Nonlocal PDE-constrained optimization: Modelling and numerics

点击翻译按钮获取中文摘要

Optimal control involves engineering physical processes to achieve idealised outcomes, while also optimising a quality measure. A suitable landscape for its applicability is parameter learning. My focus lies in discovering controls associated with nonlocal operators; i.e., operators that input information from large clouds of points in the domain of interest. Nonlocalities add additional complexity, as existence results are limited and problem-specific, while discretisation of nonlocal terms often leads to dense and ill-conditioned systems. Consequently, I am dedicated to develop efficient and high-resolution numerical solutions to tackle nonlocal systems.