We consider an optimal flow control problem in a patient-specific coronary artery bypass graft with the aim of matching the blood flow velocity with given measurements as the Reynolds number varies in a physiological range. Blood flow is modelled with the steady incompressible Navier-Stokes equations. The geometry consists in a stenosed left anterior descending artery where a single bypass is performed with the right internal thoracic artery. The control variable is the unknown value of the normal stress at the outlet boundary, which is need for a correct set-up of the outlet boundary condition. For the numerical solution of the parametric optimal flow control problem, we develop a data-driven reduced order method that combines proper orthogonal decomposition (POD) with neural networks. We present numerical results showing that our data-driven approach leads to a substantial speed-up with respect to a more classical POD-Galerkin strategy proposed in [59], while having comparable accuracy.
@article{arxiv.2206.15384,
title = {A data-driven Reduced Order Method for parametric optimal blood flow control: application to coronary bypass graft},
author = {Caterina Balzotti and Pierfrancesco Siena and Michele Girfoglio and Annalisa Quaini and Gianluigi Rozza},
journal= {arXiv preprint arXiv:2206.15384},
year = {2022}
}