핵심 개념
ResDMD simplifies spectral analysis of Koopman operators with fewer snapshots, offering robustness and versatility.
초록
The article discusses Residual Dynamic Mode Decomposition (ResDMD) for accurate computation of Koopman operator spectral properties. It overcomes issues associated with finite truncations, providing insights into complex systems. The method eliminates the need for two datasets by solving a dual least-squares problem. Three examples showcase its application in various dynamical systems.
Introduction to discrete-time dynamical systems.
Exact DMD and Kernelized EDMD methods.
Challenges in truncating infinite-dimensional problems.
Residual DMD approach and computational strategies.
Application examples: cylinder wake, aerofoil cascades, shockwave data compression.