Speaker: Claire Valva, New York University
Date: May 4, 2023
Abstract: Koopman operators and transfer operators transform nonlinear dynamics in phase space to linear dynamics on vector spaces of functions, enabling the use of spectral techniques without modeling constraints such as linearity. The extraction of approximate Koopman eigenfunctions (and the associated eigenfrequencies) from an unknown system is nontrivial, particularly if the system has mixed or continuous spectrum. We discuss a spectrally-accurate approach to approximate the Koopman operator from data via a “compactification” of the resolvent of the Koopman generator. This approach employs kernel integral operators to approximate the skew-adjoint generator in measure-preserving systems by a family of skew-adjoint operators with compact resolvent, whose spectral measures converge in a suitable asymptotic limit, and whose eigenfunctions are approximately periodic. We explore implementations of this technique using data from several different example systems including Lorenz 63.