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