Subgrid stress modelling with multidimensional state space sequence models

Large eddy simulations (LES) are becoming increasingly viable due to the growth in computational power over the last few decades, and subgrid stress modelling plays a large role in the accuracy of LES. A new class of neural network models, S4 and S4ND models, allow for learning a continuous representation of the discrete dataset, which facilitates a principled approach to incorporating grid dependence in neural network subgrid stress modelling. A S4ND U-Net neural network architecture is proposed and trained on both forced homogeneous isotropic turbulence (HIT) and channel flow. A priori , this architecture is able to extrapolate to grid spacings that are coarser than the training set grid spacings, while simpler artificial neural network (ANN) models fail. A posteriori tests on both forced HIT and channel flow indicate that the S4ND model is more accurate than traditional models and ANN-based models on grid sizes that are in the training set. The S4ND model is also able to extrapolate robustly to grid sizes that are coarser than the training set a posteriori , and is more accurate than many traditional subgrid stress models. Finally, the proposed model is also evaluated on flows at increasing Reynolds numbers, where it is seen that the proposed neural network remains stable even at a Reynolds number that is 500 000 times larger than what was seen in the training set.