Konstantin Mischaikow - Rutgers
Date/Time/Location
Thursday, April 2, 2026, 12:10 pm; Hill Center 705
Rigorously Characterizing Dynamics with Machine Learning
The identification of dynamics from time series data is a problem of general interest. It is well established that dynamics on the level of invariant sets, the primary objects of interest in the classical theory of dynamical systems, is not computable.
I will describe a coarser characterization of dynamics based on order theory and algebraic topology. An important property of this characterization is that it is based on well-defined levels of resolution. I will outline the proof that this characterization can be identified using approximations. As a consequence, for a fixed level of resolution, given appropriate data and a large enough machine the dynamics at this level can be learned.
This is based on joint work with M. Gameiro and B. Gelb