  In this work, we present a novel data-based approach to turbulence modelling
for Large Eddy Simulation (LES) by artificial neural networks. We define the
exact closure terms including the discretization operators and generate
training data from direct numerical simulations of decaying homogeneous
isotropic turbulence. We design and train artificial neural networks based on
local convolution filters to predict the underlying unknown non-linear mapping
from the coarse grid quantities to the closure terms without a priori
assumptions. All investigated networks are able to generalize from the data and
learn approximations with a cross correlation of up to 47% and even 73% for the
inner elements, leading to the conclusion that the current training success is
data-bound. We further show that selecting both the coarse grid primitive
variables as well as the coarse grid LES operator as input features
significantly improves training results. Finally, we construct a stable and
accurate LES model from the learned closure terms. Therefore, we translate the
model predictions into a data-adaptive, pointwise eddy viscosity closure and
show that the resulting LES scheme performs well compared to current state of
the art approaches. This work represents the starting point for further
research into data-driven, universal turbulence models.
