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.
翻译:我们认为,在特定病人的冠心动脉切除中,最佳的流量控制问题在于将血液流速与特定测量量相匹配,因为雷诺兹的数字在生理范围上各不相同。血液流与稳定的不压缩纳维-斯托克斯方程式的模式是模范的。几何法由左侧的骨质下方动脉组成,其中单次绕动脉与右内心动脉一起进行。控制变量是出口边界正常应力的未知值,这需要正确设置外缘条件。关于参数最佳流控问题的数字解决方案,我们开发了一种数据驱动的减序方法,将正常的或硫的分解状态与神经网络结合起来。我们提供的数字结果显示,我们的数据驱动方法导致在 [59] 中提出的更古典的 POD-Galerkin 战略的大幅加速,同时具有相似的精确性。