Time: 14:00-16:00, Friday, September 5 2025
Venue：E4-233
Host： Zhennan Zhou, ITS
Speaker：Enrique Zuazua, Friedrich-Alexander-Universität
Biography：Enrique Zuazua holds, since September 2019, the Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship at the Department of Mathematics of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) in Germany and part-time appointments at Universidad Autónoma de Madrid (UAM) and Fundación Deusto, Bilbao. He is also a member of the Basque Academy "Jakiunde", Fellow of the Artificial Intelligence Industry Academy (AIIA) and of the Academia of Europaea, and cooperates with the artificial intelligence company Sherpa AI in Bilbao and with SHARE-Schaeffler in Erlangen.
Title：PDEs Meet Machine Learning
Abstract: Partial Differential Equations (PDEs) have long been at the core of mathematical modeling across the physical, biological, and engineering sciences, motivating key advances in analysis, numerical simulation, and applied mathematics. The recent explosion of Machine Learning (ML) and Artificial Intelligence (AI) presents transformative opportunities—but also significant challenges—for traditional PDE-based methodologies.
In this lecture, we adopt an interdisciplinary viewpoint at the intersection of PDE theory, control, and machine learning. We begin by revisiting the historical foundations of cybernetics—from Ampère to Wiener—driven by the longstanding vision of designing intelligent systems. Building on this perspective, we explore recent progress in addressing some of the most compelling questions in the field:
• Why does ML generalize so effectively?
• How can data-driven models be rigorously integrated into the analytical and numerical framework of PDEs?
• In what ways can PDE theory contribute to explaining the remarkable performance of generative AI?
