Variance representations and convergence rates for data-driven approximations of Koopman operators

Understand

We rigorously derive novel error bounds for extended dynamic mode decomposition (EDMD) to approximate the Koopman operator for discrete- and continuous time (stochastic) systems; both for i.i.d.

• and ergodic sampling under non-restrictive assumptions.
• We show exponential convergence rates for i.i.d.
• sampling and provide the first superlinear convergence rates for ergodic sampling of deterministic systems.