Explore the intricacies of choosing an effective library of candidate terms for the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm in this 27-minute video lecture. Delve into extending SINDy to incorporate control variables and bifurcation parameters, as well as including more general rational functions. Learn strategies to overcome the curse of dimensionality using SVD, autoencoders, and the tensor train formulation. Discover how to leverage physical symmetries to constrain the library. The lecture covers topics such as SINDy as a generalized linear regression, SINDy with control, bifurcation parameters, rational functions, and exploiting symmetries. Access additional resources, including the original SINDy paper and the speaker's social media, for further exploration of this advanced topic in nonlinear dynamics modeling.