  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.
