Explore Koopman operator theory for dynamical systems in this 28-minute video lecture. Delve into the history and recent resurgence of interest in Koopman operators due to increased data availability and advanced regression algorithms. Learn about open problems, key challenges, and emerging techniques in the field. Examine dynamical systems through the lens of Koopman operators, including examples of Koopman linear embedding and cases without easy closure. Understand how Koopman eigenfunctions define invariant subspaces and discover the Dynamic Mode Decomposition (DMD) technique. Gain valuable insights from Steve Brunton's expertise in this comprehensive overview of Koopman spectral analysis.
Overview
Syllabus
Intro
Open Problems, Key Challenges, Emerging Techniques
Dynamical Systems: Koopman and Operators
Example: Koopman Linear Embedding
Example: No easy closure
Koopman Eigenfunctions Define Invariant Subspaces
Dynamic Mode Decomposition (DMD)
Taught by
Steve Brunton
Related Courses
-
Residual Dynamic Mode Decomposition- Rigorous Data-Driven Computation of Spectral Properties of Koopman Operators for Dynamical Systems
-
Hankel Alternative View of Koopman Analysis
-
Koopman Analysis
-
Dynamical Systems
-
Data-Driven Dynamical Systems with Machine Learning
-
Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces
