Uploaded May 2021 | Updated September 2026, 18 hours ago
Get rid of the Koopman operator and discretizations of continuous time systems. Koopman operators are suited for discrete time systems, and there is a small number of continuous time systems that can actually be discretized. Instead, we use Liouville operators (sometimes called "Koopman Generators" when discretization is possible) and Occupation Kernels to make a routine for Dynamic Mode Decomposition that doesn't impose the additional assumption of forward invariance on your system.
And IT WORKS! You can find a breakdown of the MATLAB code at the end of the video.
Code Link: bitbucket.org/joelrosenfeld/continuous-occupation-kernel-dmd
Music:
Come 2gether by Ooyy
Pandoras Box by Squiid
Video Call from Los Angeles by Trevor Kowalski
Wrong by Dan Henig
Sunrise in Paris by Dan Henig
Guardians + Tek by Craig Hardgrove
0:00 Start and Media
0:48 Introduction
2:30 Summer Plans
4:53 Occupation Kernels and Liouville Operators
7:22 Eigenfunctions for Liouville Operators
9:30 The DMD Algorithm for Continuous Time Systems
17:28 MATLAB Discussion
21:05 MATLAB Code
Get rid of the Koopman operator and discretizations of continuous time systems. Koopman operators are suited for discrete time systems, and there is a small number of continuous time systems that can actually be discretized. Instead, we use Liouville operators (sometimes called "Koopman Generators" when discretization is possible) and Occupation Kernels to make a routine for Dynamic Mode Decomposition that doesn't impose the additional assumption of forward invariance on your system.
And IT WORKS! You can find a breakdown of the MATLAB code at the end of the video.
Code Link: bitbucket.org/joelrosenfeld/continuous-occupation-kernel-dmd
Music:
Come 2gether by Ooyy
Pandoras Box by Squiid
Video Call from Los Angeles by Trevor Kowalski
Wrong by Dan Henig
Sunrise in Paris by Dan Henig
Guardians + Tek by Craig Hardgrove
0:00 Start and Media
0:48 Introduction
2:30 Summer Plans
4:53 Occupation Kernels and Liouville Operators
7:22 Eigenfunctions for Liouville Operators
9:30 The DMD Algorithm for Continuous Time Systems
17:28 MATLAB Discussion
21:05 MATLAB Code
