  A filtered density function (FDF) model based on deep neural network (DNN),
termed DNN-FDF, is introduced for large eddy simulation (LES) of turbulent
flows involving conserved scalar transport. The primary objectives of this
study are to develop the DNN-FDF models and evaluate their predictive
capability in accounting for various filtered moments, including that of
non-linear source terms. A systematic approach is proposed to select DNN
training sample size and architecture via learning curves to minimize bias and
variance. Two DNN-FDF models are developed, one utilizing FDF data from Direct
Numerical Simulations (DNS) of constant-density temporal mixing layer, and the
other from zero-dimensional pairwise mixing stirred reactor simulations. The
latter is particularly intended for cases where generating DNS data is
computationally infeasible. DNN-FDF models are applied for LES of a
variable-density temporal mixing layer. The accuracy and consistency of both
DNN-FDF models are established by comparing their predicted filtered scalar
moments with those of conventional LES, where moment transport equations are
directly solved. The DNN-FDF models are shown to outperform a widely used
presumed-FDF model, especially for multi-modal FDFs and higher variance values.
Results are further assessed against DNS and the transported FDF method. The
latter couples LES with Monte Carlo for mixture fraction FDF computation. Most
importantly, the study shows that DNN-FDF models can accurately filter highly
non-linear functions within variable-density flows, highlighting their
potential for turbulent reacting flow simulations. Overall, the DNN-FDF
approach is shown to offer an accurate yet computationally economical approach
for describing turbulent scalar transport.
