Physics-constrained neural-network sub-grid-scale models for turbulent premixed flames

Neural-network (NN) sub-grid-scale (SGS) models are developed for large-eddy simulation (LES) of turbulent reacting flows. Models are trained a posteriori: the objective function measures the deviation of the model-predicted solution from some trusted data, which is a filtered direct numerical simulation (DNS) for this demonstration. The end-to-end optimization requires an adjoint solve, which couples the training process to the represented physics. Several constraints are directly enforced on the model design, including conservation properties, scalar boundedness, and Galilean invariance. Models are demonstrated for simulations of a statistically planar premixed flame, freely propagating in a rectangular domain, governed by a single-species single-step irreversible reaction, and embedded in high-speed turbulence. An under-resolved simulation yields an inaccurate prediction of flame folding processes, posing an SGS challenge for our model. Predictions by models trained for different objective functions are compared to inform understanding of how they work.