Sharp Spectral Rates for Koopman Operator Learning

Understand

Nonlinear dynamical systems can be handily described by the associated Koopman operator, whose action evolves every observable of the system forward in time.

• Learning the Koopman operator and its spectral decomposition from data is enabled by a number of algorithms.
• In this work we present for the first time non-asymptotic learning bounds for the Koopman eigenvalues and eigenfunctions.
• We focus on time-reversal-invariant stochastic dynamical systems, including the important example of Langevin dynamics.