Thie gives an overview of the dynamic mode decomposition (DMD) and its algorithmic structure. Highlighted is its usefulness in approximating dynamical systems from data alone.
Пікірлер: 46
@fzigunov6 жыл бұрын
You're a legend. Watched explanations from other professors and yours is by far the easiest to follow. Thanks, Prof. Kutz!
@Drewbie_T3 жыл бұрын
the matthew mcconaughey of dynamical systems. amazing
@levpopov5688 Жыл бұрын
They both have simular vocabulary for miscellaneous words and expressions on top of similar intonations.
@uqyge Жыл бұрын
lol😂,now i c why 'magic mike' is also on my youtube recommendation.
@GFGentil4 жыл бұрын
Man, I found this by accident, but OMG u r the best. AC/DC reference was perfect.
@zhonghaozhao9193 жыл бұрын
got to this place by videos of Steven Bruntons. Hereby, I realize how smart you guys are! Salute, that's not teaching, but art of teaching. Respect!
@mattd91715 жыл бұрын
DMD, and SINDy, is amazing stuff. I was exposed to SINDy through a schoolmate and have just found this entire subject extremely fascinating.
@professionalprocrastinator81036 жыл бұрын
Your teaching is inspirational Nathan, and the material is top notch, as always! Thank you so much
@miguelalfonsomendez22245 жыл бұрын
Very interesting for the novice and very nicely presented. I can't think of a better introduction to the topic, and I can't think of a more charismatic and didactical presentation. Thank you 10000 times for sharing this. On the other hand, I believe that there's room for improvement in several parts that are quite incorrect and very superficial. At least, one could give a hint to the possible problems that occur when using the algorithm in real life applications. For example, it is not true what stated at 29:27 that Atilde = U^* A U is a similarity transform because U is not a square matrix. A tilde and A do not generally share the same eigenvalues (not even the dominant ones). Moreover, trying to propagate a linear system in a reduced space could be a very badly conditioned problem. What happens if the SVD basis selects only 2 modes (r=2) and each of these evolves with more than 2 frequencies? (very possible, since the SVD gives no constraints to the frequency content of its structures) Well, the algorithm will not move past step 2.
@AdityaDendukuri2 жыл бұрын
Correct me if I'm wrong but isn't the point of reducing the dimensionality was to only consider the non-singular subspace of the system? That would mean the system would actually be well-conditioned after the dimensionality reduction step as it is not singular.
@celestialoutcomes17423 жыл бұрын
WOW. I wish I had teachers like you.
@KjetilAndreJohannessen6 жыл бұрын
At 17:58 the matrix A is defined to be both the rate of change at state x as well as the mapping from one timestep to the next. Given the first definition x2=x1+dt*Ax1 (eulers method for timestepping), while for the latter you would have x2=Ax1.
@johnfinn9495 Жыл бұрын
The later `A' could be I+hA (h=\delta t) for Euler integration or (I-hA/2)^{-1}(I+hA/2) for implicit midpoint, or whatever. But if we find the later A, do we really need to find the original (ODE) A?
@alvinjamur111 ай бұрын
Absolutely fantastic!! This is truly fantastic and a treasure. Thank You!!
@SRIMANTASANTRA2 жыл бұрын
Professor Nathan, so lovely and enjoying your class.
@GBabuu4 жыл бұрын
its such a pleasure watching this !!!!! LOVE THE PRESENTATION
@rudypieplenbosch67524 ай бұрын
This is a great lecture 👌
@anima_kujurАй бұрын
I'm in love with you and your lecture 😍😅
@jeromeblacq75282 жыл бұрын
Amazing lecture, asolutely enjoyed it.
@ilyassayunus88 Жыл бұрын
I really enjoy watching this lecture
@mhchitsaz2 жыл бұрын
Excellent lecture, thank you for sharing
@joelrosenfeld61055 жыл бұрын
I remember the AC/DC song Dynamite Mode Decomposition. It is quite catchy.
@alessioalessi97426 жыл бұрын
I've never seen a math teacher talking about the AC/DC during the lecture... XD
@jupitermu26214 жыл бұрын
Can't agree more
@celestialoutcomes17423 жыл бұрын
I've had a physics techer talk about it... Get it?
@senkialfonz895 Жыл бұрын
Excellent.
@sulavghimire64733 жыл бұрын
Is it just me or the professor looks like Matthew McConaughey?
@drscott13 жыл бұрын
Amazing. Thank you
@user-vg7zv5us5r Жыл бұрын
35:36 What if somebody jumps into the flow you're measuring thus destroying a house of cards you've decided to be a sound depiction of physical world? You cannot predict when the fellow conscience being decides to have fun diving into the hotel pool.
@crazyfrog1313 жыл бұрын
where is the link for next lecture on "sparse identification of nonlinear dynamics" ?
@strange69736 жыл бұрын
You almost gave me a heart attack! It was Malcolm who passed.
@joesullivan21446 жыл бұрын
What course was this covered in at Washington?
@muzhiralani37325 жыл бұрын
very interesting subject.
@ilyassayunus88 Жыл бұрын
Legend 👏
@alexmallen57653 жыл бұрын
At 33:28, shouldn't he be using U_r for the similarity transform so that it reduces the number of dimensions down to r?
@cjcrowley3 жыл бұрын
Yes. After he wrote U_r, V_r and Sigma_r on the board, it should be assumed that they are all subscript r in the rest of the discussion.
@thomasfranzstockhammer78462 жыл бұрын
Lg Clear structural unnderstand lection !
@user-vg7zv5us5r Жыл бұрын
22:55 Dirac delta function.
@samlaf924 жыл бұрын
The fundamental assumption is that we want a linearization that works "well" at every point in the state space. Why does that even make sense to assume? For some arbitrary nonlinear ODE, linearization will be very different at different points in the domain.
@celestialoutcomes17423 жыл бұрын
It's just an approximation. A regression.
@vincenthel12 жыл бұрын
There are very few global statements to be made about non linear differential DEs and require assumptions to be made by the designer. However, we generally only want to know local behaviour of the system as phenomena are commonly constraint to a subset of the domain space. Furthermore, prediction tasks can be modeled effectively linearly given the system is sufficiently stable.
@hger84954 жыл бұрын
Hi, Can dmd also work for low dimensional non linear systems. Say for example 10 measurements per snapshot?
@celestialoutcomes17423 жыл бұрын
Sometimes. If
@vasanthakumar19916 жыл бұрын
What is meant by mode? Why is it named as DYNAMIC MODE DECOMPOSITION?
@joelrosenfeld61055 жыл бұрын
The mode is the eigenfunctions that you get from the system. The idea is that this method transforms the nonlinear dynamical system into a linear dynamical system, and the eigenfunctions you get are "modes" for the nonlinear dynamics.
@jenkinsj92242 жыл бұрын
This guy looks like Matthew Mcgonagall from Interstellar movie