# Hyperelastic Registration

Starting from noisy velocity images, unsteady three-dimensional blood flow and elastic vessel-wall motion can be reconstructed together without a prescribed inlet waveform or initial velocity. The solver alternates a fluid update, in which a physics-informed network fits the observations while enforcing the incompressible Navier–Stokes equations on the moving domain, with a geometry update, in which registration plus interface traction continuity and an elastic momentum residual constrain wall displacement. On a converging channel and a patient-like aorta, the PirateNets version reaches velocity relative errors of 0.0243 and 0.0372, below the 0.1066 and 0.1305 of a standard PINN of the same depth and width.

Starting from noisy velocity images, unsteady three-dimensional blood flow and elastic vessel-wall motion can be reconstructed together without a prescribed inlet waveform or initial velocity. The solver alternates a fluid update, in which a physics-informed network fits the observations while enforcing the incompressible Navier–Stokes equations on the moving domain, with a geometry update, in which registration plus interface traction continuity and an elastic momentum residual constrain wall displacement. On a converging channel and a patient-like aorta, the PirateNets version reaches velocity relative errors of 0.0243 and 0.0372, below the 0.1066 and 0.1305 of a standard PINN of the same depth and width.