Time: June 23, 10:30
S2 416-1

Titel: Operator Learning for Structured Dynamical Data: Nonlocal Methods and Applications

Abstract: 

Operator learning has emerged as a powerful paradigm for modeling complex systems whose behavior is naturally described at the level of maps between function spaces rather than finite-dimensional vectors. In this talk, I will present a research program centered on the learning of nonlocal operators, with particular emphasis on mathematically grounded architectures and their use in dynamical settings. I will begin by giving an overview of operator-learning methods and explaining why nonlocal formulations are especially well suited for systems with long-range spatiotemporal dependencies. I will then discuss several theoretical aspects of this framework, including approximation and stability considerations together with topological viewpoints motivated by fixed point theory, which help explain the expressive power of these models. Finally, I will present applications to fluid dynamics and brain science.