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.

Intro
Operator viewpoint
Koopman mode decomposition
Build the matrix: Dynamic Mode Decompositio
ResDMD: avoiding "too little"
Setup for continuous spectra
Spectral decomposition of operators
Evaluating spectral measure
Example: non-linear pendulum
Approximate eigenfunctions
Quadrature with trajectory data
Example: Verify the dictionary
Example: Trustworthy Koopman mode decom