Beijing Institute of Mathematical Sciences and Applications

Haibao Duan , Fei Han , Yong Lin , Jianzhong Pan , Guo-Wei Wei , Jie Wu , Kelin Xia , Shing Toung Yau , Chao Zhou

Konstantin Mischaikow

Thursday, May 5, 2022 9:00 AM - 10:00 AM

1120

Zoom 388 528 9728 (BIMSA)

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.

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.