Dear Prof. Brunton, Thank you so much for the beautiful lectures. They are highly insightful and explanatory. It also feels very interactive because of the way you present them and the way video editing is done. Thanks!
The last 5 minutes where you explained the invariance to unitary transformation was very helpful in understanding why this is working with projections. Thanks!
Nice video, I've been following your channel for a while....it's been a great journey. I also wanted to talk about the possibility of using neural networks to compute a downsampled version of the higher dimensional state space, so that DMD can be performed on the downsampled frames, and the low dimensional modes we get can then be upsampled by yet another neural network for better visualisation. Well, this would be assuming that the hardware in question have enough resources to load these higher dimensional frames and downsample them with a neural net for DMD
Is there a theoretical lower bound on the density of observations required? In other words, how does the residual norm grow as the spatial and temporal density of observations decreases, relative to the characteristic spatial and temporal scales of the observed phenomenon?
Thank you Prof. Brunton, I have a question about the application of DMD method. I have some data where I look to formulate it as y=Ax+Bu. I find A with DMD, but not B. Can you please guide me? Thank you
Dear Steve Please, I tried to use FFT, DCT, DWT and DMWT, to get the percentage of the compression and I tried to calculate and compare the result for there MER & PNSR for all the transforms but unfortunately all the result same because all the input image are same size, so bpp are also same :( I would like to ask you, how can I get the compression ratio of DMWT? Also, how got I a different result of MER & PNSR for FFT, DCT, DWT, and DMWT to compare the result between them. Many thanks Nada
@@Eigensteve Aha, thanks sir. Seems to be a little bit hard. Could you pls provide more information about that? For example, how did you specify the matrix C in processing the data of flow over the cylinder, or do you have some papers for recommdation. :)
Thanks bro, Im a 18 noob student of computer science, what's the function of the random measurement matrix?, I understand Y its an small meauserment of X, and a are the coefficients of the Fourier transforms of the image.
![Hankel Alternative View of Koopman (HAVOK) Analysis [FULL]](http://i.ytimg.com/vi/831Ell3QNck/mqdefault.jpg)
![Hankel Alternative View of Koopman (HAVOK) Analysis [FULL]](/img/tr.png)
Dear Prof. Brunton,
Thank you so much for the beautiful lectures. They are highly insightful and explanatory. It also feels very interactive because of the way you present them and the way video editing is done. Thanks!
The last 5 minutes where you explained the invariance to unitary transformation was very helpful in understanding why this is working with projections. Thanks!
You're very welcome!
Thank You. Steven Sir. Your way of explaining things in such a smooth manner is simply amazing. :-)
Many thanks!
I really need to change the base of finite functions on a complex infinite projection, can't wait to get to that part, hoping you cover it!
Nice video, I've been following your channel for a while....it's been a great journey.
I also wanted to talk about the possibility of using neural networks to compute a downsampled version of the higher dimensional state space, so that DMD can be performed on the downsampled frames, and the low dimensional modes we get can then be upsampled by yet another neural network for better visualisation.
Well, this would be assuming that the hardware in question have enough resources to load these higher dimensional frames and downsample them with a neural net for DMD
Is there a theoretical lower bound on the density of observations required? In other words, how does the residual norm grow as the spatial and temporal density of observations decreases, relative to the characteristic spatial and temporal scales of the observed phenomenon?
Thank you Prof. Brunton, I have a question about the application of DMD method. I have some data where I look to formulate it as y=Ax+Bu. I find A with DMD, but not B. Can you please guide me? Thank you
Another great video! Thank you!
Dear Steve
Please, I tried to use FFT, DCT, DWT and DMWT, to get the percentage of the compression and I tried to calculate and compare the result for there MER & PNSR for all the transforms but unfortunately all the result same because all the input image are same size, so bpp are also same :(
I would like to ask you, how can I get the compression ratio of DMWT?
Also, how got I a different result of MER & PNSR for FFT, DCT, DWT, and DMWT to compare the result between them.
Many thanks
Nada
Excellent lecture! But I stll have a question. Generally how can I obtain the matrix C?
Usually you actively design the matrix C. Sometimes the physical measurement process will limit the types of C that are available.
@@Eigensteve Aha, thanks sir. Seems to be a little bit hard. Could you pls provide more information about that? For example, how did you specify the matrix C in processing the data of flow over the cylinder, or do you have some papers for recommdation. :)
Great lecture, thank you for sharing!
Thanks bro, Im a 18 noob student of computer science, what's the function of the random measurement matrix?, I understand Y its an small meauserment of X, and a are the coefficients of the Fourier transforms of the image.
Thank you so much..how we can apply it in MATLAB?
The open source code is linked in my paper on the topic. And I also link the code in the video comments.
Thank you!
J