Generative subgrid-scale modeling

The mismatch between the a-priori and a-posteriori error is ubiquitous in data-driven subgrid-scale (SGS) modeling, which is an important ingredient in large eddy simulations. In this work, we investigate the cause of this mismatch in depth and attribute it to two issues: data imbalance and multi-valuedness. Based on this understanding, we propose a generative modeling approach for the SGS stresses that resolves the issue of multi-valuedness and demonstrate its effectiveness in the Kuramoto-Sivashinsky equation.