Neural Network Driven Subgrid Stress Modeling: Narrowing the A priori vs A posteriori Gap

Deep neural networks, when applied to subgrid stress modeling, often suffer in performance a posteriori as compared to their a priori performance. In addition, when assembling the training data, choosing which filter to use to process the DNS data is often overlooked. To explore this, training data is created with multiple types of filters, and neural networks are trained on the whole training set. A priori, it is seen that the neural networks trained on multiple types of filters have the same performance as neural networks trained on only one filter width. Furthermore, a posteriori, over a wide range of input and output normalizations, the neural networks trained with training data that consist of multiple filters are far more accurate when integrated in a Large Eddy Simulation (LES) of Homogenous Isotropic Turbulence (HIT) in a spectral solver with two-thirds dealiasing. The evaluation of training with various filters is also explored for differing numerical schemes a posteriori, and the robustness associated with this training procedure will be presented. By expanding the expressiveness of the training data, the gap in accuracy between a priori and a posteriori results when compared to filtered DNS can be reduced.