A data-driven reduced order method for parametric optimal blood flow control: Application to coronary bypass graft

Abstract

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 [62], while having comparable accuracy.

A non-intrusive data-driven reduced order model for parametrized CFD-DEM numerical simulations

“…To demonstrate the network architecture associated with the LSTM model, we first introduce a simple Artificial Neural Network (ANN), followed by its extension to a Recurrent Neural Network (RNN) and finally to an LSTM network. ANN is a modelling technique able to formulate a nonlinear functional relationship between input and output data: see, e.g., [52,53,54,55,56]. In our case the input-output data are the pairs…”