POD for Partial Differential Equations

This lecture highlights the basic mathematical structure of the Proper Orthogonal Decomposition (POD). The POD modes are used for model reduction by producing an optimal subspace on which to project data and governing equations.

[BCarli]

Thanks, Professor. Recently ordered your book and find these video lectures to be very helpful as I go through a chapter. Students have different styles of learning and I find my understanding is facilitated by hearing as well as reading the material. I stumbled upon your (and Steve Brunton’s) videotaped engineering math lectures to students at U of Washington a few years back and have watched most of them — well done..
I recommend the book, “Data-Driven Science and Engineering”, to all students of applied math. I was one of the first buyers of “Introduction to Applied Mathematics” about 35 years ago when Gilbert Strang had just started with Wellesley-Cambridge (he was nice enough to send a personal letter, regrettably misplaced, with my copy of the book). Your book has just the right blend of rigor and “hands-on” application (Python and Matlab code, website, examples and full-color illustrations) as Professor Strang’s books and I can find no higher compliment to give. It has been interesting to see the field of applied math evolve as computational math and data science have developed.

[carlosayam]

Best exposition I've seen of solving numerically non-linear PDEs. Thank you!

[AnimationsJungle]

one of the best lectures .I learnt a lot from this lecture. Thank you for uploading this lecture sir. God bless you.

[florianarbes]

Great overview and very comprehensible. Thank you! Also thanks for the link to the book.
I wondered if it is the same as the ebook you are selling?

[cheikhbrahimabed]

Thank you for this amazing course. Can we apply this method for steady Partial Differential Equations?

[sinahamedi]

Thanks Dr. Kutz, I know it is a little bit off-topic but it would be great if you can make a video on choosing basis functions (FFT, Chebychev, Legendre, etc.) for PDEs based on boundary conditions. You usually use FFT which is not appropriate for non-periodic BCs, and in fluid dynamics we usually have other types of BCs.