北京雁栖湖应用数学研究院 北京雁栖湖应用数学研究院

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关于我们
院长致辞
理事会
协作机构
参观来访
人员
管理层
科研人员
博士后
来访学者
行政团队
学术研究
研究团队
公开课
讨论班
招生招聘
教研人员
博士后
学生
会议
学术会议
工作坊
论坛
学院生活
住宿
交通
配套设施
周边旅游
新闻
新闻动态
通知公告
资料下载
清华大学 "求真书院"
清华大学丘成桐数学科学中心
清华三亚国际数学论坛
上海数学与交叉学科研究院
BIMSA > AMSS-YMSC-BIMSA拓扑及应用进展联合讨论班 Identifying Nonlinear Dynamics with High Confidence from Sparse Time Series Data
Identifying Nonlinear Dynamics with High Confidence from Sparse Time Series Data
组织者
段海豹 , Fei Han , Yong Lin , 潘建中 , 魏国卫 , 吴杰 , 夏克林 , 丘成栋 , Chao Zhou
演讲者
Konstantin Mischaikow
时间
2022年05月05日 09:00 至 10:00
地点
1120
线上
Zoom 388 528 9728 (BIMSA)
摘要
I will introduce a novel 5 step procedure that given time series data generated by a stationary deterministic nonlinear dynamical system provides a lower bound on the probability that the system generates specific local and/or global dynamic behavior. More precisely, the time series data is used to define a Gaussian process (GP). The mean of this GP provides a surrogate model. The dynamics of the surrogate model is interrogated using combinatorial methods and characterized using algebraic topological invariants (Conley index). The GP predictive distribution provides a lower bound on the probability that these topological invariants (and hence the characterized dynamics) apply to the unknown dynamical system (a random path of the GP). The focus of this talk is on explaining the ideas, thus I restrict our examples to one-dimensional systems and show how to capture the existence of fixed points, periodic orbits, connecting orbits, chaotic dynamics, and bistability. This is based on joint work with B. Batko, M. Gameiro, Y. Hung, W. Kalies, E. Vieira, and C. Thieme.
演讲者介绍
Prof. Konstantin Mischaikow received his Phd from University of Wisconsin-Madison in 1985. He has worked as assistant professor and associated professor at Michigan State University and Georgia Tech. He is the director of CDSNS at Georgia Tech for eight years. Currently, he is the distinguished professor at Rutgers University. Prof. Konstantin Mischaikow is a world-leading expert in computational homology, Conley index, and their applications in dynamic systems. He has published more than 300 papers with a total citation > 9000.
北京雁栖湖应用数学研究院
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No. 544, Hefangkou Village Huaibei Town, Huairou District Beijing 101408

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北京雁栖湖应用数学研究院 101408

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