Determining pressure from velocity via physics-informed neural network

This paper describes a physics-informed neural network (PINN) for determining pressure from velocity where the Navier-Stokes (NS) equations are incorporated as a physical constraint, but the boundary condition is not explicitly imposed. The exact solution of the NS equations for the oblique Hiemenz flow is utilized to evaluate the accuracy of the PINN and the effects of the relevant factors including the boundary condition, data noise, number of collocation points, Reynolds number and impingement angle. In addition, the PINN is evaluated in the two-dimensional flow over a NACA0012 airfoil based on computational fluid dynamics (CFD) simulation. Further, the PINN is applied to the velocity data of a flying hawkmoth (Manduca) obtained in high-speed schlieren visualizations, revealing some interesting pressure features associated with the vortex structures generated by the flapping wings. Overall, the PINN offers an alternative solution for the problem of pressure from velocity with the reasonable accuracy and robustness.