Abstract

The Koopman Operator, Diffusion Maps, and Partially Known Dynamics

Ryan Mohr
University of California, Santa Barbara (UCSB)

In this talk, we discuss a consistent framework that relates the Diffusion Maps methodology and the Koopman operator. In this framework, we obtain a family of operators that are parameterized by the amount of knowledge that we possess about the dynamics. At one limit, complete lack of information, the dynamics consist of a pure diffusion process and we recover the Diffusion Maps operator. At the limit of full information on the dynamics, we recover a stochastic version of the Koopman operator.