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

该项目的重点是开发，分析和实施高效的数值优化算法，使用自动微分技术的流量控制问题，包括高度非线性PDE约束的背景下。所开发的偏微分方程约束优化算法将被应用到涉及非牛顿流体的流动的稳定，例如血液流动和沉降问题。所考虑的模型包括例如导致复杂和高度非线性状态方程的流体的记忆效应。这些问题有一个共同点，即确定伴随或灵敏度所需的线性化状态方程，如果可能的话，将是一项极其繁琐的任务。我们的目标是以系统的方式在这种情况下应用自动区分技术。一个特别强调的是目标导向的自适应性，最佳实验设计模型校准，并在该框架中的并行处理。

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.