Learning Bayesian digital twins of flows from PC-MRI data

I formulate a Bayesian digital twin approach to the reconstruction of velocity fields from noisy and possibly sparse phase-contrast magnetic resonance imaging data. The method learns the most probable fluid dynamics model that fits the data by solving a Bayesian inverse Navier–Stokes (N-S) boundary value problem. This jointly reconstructs and segments the velocity data, and at the same time infers hidden quantities such as the hydrodynamic pressure and the wall shear stress, as well as their uncertainties. Using a Bayesian framework, I regularize the inverse problem by introducing a priori information about the unknown N-S parameters in the form of Gaussian random fields. This prior information is updated using the Navier–Stokes problem, an energy-based segmentation functional, and by requiring that the reconstruction is consistent with the data. I create an algorithm that solves this inverse problem, and test it for an experimental flow through a 3D-printed physical model of an aortic arch. I show that the method can successfully reconstruct noisy flow-MRI data in realistic geometries and high Reynolds numbers. Although this method has been developed for flow-MRI, it extends to other velocimetry methods such as ultrasound Doppler velocimetry, particle image velocimetry (PIV) and scalar image velocimetry (SIV). The reconstruction of in vivo cardiovascular and porous media flows are among the most interesting applications of this work.