Abstract

We formulate a digital twin approach to the reconstruction of noisy and sparse velocity images. The method learns the most probable fluid dynamics model that fits the data by solving a Bayesian inverse Navier–Stokes boundary value problem. This jointly reconstructs and segments the velocity field, and at the same time infers hidden quantities such as the hydrodynamic pressure and the wall shear stress. Using a Bayesian framework, we regularize the problem by introducing a priori information about the unknown parameters in the form of Gaussian random fields. This further allows us to estimate the uncertainties of the unknowns by approximating their posterior covariance with a quasi-Newton method. Although this method has been developed for magnetic resonance velocimetry (flow-MRI), it extends to other velocimetry methods such as ultrasound Doppler velocimetry, particle image velocimetry (PIV) and scalar image velocimetry (SIV).