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