We discuss recent developments around Hilbert's sixth problem about the passage from kinetic models to macroscopic fluid equations. We employ the technique of slow spectral closure to rigorously establish the existence of hydrodynamic manifolds and derive new non-local fluid equations for rarefied flows independent of Knudsen number. We show the singularity of certain scaled solutions, including the divergence of the Chapman--Enskog series for an explicit example, and apply neural nets to learn the optimal hydrodynamic closure from data. The new dynamically optimal constitutive laws are applied to a rarefied flow problem and we discuss the classical problem of the number of macroscopic rarefied fluid fields from a data-driven point of view.

Bio: Florian Kogelbauer is a Senior Research Fellow at ETH Zürich’s Department of Mathematics, affiliated with RiskLab and the Finsure Tech Hub. His research centres on nonlinear dynamical systems, kinetic theory, and fluid dynamics, with recent work on hydrodynamic closures and spectral theory for kinetic equations. He previously held academic and research roles at the University of Vienna and AIST-Tohoku University in Japan, alongside consulting positions at KPMG Austria.