Though PINNs (physics-informed neural networks) are now deemed as a
complement to traditional CFD (computational fluid dynamics) solvers rather
than a replacement, their ability to solve the Navier-Stokes equations without
given data is still of great interest. This report presents our
not-so-successful experiments of solving the Navier-Stokes equations with PINN
as a replacement for traditional solvers. We aim to, with our experiments,
prepare readers for the challenges they may face if they are interested in
data-free PINN. In this work, we used two standard flow problems: 2D
Taylor-Green vortex at Re=100 and 2D cylinder flow at Re=200. The PINN method
solved the 2D Taylor-Green vortex problem with acceptable results, and we used
this flow as an accuracy and performance benchmark. About 32 hours of training
were required for the PINN method's accuracy to match the accuracy of a 16x16
finite-difference simulation, which took less than 20 seconds. The 2D cylinder
flow, on the other hand, did not produce a physical solution. The PINN method
behaved like a steady-flow solver and did not capture the vortex shedding
phenomenon. By sharing our experience, we would like to emphasize that the PINN
method is still a work-in-progress, especially in terms of solving flow
problems without any given data. More work is needed to make PINN feasible for
real-world problems in such applications.Comment: 8 pages, 9 figure