报告题目：From Integrating to Learning Dynamics: New Studies on Linear Multistep Methods

主 讲 人：杜 强

单 位：哥伦比亚大学

时 间：7月25号9:00

ZOOM ID：567 306 5241

密 码：123456

摘 要：

Linear Multistep Methods (LMMs) are among the most widely used algorithms for numerically integrating dynamic systems. A comprehensive mathematical theory has been developed over the last century and has become textbook materials. Yet, there seems to be a new story when LMMs are used in a black box machine learning formulation for solving the inverse problem of discovering unknown dynamics from observation data. A natural question is concerned with whether a convergent LMMs for integrating dynamics is also suitable for dynamics discovery. We show in this lecture that the conventional theory of consistency, stability and convergence of LMM for time integration must be reexamined for dynamics discovery, which leads to new results on LMM that have never been given attention to in the past. We present refined concepts and algebraic criteria to assure stable and convergent discovery of dynamics in some idealized settings. We then apply the theory to some popular LMMs.

简 介：

杜强现任哥伦比亚大学应用数学讲席教授和专业主任，数据研究院数据驱动科学计算体系中心共同主任。美国数学会会士，美国科学促进协会会士、工业与应用数学学会会士、国际数学家大会邀请报告人。冯康科学计算奖获得者，曾任科技部第二批973计划“大规模科学计算研究”首席科学家。