课程名称: PDEs Meet Machine Learning: Integrating Numerics, Control, and Machine Learning

授课人: Enrique Zuazua教授 (德国埃尔朗根-纽伦堡大学)

课程日期: 2025年7月21日-7月23日 9:00 – 11:00 

课程地点: 正新楼209，吉林大学，长春；Zoom ID: 904 645 6677, 密码: 2025

摘要:

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.

授课人简介:

Enrique Zuazua，德国埃尔朗根-纽伦堡大学数学系教授，欧洲科学院院士，分布参数系统控制领域国际领军人物，曾获得美国工业与应用数学学会W.T. and Idalia Reid奖；先后担任J. Math. Pures Appl.、SIAM J. Control Optim.、J. Differential Equations和ESAIM: Control Optim. Calc. Var.等刊编委、副主编或主编，曾在2006年国际数学家大会作45分钟邀请报告，应邀将在2026年国际数学家大会作一小时报告。

课程QQ群二维码：