What is phi backslash x0 The backslash do as operation???? I understand these are initial conditions

The amplitude is growing when the perturbation frq is half of the natural frq of the system? Proof?

I don't understand why we need M, when we can find gappy modes directly from the original higher dimension modes: U_gappy = P@U_r ?

Thank you! Your auto-white board and your emphasis on what is important in the equations helps me focus!

Outstanding explanation with a clear emphasis on eigenfunction expansion using an orthonormal basis.

Nathan Kutz for president! Very nice and informative lecture.

Thank you Professor🙏

What does it cost to have a QR decomposition or a SV decomposition?

Wow, great explanations! It makes sense.

A gem channel 😊, brilliant guy

Thats BS dude, its just a silencer, those things are extremely loud. They were used as terror weapons in ww2 for a reason. Theres ways of using the same thing, and making it quieter, and more practical

I would like to thank you, Professor Kutz, for the tremendous effort and dedication you have put into creating this video and so many others over the years. Your commitment to spreading knowledge to everyone has been truly impactful, as you have opened doors to learning opportunities that many can't afford or access. I sincerely hope you continue this extraordinary work, not only because of its immense value to others, but more importantly because it is clear that you find true joy and fulfillment in what you do. Your passion for research and teaching is motivating and drives so many to follow your paths. Your work truly makes a difference, and I wish you nothing but continued happiness and success in all that you do.

nice

Love the video, but I think it can be a bit confusing going from 5:30 where you just have "f(x_k, A_2, ..., A_M)" to 9:40 where you have "f_k(x_k, A_2, ..., A_M)." Looking at this, I initially thought that you might have a new fitting function for each data point, rather than the fitting function with the kth data point plugged in.

No audio unfortunately.

In minute 18, shouldn't it be sqrt of lambda in u(x)?

My god thank you so much for that piece of art, I might survive fourier

Wow, this explanation is incredible! You truly make complex ideas feel simple and exciting-just like Richard Feynman did. You're the Feynman of this era!

Watching this again and realized the problem of over-fitting is analogous to the 'no true Scotsman' fallacy in philosophy where someone has given themselves so many parameters that they can fit any data.

thank you

absolutely great explaination, great work

Thanks sweetie pumpkin

Amazing hoow simple these concepts seem when explained calmly and in full sentences. Thank you!

The phases of the stereo channels in the audio are inverted relative to one and other.

30:40

15:00!

choose a different way of explaining other than by saying "kick"-- it was confusing to me. Start out precise and once it's clear then you can say "kick" all you want

The "Logistic Equation Map" is involved in this somehow ?? . . . i.e. "Bifurcation" 🤔

this should be classified.

Thanks so much for sharing this professor! I have a question: at time 5':30" of your lecture you said unlike PCA, this associates every mode with the time dynamics. Is this also true for Singular Spectrum Analysis? Thanks!

You are amazing👏👏👏👏

Professor, I wasted my time in countless other lectures before coming to yours. How easily you can explain complex things using such basic terminology is wonderful. Mind blown.

best explanation out there

nice!

nice!

great video!

Low rank structure... Or a low dimensional manifold

Make Things Linear Again

omg nathan r u okay???? 19:45

also love that he is wearing a coat!!!

What book can i use to follow?

what camera were they using?

at 4:23 in the continious-time shifting example, isn't the shifted signal below supposed to be x(t+t0) since the signal is shifted to the left?

How you mentioned the "tuning" part, it seems like there's still an "art" to neural networks

I'm assigning this as a course project for a grad student. Thanks

At 26:00, in the figures you are representing the real parts of e^[iw•n], ie. cos(w•n). The fact that you noticed is a symmetry of the signals around frequency π. In fact due to cosine properties we have, for all n, cos([w+π]•n)=cos([w-π]•n) even if the complex signals e^(i[w+π]•n)≠e^(i[w-π]•n) due to the fact that sin([w+π]•n)=-sin([w-π]•n).

Wow I am not working hard enough😅

Thank you for a very informative and simiplified explination for LMS and gradient descent algorithms and how it is related and integrated with neural networks and ML.

Hipolito Drive