Random features approximate Koopman generators of continuous-time systems
Original title: Data-driven Random-feature Approximation of Koopman Generators of Nonlinear Continuous-time Systems
A data-informed dictionary for gEDMD is reported faster than iterative optimization, with convergence proofs and a boundedness counterexample.
The paper proposes a data-driven random-feature method for Galerkin approximation of Koopman generators of nonlinear continuous-time systems, including gEDMD. The dictionary is built from data rather than chosen without regard to the samples. Authors report accurate forecasting and system analysis that is faster than iterative optimization, plus convergence of the vector field and trajectories. They also give a semigroup convergence criterion and a counterexample showing gEDMD does not always preserve exponential boundedness.
Unconfirmed: Accuracy and speed claims are the authors' numerical results, not an independent evaluation.
- The method approximates continuous-time Koopman generators, not discrete operators.
- The finite dictionary is data-informed and aimed at methods such as gEDMD.
- Authors say forecasting is accurate and faster than iterative optimization.
- Proofs cover the approximated vector field and resulting trajectories.
- A counterexample shows gEDMD need not preserve exponential boundedness.
From the original article
1 min read at arxiv.orgLearning continuous-time dynamical systems from data is an active area of research. The Koopman formalism is often used here, because it is a flexible approach that is informative about the system's fundamental properties. The formalism represents dynamical systems through linear operators acting on a suitable function space.
By Ana Čukarska · arxiv.org
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