Axel Kröner

Prof. Dr. Axel Kröner is a Professor of Optimization at the Institute of Mathematics, Martin-Luther-Universität Halle-Wittenberg, within the Faculty of Natural Sciences II. His research focuses on optimal control and numerical methods for partial differential equations (PDEs), stochastic control, and feedback mechanisms in complex systems.

Academic Background:

• Ph.D. in Mathematics, Technische Universität München (2011)
• Diploma in Mathematics, Ruprecht-Karls-Universität Heidelberg (2007)

Axel Kröner's research spans PDE-constrained optimization, numerical analysis, and control theory. Key areas include feedback control for hyperbolic and parabolic equations, stochastic optimal control for infinite horizon problems, and adaptive finite element methods for PDE discretization. His work bridges theoretical and computational aspects, with applications in elasticity, fluid dynamics, and quantum mechanics.

Recent publications highlight advancements in Hamilton-Jacobi-Bellman equations for feedback control, bilevel optimization for parameter learning, and Runge-Kutta-based neural networks. Methodologies often integrate dynamic programming, Galerkin approximations, and error estimation for efficient solutions.

Advising and Projects: He has supervised numerous Master's and Bachelor's theses on topics like wave equation control, inverse problems, and neural network optimization. Funding includes support from the German Academic Exchange Service (DAAD) and the Gaspard Monge Program for Optimization and Operations Research (2015-2018).

Professional Activities: Kröner has organized major conferences such as the International Workshop on PDE Constrained Optimization and contributed to teaching at institutions including Humboldt-Universität zu Berlin and University Paris-Saclay.