  Fluid turbulence is an important problem for physics and engineering.
Turbulence modeling deals with the development of simplified models that can
act as surrogates for representing the effects of turbulence on flow evolution.
Such models correspond to a range of different fidelities, from simple
eddy-viscosity-based closures to Reynolds Stress Models. Till now the focus of
the data-driven turbulence modeling efforts has focused on Machine Learning
augmented eddy-viscosity models. In this communication, we illustrate the
manner in which the eddy-viscosity framework delimits the efficacy and
performance of Machine learning algorithms. Based on this foundation we carry
out the first application of Machine learning algorithms for developing
improved Reynolds Stress Modeling-based closures for turbulence. Different
machine learning approaches are assessed for modeling the pressure strain
correlation in turbulence, a longstanding problem of singular importance. We
evaluate the performance of these algorithms in the learning dataset, as well
as their ability to generalize to different flow cases where the inherent
physical processes may vary. This explores the assertion that ML-based
data-driven turbulence models can overcome the modeling limitations associated
with the traditional turbulence models and ML models trained with large amounts
of data with different classes of flows can predict flow field with reasonable
accuracy for unknown flows with similar flow physics.
