Docent lecture, Axel Ringh

Abstract: Many problems in science and engineering can be addressed using methods from applied mathematics. This includes problems such as estimating unobserved states of a dynamical system, reconstructing images of an object’s interior from indirect measurements, and certifying stability of feedback interconnections of dynamical systems. Solutions to these problems often leverage techniques from optimization, systems theory, inverse problems, and machine learning.

In this presentation, I will provide an overview of my research, which focuses on developing methods for solving problems within these four above-mentioned areas. I will discuss various topics that I have explored and that I am currently working on, including computational methods for optimal transport, the problem of inverse optimal control, rational solutions to moment problems, and the application of machine learning techniques to optimization and inverse problems. The goal is to illustrate both similarities as well as differences between the topics.