Sparse Nonlinear Dynamics Models with SINDy, Part 3: Effective Coordinates for Parsimonious Models

This video discusses how to choose good coordinates for the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm. Specifically, we consider high dimensional and low dimensional measurements of a nonlinear dynamical system. For high dimensional systems, we recommend either the singular value decomposition (SVD), also known as principal component analysis (PCA), or a deep autoencoder neural network. For low dimensional data, we recommend time delay coordinates, which are connected to Koopman theory.

Citable link for this video at: https://doi.org/10.52843/cassyni.5z2jld
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
5:26 SVD/PCA/POD Coordinates
8:30 Autoencoder Neural Networks
13:03 Limited Measurements (Lift and Drag)
14:50 Time Delay Coordinates