For example; can the dynamical systems theory help us find underlying general structures of the systems to make more accurate models?. Perhaps some data reflect these structures that are not evident by analyzing them from a purely statistical point of view. Having in mind that the data usually comes from dynamic systems.
Are there any works that relate to these areas? Or is it just a naive question?
Thanks,
There is quite some work on the intersection of dynamical systems (ODEs and PDEs) and data science. A bunch of paper are co-authored by Igor Mezic:
https://mgroup.me.ucsb.edu
dealing with the so-called Koopman operator. There are other researches looking at this, but I mention this one because he is a bit more math oriented than the rest.
Google on google scholar "Koopman operator dynamical systems" and you'll get many papers on the subject.
Hope this helps.
Best regards,
Cristina
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