Data-Driven Averaging - Data-Driven Dynamics | Lecture 10

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/DataDr...

Learn more about the theory of averaging for dynamical systems:    • Averaging - Dynamical Systems Extra Credit...  

Get the book here: https://epubs.siam.org/doi/10.1137/1....

Scripts and notebooks to reproduce all examples: https://github.com/jbramburger/DataDr...

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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