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DTSTAMP:20260416T003356Z
DESCRIPTION:Title: Machine Learning and dynamical systems meet in reproduci
 ng kernel Hilbert spaces\n\nAbstract:The intersection of the fields of dyn
 amical systems and machine learning is largely unexplored and the objectiv
 e of this talk is to show that working in reproducing kernel Hilbert space
 s offers tools for a data-based theory of nonlinear dynamical systems. We 
 use the method of parametric and nonparametric kernel flows to predict som
 e prototypical chaotic dynamical systems as well as geophysical observatio
 nal data.\n	\n	We also consider microlocal kernel design for detecting criti
 cal transitions in some fast-slow random dynamical systems. We then show h
 ow kernel methods can be used to approximate center manifolds\, propose a 
 data-based version of the center manifold theorem and construct Lyapunov f
 unctions for nonlinear ODEs.\n	\n	We also introduce a data-based approach to
  estimating key quantities which arise in the study of nonlinear autonomou
 s\, control and random dynamical systems. Our approach hinges on the obser
 vation that much of the existing linear theory may be readily extended to 
 nonlinear systems-- with a reasonable expectation of success- once the non
 linear system has been mapped into a high or infinite dimensional Reproduc
 ing Kernel Hilbert Space. In particular\, we develop computable\, non-para
 metric estimators approximating controllability and observability energies
  for nonlinear systems. We apply this approach to the problem of model red
 uction of nonlinear control systems. It is also shown that the controllabi
 lity energy estimator provides a key means for approximating the invariant
  measure of an ergodic\, stochastically forced nonlinear system.\n
DTSTART:20221122T203000Z
DTEND:20221122T210000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Boumediene Hamzi (Johns Hopkins University)
URL:https://www.mcgill.ca/mathstat/channels/event/boumediene-hamzi-johns-ho
 pkins-university-343759
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