Incompressible flow and dynamic vortex shedding past a circular cylinder at Re=100. The spatio-temporal training data correspond to the depicted rectangular region in the cylinder wake. Locations of training data-points for the the streamwise and transverse velocity components.

Predicted versus exact instantaneous pressure field at a representative time instant. By definition, the pressure can be recovered up to a constant, hence justifying the different magnitude between the two plots. This remarkable qualitative agreement highlights the ability of physics-informed neural networks to identify the entire pressure field, despite the fact that no data on the pressure are used during model training. Correct partial differential equation along with the identified one.

Arxiv [URL]