  In this work, we use ML techniques to develop presumed PDF models for large
eddy simulations of reacting flows. The joint sub-filter PDF of mixture
fraction and progress variable is modeled using various ML algorithms and
commonly used analytical models. The ML algorithms evaluated in the work are
representative of three major classes of ML techniques: traditional ensemble
methods (random forests), deep learning (deep neural networks), and generative
learning (variational autoencoders). The first two algorithms are supervised
learning algorithms, and the third is an unsupervised learning algorithm. Data
from direct numerical simulation of the low-swirl burner (Day et al. 2012) are
used to develop training data for sub-filter PDF models. Models are evaluated
on predictions of the sub-filter PDFs as well as predictions of the filtered
reaction rate of the progress variable, computed through a convolution of the
sub-filter PDF and the conditional means of the reaction rate. This a-priori
modeling study demonstrates that deep learning models for presumed PDF modeling
are three times more accurate than analytical beta-beta PDF models. These
models are as accurate as random forest models while using five times fewer
trainable parameters and being 25 times faster for inference. We illustrate how
models generalize to other regions of the flow and develop criteria based on
the Jensen-Shannon divergence to quantify the performance of a model on new
data.
