JLU Short course: PDEs Meet Machine Learning: Integrating Numerics, Control, and Machine Learning by E. Zuazua

Event: JLU Short-course
Date: Mon.-Tue. July 21-23, 2025

Title: PDEs Meet Machine Learning: Integrating Numerics, Control, and Machine Learning
Speaker: Prof. Enrique Zuazua. FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg (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.

WHEN
From Mon.-Tue. July 21 – 23, 2025 at 09:00H – 11:00H (local time)

WHERE
On-site / Online