  There is a growing interest in developing data-driven subgrid-scale (SGS)
models for large-eddy simulation (LES) using machine learning (ML). In a priori
(offline) tests, some recent studies have found ML-based data-driven SGS models
that are trained on high-fidelity data (e.g., from direct numerical simulation,
DNS) to outperform baseline physics-based models and accurately capture the
inter-scale transfers, both forward (diffusion) and backscatter. While
promising, instabilities in a posteriori (online) tests and inabilities to
generalize to a different flow (e.g., with a higher Reynolds number, Re) remain
as major obstacles in broadening the applications of such data-driven SGS
models. For example, many of the same aforementioned studies have found
instabilities that required often ad-hoc remedies to stabilize the LES at the
expense of reducing accuracy. Here, using 2D decaying turbulence as the
testbed, we show that deep fully convolutional neural networks (CNNs) can
accurately predict the SGS forcing terms and the inter-scale transfers in a
priori tests, and if trained with enough samples, lead to stable and accurate a
posteriori LES-CNN. Further analysis attributes these instabilities to the
disproportionally lower accuracy of the CNNs in capturing backscattering when
the training set is small. We also show that transfer learning, which involves
re-training the CNN with a small amount of data (e.g., 1%) from the new flow,
enables accurate and stable a posteriori LES-CNN for flows with 16x higher Re
(as well as higher grid resolution if needed). These results show the promise
of CNNs with transfer learning to provide stable, accurate, and generalizable
LES for practical use.
