In the previous lecture we saw that time delay coordinates combined with the SVD to reduce the complexity of temporal dynamics. In this lecture we take this concept further by introducing the Koopman operator. Named after Bernard Koopman and introduced in the 1930s, the Koopman operator has seen a massive resurgence in interest in the past decade for its capabilities for understanding dynamic data sets. Here we introduce the basics, provide a simple example, and then examine how we can approximate the Koopman operator directly from data through extended DMD (EDMD). The lecture concludes with a coding demonstration where we implement EDMD and discuss in details its strengths and weaknesses.
Coding demonstration in MATLAB comes from EDMD.m here: https://github.com/jbramburger/DataDrivenDynSyst
Get the book here: https://epubs.siam.org/doi/10.1137/1.9781611978162
Scripts and notebooks to reproduce all examples: https://github.com/jbramburger/DataDrivenDynSyst
This book provides readers with:
- methods not found in other texts as well as novel ones developed just for this book;
- an example-driven presentation that provides background material and descriptions of methods without getting bogged down in technicalities;
- examples that demonstrate the applicability of a method and introduce the features and drawbacks of their application; and
- a code repository in the online supplementary material that can be used to reproduce every example and that can be repurposed to fit a variety of applications not found in the book.
More information on the instructor: https://hybrid.concordia.ca/jbrambur/
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