  In the present work, we explore the capability of artificial neural networks
(ANN) to predict the closure terms for large eddy simulations (LES) solely from
coarse-scale data. To this end, we derive a consistent framework for LES
closure models, with special emphasis laid upon the incorporation of implicit
discretization-based filters and numerical approximation errors. We investigate
implicit filter types, which are inspired by the solution representation of
discontinuous Galerkin and finite volume schemes and mimic the behaviour of the
discretization operator, and a global Fourier cutoff filter as a representative
of a typical explicit LES filter. Within the perfect LES framework, we compute
the exact closure terms for the different LES filter functions from direct
numerical simulation results of decaying homogeneous isotropic turbulence.
Multiple ANN with a multilayer perceptron (MLP) or a gated recurrent unit (GRU)
architecture are trained to predict the computed closure terms solely from
coarse-scale input data. For the given application, the GRU architecture
clearly outperforms the MLP networks in terms of accuracy, whilst reaching up
to 99.9% cross-correlation between the networks' predictions and the exact
closure terms for all considered filter functions. The GRU networks are also
shown to generalize well across different LES filters and resolutions. The
present study can thus be seen as a starting point for the investigation of
data-based modeling approaches for LES, which not only include the physical
closure terms, but account for the discretization effects in implicitly
filtered LES as well.
