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Thanks for the series!

More on data-driven methods for physical systems: ruclips.net/video/rcBp-TIs_-0/видео.htmlsi=u2j2pTiZd32qob9i

✅ For an introduction to SVD: ruclips.net/video/2WJ4Zffbqek/видео.htmlsi=2Kiwx4H0h4c2DzXC

Thanks for the video. I have a few questions: 1) Is Y a vector px1? 2) is C a matrix pxn? 3) is X a vector nx1? 4) Are columns of C matrix associated to different places along a line or are they associated to different times (e.g. if X is a signal)? 5) What particular solution among the infinite to the power of (n-p) solutions would I obtain in reconstructing X from Y if I did multiply C+ times Y? 6) what is the optimization problem we are trying to solve when we have the reading Y and the known matrix C? (what are we trying to minimize, L1(reconstructed X)? what space are we searching over?) 7) is the optimal basis (i.e. the Psi associated with the sparsed s) obtained by solving the optimization problem of minimizing L1(s) over the whole spaces of Psis? 8) could you remind me in a nutshell what a "convex optimization problem" is? Thank you for your time

Thanks for the video. I am a bit confused and I have a few questions (sorry if they are too many for a comment on youtube): 1) is X a matrix nxm, index i going from 1 to n and index j from 1 to m, containing, in the example in the video, only 1s and 0s? 2) are the basis elements e sub ij matrices the same size as capital X? 3) is eij a null matrix with just one pixel (at location i j) set to 1 ("on")? 4) is the component xij just a scalar having 0 and 1 as possible values? 5) can s sub k take real numbers or just binary 0 and 1? 6) are v sub k matrices the same size as capital X? 7) what is the relation (if any) between (image X , basis elements vk) and (X, phi) of POD? How are vk obtained from X? 8) can the vk obtained from a "reference" picture A be used as a basis to represent other pictures from A (a different picture B would have a different set of sks than A)? 9) Is the point of finding and storing the whole set of basis vk instead of storing the whole image that afterwards a picture can be stored just with a bunch of sks? 10) is the method useful "for similar images only" (e.g. sunset pictures with a set vks of sunset pictures, dog pictures with a a set of vks of dog pictures etc.) or are there general vks, common to dogs and sunsets valid for "a general image that is not noise"? Thanks for your time

✅ The QR algorithm to implement the optimal sensor placement is described in the next video! ruclips.net/video/gM9IciX2Uiw/видео.htmlsi=7myuqNy1CjccUfMg

✅ More on optimal sensor placement, but using deep learning: ruclips.net/video/rJofxTatW_8/видео.htmlsi=NbczKszrm5OteT45

‼️There is a typo at minute 21:48! The equation for the final POD modes should read: Phi=M^(-1/2)*Phi^hat Thanks!!

Nucleus plant cell Layer Membrane cell animal

Superb, thanks once more!

Thanks for the whole series of videos. 1) Are a sub i (t) entries of matrix capital A (capital Sigma times capital V T)? 2) If A a is nXm matrix shouldn't the Summation of the expansion have nXm terms instead of just m-1? 3) How come the first term (mean flow - zero mode) is "special" and outside the summation, i.e. with a sub 0 (t) = constant = 1? 4) I am a bit confused about data representation, is X still a 2 dimensional matrix nxm, where n=3 times the number of elements in the mesh (i.e. x-velocity, y-velocity and z-velocity are in the same column one under the other)? Thank you in advance

Professor, how about use the attention weights to optimal the sensor placement

Please tell me learning pathway, for a fresh Mechanical graduate and good foundatuon in CFD, but has no knowledge about ML.

Nice one!

The foil sure looks like a fish swimming from above

Awesome.

Awesome.

Eccellente, sono dei geni, grazie per la condivisione / excellent , thanks for sharing.

Great video. In the m as time and n as individual measurements i really like classical mechanical systems as an example for m >> n. In the case of a single motor or the pendulum on a cart, its n is only 1 or 2. The stock market is like flow-control a difficult topic. You could observe the price of your favorite company every ns in high-frequency trading, or the annual reports of the S&P500 from the last decade. I wouldn't be surprised if evolving nxm is a problem finance has to deal with in funds or budgets.

I really liked the book by Brunton and Kutz. I look forward to what you will add to the subject.

Thanks once more for the greató videos! :D

Happy studying everyone

fabulous thank you for sharing

👍👍👏👏

😮 I like it!

Great Video, Professor Venussa.

Very interesting talk! Have you tried comparing the performance of your ROM in terms of both prediction time horizon and accuray with other projection-based ROMs such as operator inference? I see that the time horizon of prediction is 50 \Delta t. Is \Delta t DNS time step?

Thank you,professor, I’ve read a lot of your papers,that’s cool!

This is the first ever video i watched about ML for CFD and find nearly five ML techniques and the way it is implemented. Thanks

Next video please.

Brilliant, thank you.

Great series of videos. If we have a PIV dataset which is not temporal and each velocity snapshot is u(x,y), the A matrix would define what property of the velocity field? Is it still temporal or \Phi defines variables in y direction and A defines streamwise variable? Many thanks

Quite informative and very well explained. Thanks for such an amazing video !

you have very nice similar energy to Ricardo, keep it up!

Well done Marcial!

Thanks as always for the videos on machine learning!

Great series. Thanks. Can you please elaborate a little bit how can we interpret the POD mode shapes? I mean by looking at the highest energy mode shape, let's say, what can we understand about the turbulent flow?

Amazing series of data driven science

Looking forward to the next video for long awaited POD details :)

I wish i was your student

Many Thanks for your valuable videos. I hope the next video is Dynamic Mode Decomposition DMD 😊

I kinda already give like before watching the full video

Thats great Professor, I am joining your session on 6th May, 2024, as well. Looking to validate some case-studies in this domain.

from Valencia? you keep working even on vacation, what a education focused man you are

Can you suggest what should be the learning pathway for applying ML in CFD? Suppose one is a fresh mechanical engineering graduate and is not a tremendously expert in CFD but has basic understanding of CFD but not much expertise in AI/ML?

stockholm!

Nice and simple explanation. Waiting for the new videos in the series.What are the total number of videos that will be uploaded in this series?

Thanks for another great video. Please make a comment on POD vs SVD in the next video !!

why didn't my notification work! good to check sometimes if new videos are up

Your videos have priceless value. Could you deal more with scientific computing and numerical linear algebra (krylov subspaces, GMRES, iterative solvers, etc...)