  This paper explores the potential of Physics-Informed Neural Networks (PINNs)
to serve as Reduced Order Models (ROMs) for simulating the flow field within
stirred tank reactors (STRs). We solve the two-dimensional stationary
Navier-Stokes equations within a geometrically intricate domain and explore
methodologies that allow us to integrate additional physical insights into the
model. These approaches include imposing the Dirichlet boundary conditions
(BCs) strongly and employing domain decomposition (DD), with both overlapping
and non-overlapping subdomains. We adapt the Extended Physics-Informed Neural
Network (XPINN) approach to solve different sets of equations in distinct
subdomains based on the diverse flow characteristics present in each region.
Our exploration results in a hierarchy of models spanning various levels of
complexity, where the best models exhibit l1 prediction errors of less than 1%
for both pressure and velocity. To illustrate the reproducibility of our
approach, we track the errors over repeated independent training runs of the
best identified model and show its reliability. Subsequently, by incorporating
the stirring rate as a parametric input, we develop a fast-to-evaluate model of
the flow capable of interpolating across a wide range of Reynolds numbers.
Although we exclusively restrict ourselves to STRs in this work, we conclude
that the steps taken to obtain the presented model hierarchy can be transferred
to other applications.
