In this lecture we see our first application of the SVD. We introduce proper orthogonal decomposition (POD) for analyzing and decomposing space-time data. The lecture begins with the theory, beginning with the history of basis expansion and then proceeding to the data-driven method of POD. The method is really just the SVD, but the interpretation of the columns of each SVD matrix holds important information for the space-time dynamics of the original data. The method is demonstrated with a coded example of spiral wave solutions to reaction-diffusion problems.
Coding demonstration in MATLAB comes from spiral_POD.m here: https://github.com/jbramburger/DataDrivenDynSyst/tree/main/Dynamical%20Systems%20Old%20and%20New
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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