Generalized Kernel-Based Dynamic Mode Decomposition
This work addresses the challenge of efficient reduced modeling for nonlinear dynamics, representing an incremental advancement over existing kernel-based methods.
The authors tackled the problem of approximating nonlinear dynamics in high-dimensional reproducing kernel Hilbert spaces by developing a generalized kernel-based dynamic mode decomposition algorithm, which demonstrated improved approximation accuracy and computational efficiency in numerical simulations.
Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based computation that generalizes a recent approach called "kernel-based dynamic mode decomposition". This new algorithm is characterized by a gain in approximation accuracy, as evidenced by numerical simulations, and in computational complexity.