Occupation kernels, Liouville operators, and dynamic mode decomposition
October 07, 2022, ESB 2001
Occupation kernels are novel tools that enable incorporation of trajectories of dynamical systems as the fundamental unit of data in a reproducing kernel Hilbert space (RKHS) framework. Occupation kernels interact with Liouville operators over RKHSs in much the same way that Liouville operators interact with occupation measures over the Banach space of continuous functions as investigated by J.B. Lasserre et al. The interaction between occupation kernels and Liouville operators can be exploited to formulate infinite dimensional linear abstractions of nonlinear finite-dimensional learning problems. The infinite dimensional linear programs can then be solved efficiently using finite-dimensional representations of the corresponding infinite dimensional operators. The focus of this talk is to provide an introduction to RKHSs, occupation kernels, and Liouville operators and to demonstrate the utility of occupation kernels to solve data-driven learning problems such as system identification, motion tomography, and dynamic mode decomposition.
Rushikesh Kamalapurkar received his M.S. and his Ph.D. degree in 2011 and 2014, respectively, from the Department of Mechanical and Aerospace Engineering at the University of Florida. After working for a year as a postdoctoral researcher with Dr. Warren E. Dixon, he was appointed as the 2015-16 MAE postdoctoral teaching fellow. In 2016 he joined the School of Mechanical and Aerospace Engineering at the Oklahoma State University as an Assistant professor. His primary research interests lie on the intersection of machine learning and systems theory.