Automatic Differentiation for large scale flow control with application to non-Newtonian flows

这个项目的重点是开发、分析和实现有效的数值优化算法，使用自动微分技术在流量控制问题的背景下，包括高度非线性PDE约束。开发的pde约束优化算法将应用于涉及非牛顿流体的流动的稳定，例如血液流动和沉降问题。所考虑的模型包括流体的记忆效应，它会导致复杂和高度非线性的状态方程。这些问题的共同之处在于，如果可能的话，确定伴随阵或灵敏度所需的线性化状态方程将是一项极其繁琐的任务。我们的目标是以一种系统的方式在这种情况下应用自动区分技术。特别强调了目标导向的适应性、模型校准的最佳实验设计以及该框架下的并行处理。

This project focuses on the development, analysis, and implementation of efficient numerical optimization algorithms using Automatic Differentiation techniques in the context of flow control problems including highly nonlinear PDE constraints. The developed PDE-constrained optimization algorithms will be applied to the stabilization of flows involving non-Newtonian fluids as for example blood flows and sedimentation problems. The considered models include e.g. memory effects of the fluid which lead to complex and highly nonlinear state equations. These problems have in common that the determination of the linearized state equation needed for the adjoints or for the sensitivities would be an extremely tedious task if possible at all. Our goal is to apply in a systematic way techniques of automatic differentiation in that context. A special emphasis is given to goal oriented adaptivity, optimal experimental design toward model calibration, and parallel processing in that framework.