The previous lecture introduced the concept of learning mappings using SINDy. In this lecture we present a method of averaging multiscale signals by combining sliding window DMD and the SINDy method for maps. The result is a powerful method of separating out the predictable fast timescale motion of a dynamic signal to obtain the slower background evolution that is often more complicated. After a theoretical introduction, we demonstrate this method in MATLAB on a simple periodically forced logistic model and on the motion of Saturn and Jupiter.
Coding demonstration in MATLAB comes from averaging.m here: https://github.com/jbramburger/DataDrivenDynSyst/tree/main/Identifying%20Nonlinear%20Dynamics
Learn more about the theory of averaging for dynamical systems: https://www.youtube.com/watch?v=aSQIialGmMg
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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