Finite-data error bounds for Koopman-based prediction and control

Understand

The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems, e.g., via extended dynamic mode decomposition.

• Despite its popularity, convergence results and, in particular, error bounds are still scarce.
• In this paper, we derive probabilistic bounds for the approximation error and the prediction error depending on the number of training data points; for both ordinary and stochastic differential equations while using either ergodic trajectories or i.i.d.
• samples.