Now that we have examines variations of DMD for identifying linear descriptions of nonlinear dynamics, we turn to identifying nonlinear models. In this video we present the Sparse Identification of Nonlinear Dynamics (SINDy) method for discovering ODEs and discrete-time mappings. We begin with a presentation of the method and a coding demonstration in MATLAB to data from the Lorenz system. We then discuss a variant of the SINDy method, so-called weak SINDy, that better handles noisy/corrupted data. Again, a demonstration in MATLAB is given to exemplify the weak SINDy method.
Coding demonstration in MATLAB comes from SINDy.m here: https://github.com/jbramburger/DataDrivenDynSyst/tree/main/Identifying%20Nonlinear%20Dynamics
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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