ICBS2025: PDEs Meet Machine Learning: Integrating Numerics, Control, and Machine Learning by E. Zuazua

Event: ICBS2025, International Congress of Basic Science 2025
Date: Tue. July 15, 2025 at 15:30 (local time)

Talk: PDEs Meet Machine Learning: Integrating Numerics, Control, and Machine Learning
Speaker: Prof. Enrique Zuazua, FAU – Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)
Slides

VIDEO

Watch this talk @YouTube:
https://youtu.be/DbIRNH9ZsnM?si=Lfvo-M3-Q4LzRgJp

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.

WHEN
Tue. July 15, 2025 at 09:00H (local time)
See schedule

WHERE
On-site:
A7-101. BIMSA, Beijing Institute of Mathematical Sciences and Applications
No. 544, Hefangkou Village Huaibei Town
Huairou District Beijing 101408

Online (Live-YouTube):
https://www.youtube.com/live/UbVchOrC5Ho

About ICBS2025
The #ICBS2025, International Congress of Basic Science 2025 is an annual event that brings together leading experts from all around to celebrate basic sciences – Mathematics, Physics and Information Science and Engineering organized in Beijing by the Beijing Institute of Mathematical Sciences and Applications (BIMSA) on July 13-25, 2025.

The program spans 13 days and will feature hundreds of lectures, satellite meetings and engaging exchange events. Numerous academicians from China, the United States, and European nations, including Nobel laureate, Fields Medalists, Turing Medal winners, and distinguished scholars.

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See more:
Official page of the event: https://www.icbs.cn/
This event at BIMSA
This event at Tsinghua University