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报告题目：Machine Learning algorithms inspired by Complex Analysis, Dynamics and Whitney Embedding Theorem

报 告 人：夏志宏 教授（大湾区大学（筹）高等研究院）

报告时间：2025年5月6日（星期二） 16:00-17:00         

报告地点：37号楼3A02

邀 请 人：刘锐 教授、陈培 教授

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数学8297至尊品牌游戏官方网站

2025年5月5日

报告摘要：

At its core, AI and machine learning algorithms represent our mathematical communication with computers. Current algorithms are the product of iterative trial and error. In our work, we propose novel machine learning algorithms derived from complex analysis. Testing results indicate that these algorithms are highly efficient in solving both mathematical and physical problems, surpassing existing Physical Informed Neural Networks (PINNs) used for solving Partial Differential Equations (PDEs) and other scientific computations, achieving improvements in both speed and accuracy—often by several orders of magnitude. Our algorithms also show strong performance in tasks like image recognition and other AI applications.

To understand the essence of AI, we pose a simple question: Given a Sun-Earth-Jupiter three-body system, where we observe the position of Jupiter from Earth every night, and assume we know nothing about Newtonian mechanics, calculus, or universal gravitation, can a machine predict the future motion of Jupiter? The surprising answer is yes—provided there is enough data. More generally, for any dynamical system on a manifold, enough sequential data from a single, generic observable can fully recover the original system. This is based on the Whitney Embedding Theorem (or Takens' delayed embedding). It turns out that the Cauchy algorithm is most suited to implement this predicative algorithm..

报告人简介：

夏志宏教授，美国西北大学Pancoe讲席教授，大湾区大学（筹）讲席教授，国际知名数学家和天文学家。主要研究动力系统，天体力学，曾解决百年数学难题庞勒维猜想（the Painlevé Conjecture），天体运动的混沌性，Hamilton系统的通有性质和遍历理论中关于拓扑熵的一系列问题。获得多项重大学术奖励，其中包括美国总统青年研究者奖，Sloan Research Fellowship，首届Blumenthal纯数学进步奖等奖项。2015年创立南方科技大学数学系。