Sparse Nonlinear Dynamics Models with SINDy, Part 4: The Library of Candidate Nonlinearities

This video discusses how to choose an effective library of candidate terms for the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm. We discuss how to extend SINDy to include control variables and bifurcation parameters, as well as to include more general rational functions. We also discuss how to avoid the curse of dimensionality with the SVD, autoencoders, and the tensor train formulation. Finally, we show how to use physical symmetries to constrain the library.

Citable link for this video at: https://doi.org/10.52843/cassyni.p7t7ds
Original SINDy paper: https://www.pnas.org/content/113/15/3932

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This video was produced at the University of Washington

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0:00 Introduction & Recap
2:35 SINDy as a Generalized Linear Regression
6:42 SINDy with Control
11:02 Bifurcation Parameters
12:22 Rational Functions
18:01 Curse of Dimensionality
24:22 Exploiting Symmetries