Koopman Theory + Embeddings

This highlights how to think and construct Koopman embeddings for nonlinear dynamical systems. By appropriate choice of an observable (or coordinate system), the dynamics can be made weakly nonlinear and the dynamic mode decomposition can be used to approximate the evolution.

[@enochyeung1978]

Nathan, when you said "boom, smackdown, I was with you. I was legitimately excited. Love the way you introduce these topics and motivate their utility!"

[@longchen5188]

So exciting to see a nonlinear ODE can be changed to a nonlinear one. Great lecture.

[@erockromulan9329]

"Let's just make something up." Love it!

[@Savedbygrace952]

I love you Nathan. you are truly an awesome professor!

[@quantummath]

Damn he's one fun professor. Hopefully in a few years I'll become one.

[@MathPhysicsFunwithGus]

amazing and insightful video!

[@mengjiezhao7250]

I was laughing watching this video in the library

[@gegebao5363]

me is also excited, thanks a lot!

[@BrunoJedynak]

Nice. Thank you, Nathan.

[@user-vg7zv5us5r]

8:05 That mad lad Koopman multiplies functions by the operator named after himself.

[@jawadmezaal5192]

Can Koopman method be used instead of taylor series?

[@abrahamsilas227]

Absolutely! In fact Koopman proves to be better than Taylor series and Lyapunov.

[@abrahamsilas227]

Absolutely yes! In fact better than Taylor's series and Lyapunov

[@abrahamsilas227]

How can I get the paper for this lecture?

[@rudypieplenbosch6752]

Bit weird, you replace some variables and now it looks like a linear equation, except all the nonlinear stuff has been wiped under the carpet, but is stil there 🤔. I'm in the middle of your lecture, curious how this will work out, of course it will.

[@ajaisingh9129]

Can someone please provide me a link to the matlab code used in the lecture video ?

[@WeAsBee]

Here: dmdbook.com/page10/data4bio.html

[@siddhanttandon6246]

am i the only one who thinks this lecture was damn funny ? PS : 26:19 so much fame on this board. lmao

[@ajaisingh9129]

What does Dr. Kutz mean when he says " I take snapshot of state variables " ?

[@user-vg7zv5us5r]

He captures the value of state variable. Did it make things more clear?

[@ajaisingh9129]

@@user-vg7zv5us5r yes thank you so much

[@user-vg7zv5us5r]

@@ajaisingh9129 no problem)

[@user-vg7zv5us5r]

@@ajaisingh9129 no problem)

[@user-vg7zv5us5r]

29:12 Normalization - regularization.

[@DiegoAndrade]

Hahaha 🎉 bananas 😄😄😄😄

[@user-vg7zv5us5r]

6:56 g=a(y) mechanics xP