The SINDy Method - Data-Driven Dynamics | Lecture 8

Having explored variations of DMD for identifying linear approximations of nonlinear dynamics, we now turn to discovering nonlinear models. In this lecture, we introduce the Sparse Identification of Nonlinear Dynamics (SINDy) method for uncovering both ODEs and discrete-time mappings directly from data. We begin with a clear presentation of the method, accompanied by a MATLAB demonstration using data from the Lorenz system, showing how SINDy can reveal the governing equations behind complex dynamics. We then introduce weak SINDy, a variant designed to handle noisy or corrupted data more effectively, with another MATLAB demonstration illustrating its robustness. This lecture highlights how modern data-driven techniques can extract accurate, interpretable models from even challenging datasets. Coding demonstration in MATLAB comes from SINDy.m here: https://github.com/jbramburger/DataDr... 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/ Follow @jbramburger7 on Twitter for updates.