PDEs and Machine Learning:
A Two-Way Dialogue
报告专家：Professor Enrique Zuazua（西班牙马德里自治大学）
报告时间：5月16日（星期五）下午15:00-16:00
报告地点：国家天元数学西南中心516报告厅
报告摘要：Partial Differential Equations (PDEs) lie at the heart of mathematical modeling in mechanics and the natural sciences. Their study has profoundly shaped the development of modern analysis, numerical methods, and the broader field of Applied Mathematics. Today, the emergence of disruptive tools from Machine Learning (ML) and Artificial Intelligence (AI) opens up a new landscape of possibilities and challenges. Can classical PDE methodologies be enhanced with ML techniques while preserving mathematical rigor? Is it possible to design a new generation of computational schemes that integrate data-driven approaches without compromising the reliability and fidelity of traditional methods? In this lecture, we will explore these foundational questions from a conceptual and interdisciplinary perspective. Without digging into technical details, we will highlight emerging trends, point to fruitful areas for future research, and reflect on how the fusion of structure (PDEs) and data (ML) may shape the next phase of scientific computation.
专家简介：Enrique Zuazua，西班牙马德里自治大学数学系教授，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。
邀请人：张旭
