Dr. Kutz, as a PhD student who has spent a lot of time researching wavelets and their applications to PDEs, I really like this method. One question that I have with DMD is its ability for prediction. I read in a recently published review on DMD for fluid dynamics that DMD can only make accurate predictions for time-resolved data. This implies (to me at least) that to predict vortices shedding from a cylinder for instance, several periods of shedding must have already occurred. So since the classic DMD is tied to Fourier modes, it necessitates a certain periodicity of the underlying dynamics, right? And I can see this in the toy example that you present in 21:13. Classical DMD is trying to classify on/off signals as periodic (with some rate of growth/decay). But we know that wavelets in general break away from this periodic nature. So my question is to what extent MR-DMD can predict phenomenon that are not periodic. Let's say shocks in fluid flow for example. Shocks are something that Fourier methods cannot handle, but wavelet methods are really great at classifying. Is this something that has been addressed in the literature? If MR-DMD can be used to make predictions about shocks, then I may have some ideas about how I could use the method. Cheers.
It certainly does seem as tho one may be able to do these same manipulation in a Fourier space, where your iterative operations probably have linear homologs. In fact, that's where I thought you were headed in this video, since continuous versions of your summations seem so Fourier kernel-like. [Your work is cool. Cheers.]
Dr. Kutz, as a PhD student who has spent a lot of time researching wavelets and their applications to PDEs, I really like this method. One question that I have with DMD is its ability for prediction. I read in a recently published review on DMD for fluid dynamics that DMD can only make accurate predictions for time-resolved data. This implies (to me at least) that to predict vortices shedding from a cylinder for instance, several periods of shedding must have already occurred. So since the classic DMD is tied to Fourier modes, it necessitates a certain periodicity of the underlying dynamics, right? And I can see this in the toy example that you present in 21:13. Classical DMD is trying to classify on/off signals as periodic (with some rate of growth/decay). But we know that wavelets in general break away from this periodic nature. So my question is to what extent MR-DMD can predict phenomenon that are not periodic. Let's say shocks in fluid flow for example. Shocks are something that Fourier methods cannot handle, but wavelet methods are really great at classifying. Is this something that has been addressed in the literature? If MR-DMD can be used to make predictions about shocks, then I may have some ideas about how I could use the method. Cheers.
"recently published review on DMD for fluid dynamics that DMD"___ Hello, may I ask the title and author of this paper please?
@@EDLAV I don't know remember which review I was referring to. There are several available with a quick google search.
Excellent explanation
It certainly does seem as tho one may be able to do these same manipulation in a Fourier space, where your iterative operations probably have linear homologs. In fact, that's where I thought you were headed in this video, since continuous versions of your summations seem so Fourier kernel-like. [Your work is cool. Cheers.]
Could you make playlists for all your video please?
and mix some AC/DC in?
yay！
Mystery of black background is solved