In this investigation, a data-driven turbulence closure framework is
introduced and deployed for the sub-grid modelling of Kraichnan turbulence. The
novelty of the proposed method lies in the fact that snapshots from
high-fidelity numerical data are used to inform artificial neural networks for
predicting the turbulence source term through localized grid-resolved
information. In particular, our proposed methodology successfully establishes a
map between inputs given by stencils of the vorticity and the streamfunction
along with information from two well-known eddy-viscosity kernels. Through this
we predict the sub-grid vorticity forcing in a temporally and spatially dynamic
fashion. Our study is both a-priori and a-posteriori in nature. In the former,
we present an extensive hyper-parameter optimization analysis in addition to
learning quantification through probability density function based validation
of sub-grid predictions. In the latter, we analyse the performance of our
framework for flow evolution in a classical decaying two-dimensional turbulence
test case in the presence of errors related to temporal and spatial
discretization. Statistical assessments in the form of angle-averaged kinetic
energy spectra demonstrate the promise of the proposed methodology for sub-grid
quantity inference. In addition, it is also observed that some measure of
a-posteriori error must be considered during optimal model selection for
greater accuracy. The results in this article thus represent a promising
development in the formalization of a framework for generation of
heuristic-free turbulence closures from data.

本文提出一种数据驱动的湍流封闭框架，利用人工神经网络预测湍流源项，建立了多个输入和输出之间的映射关系，优化分析和概率密度函数验证了子网格预测，证明了该方法可推断子网格量，为实现无启发式湍流封闭算法打下了良好的基础。