Stable a posteriori LES of forced two-dimensional turbulence using shallow artificial neural networks

Over recent years, data-driven methods to model subgrid-scale (SGS) stresses have garnered attention and been shown to outperform traditional SGS closure frameworks. It is well known that the statistical characteristics of an SGS model are more important than the accurate representation of the SGS term to obtain a stable LES. Two of the most important statistical requirements include the accurate representation of mean dissipation and the accurate prediction of the mean SGS stresses. Previous studies on data-driven SGS modeling showed that despite the accurate prediction of the inter-scale energy transfers and/or the SGS term, instabilities would often arise in an a posteriori LES, which would often require ad-hoc post-processing, one of which is to eliminate backscatter. In the present work, using forced two-dimensional turbulence test cases, we developed an SGS model using shallow (2 hidden layers) artificial neural networks that could obtain high correlation coefficients of both the SGS stresses and the inter-scale energy transfers, using a Gaussian filter with several filter widths. More importantly, the developed SGS model also resulted in a stable a posteriori LES.