  Successfully training Physics Informed Neural Networks (PINNs) for highly
nonlinear PDEs on complex 3D domains remains a challenging task. In this paper,
PINNs are employed to solve the 3D incompressible Navier-Stokes (NS) equations
at moderate to high Reynolds numbers for complex geometries. The presented
method utilizes very sparsely distributed solution data in the domain. A
detailed investigation on the effect of the amount of supplied data and the
PDE-based regularizers is presented. Additionally, a hybrid data-PINNs approach
is used to generate a surrogate model of a realistic flow-thermal electronics
design problem. This surrogate model provides near real-time sampling and was
found to outperform standard data-driven neural networks when tested on unseen
query points. The findings of the paper show how PINNs can be effective when
used in conjunction with sparse data for solving 3D nonlinear PDEs or for
surrogate modeling of design spaces governed by them.
