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报告人 Speaker：Enrique ZUAZUA
报告人所在单位 Affiliation：Friedrich-Alexander-Universität Erlangen-Nürnberg
个人简介 Bio：Enrique ZUAZUA教授的研究涵盖偏微分方程、系统控制、数值分析及机器学习，已发表学术论文300余篇，是国际数学家大会ICM 45分钟报告人(2006年)和1小时报告人（2026年），同时担任毕尔巴鄂人工智能公司Sherpa AI的科学顾问。
自2019年9月起，担任德国埃尔朗根-纽伦堡弗里德里希-亚历山大大大学（FAU）数学系“动力学、控制、机器学习与数值分析”亚历山大·冯·洪堡讲席教授。2022年获美国工业与应用数学学会（SIAM）W.T.与伊达莉亚·里德奖（W.T. and Idalia Reid Prize）。
现任Mathematical Control and Related Fields与Advances in Continuous and Discrete Models两本期刊的联合主编和其它多个期刊的编委，以及多个科研中心与机构的科学委员会委员。
报告题目 Title：机器学习：数学家的视角 Machine Learning: A Mathematician’s Perspective
时间 Time：2025-09-04 10:00-11:00
地点 Venue：Room 2201, Guanghua Eastern Main Tower, Fudan University (Handan Campus)
报告摘要 Abstract：
机器学习已成为科技领域最具变革性的力量之一。在其强大算法的背后，是深深植根于应用数学、系统控制等经典学科的数学基础。本讲座将从数学家的视角出发，探讨机器学习为何能高效发挥作用，以及如何将其数据驱动范式严谨地融入传统分析框架。
我们将重新审视机器学习与系统控制（又称控制论）之间的历史关联与概念联系。系统控制这一领域的形成，离不开安培（Ampère）与维纳（Wiener）等先驱的开创性思想。机器学习与系统控制的并行发展，不仅体现出深刻的数学统一性，也凸显了数学在复杂系统建模与推动创新方面的力量。
这种双重视角具有相互赋能的作用。一方面，机器学习提出了具有根本性的数学问题，这些问题对数学界既是挑战，也是启发；另一方面，通过发展融合数据驱动洞见的混合方法，机器学习也为拓展经典应用数学的范畴提供了机遇。
讲座最后，将概述机器学习、应用数学与控制理论交叉领域未来研究的潜在方向。
报告题目 Title：A Historical Overview of System Control
时间 Time：2025-09-08 10:00-11:00
地点 Venue：Room 1801, Guanghua Eastern Main Tower, Fudan University (Handan Campus)
报告摘要 Abstract：
Control theory—also known as cybernetics, a term first introduced by Ampère and later popularized by Norbert Wiener—deals with the science of regulation and communication in animals and machines. Its roots can be traced back to antiquity, inspired by the human aspiration to design mechanisms capable of performing tasks autonomously, thereby extending both freedom and efficiency.
The goals of control systems resonate closely with those of modern Artificial Intelligence (AI), highlighting not only the deep unity of Mathematics but also its remarkable power to model natural phenomena and to shape technological innovation.
In this lecture, we will trace the historical development of control theory, emphasize some of its fundamental mathematical principles, and reveal its connections with today’s machine learning paradigms. We will also showcase key applications and success stories that illustrate the transformative impact of this interplay between control and learning.
报告题目 Title：PDE Controllability
时间 Time：2025-09-09 11:00-12:00
地点 Venue：Room 1801, Guanghua Eastern Main Tower, Fudan University (Handan Campus)
报告摘要 Abstract：
Controllability theory for Partial Differential Equations (PDEs) lies at the crossroads of analysis, geometry, and applications. It addresses a fundamental question: to what extent can we steer the evolution of a distributed system, governed by a PDE, toward a desired state by acting through suitable inputs or controls? Over the past decades, controllability has matured into a vibrant field, with key results for parabolic, hyperbolic, and dispersive equations, and with deep connections to optimization, numerical analysis, and, more recently, machine learning. In this lecture, I will present the main ideas and techniques underlying PDE controllability: observability inequalities, unique continuation principles, microlocal analysis, and Carleman estimates. I will also highlight several emblematic results, from exact controllability of the wave equation to null controllability of the heat equation, and discuss the interplay between control cost, geometry, and system dynamics. 报告题目 Title：Solving PDEs with Machine Learning: Strengths, Limitations, and Open Challenges 时间 Time：2025-09-10 11:00-12:00 地点 Venue：Room 1801, Guanghua Eastern Main Tower, Fudan University (Handan Campus) 报告摘要 Abstract： In this talk, we discuss cooperative strategies for constructing mathematical models of physical systems from data. Conventional approaches typically rely either on data-driven, lightweight synthetic models—such as neural networks—or on high-fidelity physics-based models that can be computationally intensive. Our Hybrid-Cooperative (HYCO) approach bridges these two paradigms by hybridizing them and collapsing their complementary strengths into a unified framework. By combining the empirical insights extracted from data with the structural knowledge of the physical models generating that data, HYCO achieves robust and accurate representations of underlying physical phenomena. Through a series of numerical experiments, we demonstrate that HYCO outperforms classical methods in learning physical models, particularly in challenging scenarios involving sparse, noisy, or localized datasets. 报告题目 Title：Time-Reversal and Generative AI 时间 Time：2025-09-12 10:00-11:00 地点 Venue：Room 1801, Guanghua Eastern Main Tower, Fudan University (Handan Campus) 报告摘要 Abstract：
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