Academic Report of School of Mathematical Sciences [2026] No. 035

(Series Report for High-Level University Construction No. 1294)

Title：Thermodynamics-Informed Machine Learning for Multiscale PDE Models

Speaker：Johannes Zimmer, Professor (Technische Universität München)

Time：10:45-11:45, Apr. 30, 2026

Location：Room 2433, Office Area, Huiwen Building, Yuehai Campus, Shenzhen University

Abstract：Understanding the connection between microscopic particle dynamics and macroscopic continuum descriptions is a central challenge in modern applied mathematics. We study partial differential equations (PDEs) arising from stochastic many-particle systems, with a focus on scale-bridging and the emergence of collective behavior. Our approach emphasizes thermodynamically consistent formulations in terms of energy and entropy evolution, including variational structures closely related to large deviation theory. A particular focus is on fluctuating hydrodynamics, which captures stochastic deviations around deterministic limit equations. We combine analytical methods with data-driven techniques, leveraging ideas from thermodynamics and statistical physics—such as Otto calculus—to design machine learning approaches that infer evolution equations directly from particle data. The research further addresses the derivation of homogenized PDE models and the development of fluctuating macroscopic descriptions, with applications in mathematical physics and mechanics, including active matter.

Speaker Profile： Johannes Zimmer, since 2020, he has been a Professor of Mathematics at the Technical University of Munich (TUM), serving as Chair for Analysis and Modelling. He was previously at the University of Bath (2004–2020), where he held positions as Lecturer, Reader, and Professor, and has been a Visiting Professor there since 2020.

He received his Ph.D. in Mathematics from TUM in 2000, followed by a postdoctoral position at the California Institute of Technology and a research group leadership at the Max Planck Institute for Mathematics in the Sciences in Leipzig.

His research interests include stochastic and deterministic differential equations, dynamical systems, and multiscale modeling, with a focus on nonequilibrium problems.

Faculty and students are welcome to attend!

Invited by: Nian Yao

School of Mathematical Sciences

April 27, 2026