Data Driven Discovery of Dynamical Systems and PDEs

[@nilspin]

Didn't know prof. Kutz had a youtube channel! I took your MOOC Computational Methods for Data analysis in 2013. I didn't finish with good grade, but it really piqued my interest in diff. equations and then dynamical systems. This was an amazing lecture(although it'll need multiple viewings, esp. learning in unobserved low rank modeling and PDE generation) , and I absolutely love your candid style of teaching. I've never gotten so many 'aha' moments in one lecture with any other teacher.

[@quantummath]

Lovely! thanks for the presentation Prof. Kutz.

[@GBabuu]

Love the stuff. And you are an excellent Instructor too. Thank u for this post

[@sangeeta3844]

Very Informative.

[@quantummath]

Great video!

[@cjcrowley]

Over all, this is a GREAT explanation of many topics in data driven model discovery, but I am confused on a very important step. The notation used at 53:49 is confusing to me. This portion of the discussion is unfortunately sparse on references. Would someone provide a reference to learn more on this approach.

[@ranislavir]

Great lecture

[@DaylightDigital]

I think you may have buried the lede with the "I can make moving objects invisible to security cameras" application of DMD (51:09) ;-). Great talk though.

[@XMan-iv7ir]

excellent

[@scottmiller2591]

Ah Ky Keh = Akaike. The ai is pronounced like eye in English, which if you listen closely has 2 sounds to it - an initial ah, and a following ee, but not with the enunciation used in the lecture.

[@celestialoutcomes1742]

Can you recommend a text book?

[@jsmdnq]

Why not build a macro-system that integrates many of the different solving methods in to a unified system. E.g., Something that uses SINDY on compression sensed data to find some the underlying dynamics then use the results as a error correction for a Koopman method. Or some neural network like machine that can select and weight different methods that all can interact in a way that one can train the system to optimize speed and size over many different phenomena which then can be used to solve newer problems faster and more effectively? The idea is to sort of pass different parts of the problem to various "modules" and let them solve them. It may be that you pass lower modes discovered by DMD to SINDY to find the underlying lower mode dynamics while using compression sensing and then "averaging" the two results to get something that might be more effective for discovery of lower dynamics. Then another method can be used for the faster dynamics that is more tuned.

[@aidanokeeffe7928]

PDE discovery will do a lot to legitimize ML approaches for more traditionally oriented scientists!

[@veritasdude1358]

1:06:03 Belly Scratching Doc :-)) -- kidding, big fan from Europe.