Course: PDEs Meet Machine Learning: Integrating Numerics, Control, and Machine Learning
Location: Zhengxin Building 209，Jilin University，Changchun
Zoom ID:904 645 6677, Password : 2025
Time : 9:00 – 11:00, July 21st - July 23rd, 2025
Instructor: Enrique Zuazua (Professor, University of Erlangen-Nuremberg, Germany)
Abstract:
Partial Differential Equations (PDEs) form the cornerstone of mathematical modeling in mechanics and the natural sciences, driving advances in analysis, numerical methods, and applied mathematics. Today, the rise of Machine Learning (ML) and Artificial Intelligence (AI) presents transformative opportunities and challenges for classical PDE methodologies. Can ML enhance PDE techniques without sacrificing mathematical rigor? Can we develop hybrid computational frameworks that leverage data-driven approaches while maintaining the reliability of traditional methods?
This lecture explores these questions through an interdisciplinary lens, bridging PDE theory, control, and ML. We examine the intrinsic connections between representation, optimization, and control theory—rooted in cybernetics (from Ampère to Wiener) and historically motivated by the quest to design intelligent machines. Interestingly, the goals of control theory align closely with those of modern AI, emphasizing mathematics’ unifying power in modeling and innovation.
We discuss recent work addressing two key challenges: Why does ML generalize so effectively? and How can data-driven insights be rigorously integrated into classical applied mathematics, particularly for PDEs and numerical methods? This exploration is shaping a new paradigm of PDE+D(ata), to forge the next generation of computational tools.
Introduction of the Instructor
Enrique Zuazua, professor in the Department of Mathematics at the University of Erlangen-Nuremberg, Germany, and academician of the European Academy of Sciences, is a world-leading figure in the field of control for distributed parameter systems. He has been awarded the W.T. and Idalia Reid Prize by the Society for Industrial and Applied Mathematics (SIAM). He has successively served as an editorial board member, associate editor, or editor-in-chief for journals such as J. Math. Pures Appl., SIAM J. Control Optim., J. Differential Equations, and ESAIM: Control Optim. Calc. Var.. He delivered a 45-minute invited lecture at International Congress of Mathematicians (ICM) 2006 and has been invited to give a one-hour lecture at ICM 2026.
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