Subgrid Stress Modeling with Data Driven Structured State Space Sequence Models*

Data driven subgrid stress modeling with machine learning has shown promise in increasing the accuracy of Large Eddy Simulations (LES) compared to traditional subgrid stress models. Adapting Structured State Space sequence (S4) models to learn the subgrid stress tensor in multi-dimensional space with the S4ND model allows for global, continuous convolution kernels to be learned. The S4ND model is used in a U-net architecture to extract multi-scale spatial features of turbulence, and is trained on forced homogenous isotropic turbulence (HIT) and channel flow at two different filter widths. From a priori analysis, the S4ND U-net model is able to generalize to both interpolative and extrapolative filter widths with minimal change in the loss, even when the extrapolative filter width corresponds to situations where over 20 percent of the energy has been filtered out as compared to Direct Numerical Simulation (DNS). This is compared to other data driven subgrid models where the loss when generalizing to an extrapolative filter width increases by a factor of 1.5-3. Furthermore, a posteriori analysis involving both channel flow and forced HIT are conducted with various models to evaluate the S4ND U-net model.