  Deep learning (DL)-based Reynolds stress with its capability to leverage
values of large data can be used to close Reynolds-averaged Navier-Stoke (RANS)
equations. Type I and Type II machine learning (ML) frameworks are studied to
investigate data and flow feature requirements while training DL-based Reynolds
stress. The paper presents a method, flow features coverage mapping (FFCM), to
quantify the physics coverage of DL-based closures that can be used to examine
the sufficiency of training data points as well as input flow features for
data-driven turbulence models. Three case studies are formulated to demonstrate
the properties of Type I and Type II ML. The first case indicates that errors
of RANS equations with DL-based Reynolds stress by Type I ML are accumulated
along with the simulation time when training data do not sufficiently cover
transient details. The second case uses Type I ML to show that DL can figure
out time history of flow transients from data sampled at various times. The
case study also shows that the necessary and sufficient flow features of
DL-based closures are first-order spatial derivatives of velocity fields. The
last case demonstrates the limitation of Type II ML for unsteady flow
simulation. Type II ML requires initial conditions to be sufficiently close to
reference data. Then reference data can be used to improve RANS simulation.
