Residual Dynamic Mode Decomposition- Rigorous Data-Driven Computation of Spectral Properties of Koopman Operators for Dynamical Systems

Explore a comprehensive lecture on Residual Dynamic Mode Decomposition (ResDMD) and its application in computing spectral properties of Koopman operators for dynamical systems. Delivered by Matthew Colbrook from the University of Cambridge and Alex Townsend from Cornell University, this 57-minute talk delves into the operator viewpoint, Koopman mode decomposition, and the construction of matrices using Dynamic Mode Decomposition. Learn about the ResDMD method for addressing insufficient data, the setup for continuous spectra, and spectral decomposition of operators. Examine practical examples, including a non-linear pendulum, and discover how to evaluate spectral measures and approximate eigenfunctions. Gain insights into quadrature with trajectory data, verifying dictionaries, and achieving trustworthy Koopman mode decomposition. This lecture, part of the "Third Symposium on Machine Learning and Dynamical Systems," offers a rigorous exploration of data-driven computation techniques for analyzing dynamical systems.