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We consider an optimal flow control problem in a patient-specific coronaryartery bypass graft with the aim of matching the blood flow velocity with givenmeasurements as the Reynolds number varies in a physiological range. Blood flowis modelled with the steady incompressible Navier-Stokes equations. Thegeometry consists in a stenosed left anterior descending artery where a singlebypass is performed with the right internal thoracic artery. The controlvariable 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 thenumerical solution of the parametric optimal flow control problem, we develop adata-driven reduced order method that combines proper orthogonal decomposition(POD) with neural networks. We present numerical results showing that ourdata-driven approach leads to a substantial speed-up with respect to a moreclassical POD-Galerkin strategy proposed in [59], while having comparableaccuracy.

A data-driven Reduced Order Method for parametric optimal blood flow control: application to coronary bypass graft