Dynamical Systems in Data Science: From Kinetic Closure to Learning Dynamics
This talk explores two ways in which ideas from dynamical systems can shape the mathematics of data science.
Overview
In the first part, motivated by Hilbert’s sixth problem, we present a data-driven approach to kinetic closure in which slow manifolds reveal the appropriate reduced structure and machine learning is used to infer optimal constitutive laws. In the second part, we turn to the learning process itself and discuss a geometric formulation of training dynamics in deep linear networks, viewed as a Riemannian gradient flow with a rich slow–fast structure near equilibrium. These examples highlight a common perspective: dynamical systems provide a principled framework for both constructing and understanding learning-based models.
Presenters
Dr. Florian Kogelbauer, Senior Research Fellow, Swiss Federal Institute of Technology Zurich (ETH Zurich)
Brief Biography
Dr. Florian Kogelbauer is a Senior Research Fellow at ETH Zürich, affiliated with RiskLab and the Finsure Tech Hub. His research lies at the interface of nonlinear dynamical systems, kinetic theory, and the mathematics of machine learning, with recent work on data-driven hydrodynamic closures and geophysical fluid dynamics. He previously held academic and research positions at the University of Vienna and AIST-Tohoku University in Japan, and has also worked in consulting at KPMG Austria.