Addressing A Posteriori Performance Degradation in Neural Network Subgrid Stress Models

TL;DR

The paper addresses why neural network subgrid stress models can show strong a priori accuracy yet poor a posteriori performance in LES. It introduces a dual strategy: training with multiple explicit filters and reducing input feature complexity to lessen distribution shift between training data and LES solvers. Across two LES codes with different numerical schemes, networks trained with two filters and with simpler input sets demonstrate markedly more robust a posteriori performance, while a priori performance remains comparable. These findings provide practical guidance for designing SGS models that generalize across solvers and filter configurations, improving reliability of neural network closures in LES.

Abstract

Neural network subgrid stress models often have a priori performance that is far better than the a posteriori performance, leading to neural network models that look very promising a priori completely failing in a posteriori Large Eddy Simulations (LES). This performance gap can be decreased by combining two different methods, training data augmentation and reducing input complexity to the neural network. Augmenting the training data with two different filters before training the neural networks has no performance degradation a priori as compared to a neural network trained with one filter. A posteriori, neural networks trained with two different filters are far more robust across two different LES codes with different numerical schemes. In addition, by ablating away the higher order terms input into the neural network, the a priori versus a posteriori performance changes become less apparent. When combined, neural networks that use both training data augmentation and a less complex set of inputs have a posteriori performance far more reflective of their a priori evaluation.

Figures (4)

• Figure 1: Characterizations of the DSCF in both physical and spectral space. $\omega_c = 2 \pi f_c$ corresponds to the filter cutoff point, here designated at a $16\Delta_{DNS}$ filter width, while $\omega_c = 2 \pi f_n, f_n \in [-0.5, 0.5]$ denotes the normalized angular frequency. Two different DSCF versions are shown, one with a 17 and the other with a 33 point support.
• Figure 2: Overall graph neural network architecture. Note that "res. conn." denotes residual connections.
• Figure 3: A posteriori PadeOps HIT Spectra, SSE is given in the legend (lower the better)
• Figure 4: A posteriori Padelibs HIT Spectra, SSE is given in the legend (lower the better)