When trained from direct numerical simulation (DNS) data, state-of-the-art networks, such as convolutional may not preserve well known physical priors, which turn question their application real case-studies. To address issue, investigate hard and soft constraints into based on classical transformation invariances symmetries derived laws. From simulation-based experiments, show that proposed transformation-invariant NN outperforms both purely data-driven ones parametric models. The considered are regarded regularizers metrics during priori evaluation constrain distribution tails of predicted term be closer DNS. They also increase stability performance when used surrogate large-eddy simulation. Moreover, is shown generalize regimes have been seen training phase.