Kernel-based approximation methods offer a flexible yet rigorously analyzable framework for reconstructing functions from scattered measurements. In recent years, the focus has shifted from pure function reconstruction to learning operators, i.e., mappings between infinite-dimensional function spaces.

In this talk I will trace the development of kernel-based approximation, from scalar-valued function reconstruction approximation of vector fields with prescribed physical properties such as divergence-freeness. Building on this, I will discuss new advances in kernel-based operator learning.

For further information about the seminar, please visit this webpage.