On Tuesday June 24, 2025 Prof. Enrique Zuazua will give a talk as keynote speaker on PDEs Meet Machine Learning: Integrating Numerics, Control, and Machine Learning at the LSMS 2025 conference, 12th. Annual Meeting of the “Lebanese Society for the Mathematical Sciences” held at the American University of Beirut on June 23 – 24, 2025.
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. June 24, 2025, 2025 at 09:00H (local time)
See more: Program of the event
WHERE
Basile Antoine Mergueridche Conference Hall
Isam Fares Institute, American University of Beirut
See the official page of the LSMS 2025
