Dynamic Mode Decomposition Code

Рет қаралды 22,716

6 жыл бұрын

This lecture provides an overview of the algorithm (exact DMD) for computing DMD modes and eigenvalues. Several examples are demonstrated where the DMD provides interpretable and low-rank decompositions of the data.

Пікірлер: 18

@muhammadahsanzamee4385 3 жыл бұрын

literally, i can listen to professor Kutz for hours and not get bored. He is a genius.

@erenkeskus6132 6 жыл бұрын

I can't wait to try this on multivariate time series data. (namely security prices) . I appreciated this class, it was very explanatory. I've read an article by you about an DMD application and for me now everything is put in place. Thank you for the upload.

@casusbelli4905 Жыл бұрын

Brilliant lecture. Thank you Professor!

@dr.alikhudhair9414 Жыл бұрын

Wonderful Lec .. thank you professor

@mohammadkhezri6877 5 ай бұрын

Thank you, it was very helpful🌹

@shutaoshen8115 3 жыл бұрын

easy to understand, as a supplement of the paper of "A KERNEL-BASED METHOD FOR DATA-DRIVEN KOOPMAN SPECTRAL ANALYSIS"

@a3igner 2 жыл бұрын

@NathanKutz what’s the optimal length of the time window to use? How do you determine this? One will cutoff any long wavelength modes that are greater than the length of the time window (or T/2)

@blchen1 3 жыл бұрын

At 28:09, if we use svds(X1,r) to get the truncated singular vectors, they differ by a constant complex phase compared with those obtained by svd(X1,'econ'). But somehow that affects the eigen-modes Phi. Should I stick with svd when doing DMD or am I missing something? Thanks!

@theohlong307 4 жыл бұрын

this is something really cool, omg !!!

@nurulashikin4930 2 жыл бұрын

Hi, Prof. May I know how to plot the true mode to compare with the DMD modes and PCA signal, in addition, I would like to know how to plot the time dynamics to be compared with singular vector V. Thank you 🙏

@shabyshaby123 5 жыл бұрын

Is it correct to call Atilde a similarity transform? It's clear that eigenvalues of A and Atilde are the same, but is Ur'*A*Ur a similarity transform when Ur is not square?

@PABITRABADHUK 4 жыл бұрын

The operation is a similarity transformation from an n*n dimensional space to an r*r dimensional space.

@JeffMTX 6 жыл бұрын

Try setting f1 and f2 equal to their real parts only, before doing the POD or otherwise. It doesn't work very well. It would be really awesome to see an example that used real-valued example data!

@nikhileshnatraj331 6 жыл бұрын

J M I tried this. Setting real values f1 and f2 roughly translates to the dynamics of a standing wave (no oscillations through time for the sech and tanh functions). The X matrix then has to be transformed into a Hankel matrix ... this models the dynamics and solves the problem. Hankel matrix: take X from 1 up to n-m where n is no of time points and m is number of stacks , say 20 for n=1000. Right below X, append X from 2 to n-m+1. Below this new X, append from 3 to n-m+2 and so on... essentially you are inflating X in its height stacking on top o each other. Notice this construction introduces time dynamics and solves the problem

@goharshoukat3782 4 жыл бұрын

At 30:28, you divide by Sr. Shouldnt you multiply it with inv(Sr)? Or am I missing something?

@matthewjames7513 3 жыл бұрын

"/" is the matrix divide. It's the same thing as multiplying by the inverse.au.mathworks.com/help/fixedpoint/ref/embedded.fi.mrdivide.html

@pradnyajagtap3638 2 жыл бұрын

how x is given as summation of bj*phij*e^wjt ?

@user-rs9cg2zg2n 2 жыл бұрын

In dx/dt = Ax vector x is a set of variables and A is a transform matrix and in term of system of linear equations A has coefficients of system and x has unknown functions so Euler's method can be applied. According to it solution is x_i(t)=b_i*phi_i*e^lambda_i*t where lambda_i is eigenvalue, phi_i is eigenvector corresponding to lambda_i and b_i is initial solution when t=0