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I have been trying to understand the recently proposed Sparse Identification of Nonlinear Dynamics SINDy. Despite several attempts, I seem to fail to understand the difference between SINDy and the standard methods used for parameter identification in the field of system identification. The PNAS paper neither discusses nor compares with any existing methodologies in system identification. Both methods use least-squares to find the parameters. SINDy is claimed to be "data-driven" and based on Machine Learning; however, I do not see where ML comes into the picture. I very much appreciate any insights into this.

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    $\begingroup$ I think one of the key differences between good old least squares is using a large library of possible functions together with $L^1$ regularization as a means of model selection. Presumably this requires less advance knowledge on your part of what the dynamics are supposed to look like algebraically. You could argue that this is just a slightly new twist on the good old least squares approach and maybe doesn't merit a new acronym, or you could say this is just how marketing works and they need something with good SEO. $\endgroup$
    – Daniel Shapero
    Oct 6, 2022 at 15:33
  • $\begingroup$ As far as I know, the sparse identification via SINDy aims to find PDE of dynamical systems from the Top-Down, meaning feeding in data to receive the underlying PDE. The sparse representation is merely due to the assumption that these systems have rather few terms with regards to the PDE. The library contains derivatives, nonlinear contributions in the system, etc... The aim is then to construct a sparse vector for the superposition of these derivatives, nonlinear contributions,... to construct the measured time series. Steven Bruntons youtube videos on SINDy are an excellent source btw. $\endgroup$
    – Ron
    Oct 6, 2022 at 16:44
  • $\begingroup$ Thank you, @DanielShapero! Since one needs to choose the function/basis space, polynomial or trigonometric or both, I am not sure if it would reduce the knowledge level required. $\endgroup$
    – Chenna K
    Oct 9, 2022 at 13:41
  • $\begingroup$ @Ron, the method applies to both PDEs and ODEs. I understand how it works. My question is about novelty and the ML components of it. $\endgroup$
    – Chenna K
    Oct 9, 2022 at 13:44

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