How to organize snapshots for ParametricDMD?

[jacktang]

Hello there!

I've read parametric dmd tutorial and understood how it worked on one parameter and 1d space. And I try to make the example more complex -- extend the example to three parameters: mu1, mu2, mu3 and the 3d space (x, y, z), and the time is specified(say 2pi). My question is how to organize the snapshots?

pdmd = ParametricDMD(dmds, POD(svd_rank=-1), RBF())
# params x space x time
params = zip(mu1, mu2, mu3) or append(mu1, mu2, m3) ??
snapshots = np.arange(100*len(params)).reshape(len(params), 3, 1) # space = 1 or 3?

pdmd.fit(snapshots, params)

Thanks!

[fandreuz]

Hi @jacktang, I've just added a new section at the end of tutorial10 to deal with this case. Let me know if it helps

[jacktang]

@fAndreuzzi Thanks a lot! I get it now :)

[jacktang]

Hello @fAndreuzzi ,

The goal shape is:
$$n_{train} \times (n^1_{space} \times n^2_{space} \times \dots \times n^k_{space}) \times n_{time-instants}$$

I read it again, and the shape of snapshots should be $(n_{train} \times (n^1_{space} \times n^2_{space} \times \dots \times n^k_{space}) , n_{time-instants})$ ?

[fandreuz]

Hi @jacktang, basically this means that you need to flatten the space dimensions into a single axis. The way you flatten does not matter as long as you do exactly the reverse after you apply ParametricDMD.

Let me know if you need further explanation

[zonexo]

Hi, I just tried to use parametric DMD with 2 variables. After trying it out, I realised there's not much difference compared to a 1 variable case - You simply combine whatever cases you have and call the function. Because the final shape of the snapshots only depends on the no. of cases, it doesn't matter whether it's 1, 2 or 3 variables. I got quite good ans so I thought I should have done it correctly. Is my interpretation correct?

[jacktang]

Hello @zonexo , from you description, I think the other variables are not sensitive to the response surface. Did you do some sensitivity analysis before modeling?

[zonexo]

Sorry, that's not what I meant. I'm saying that the arrangement of the snapshots matrix does not differ much whether there are 1,2 or more variables. They are simply stacked up. It is also shown in the example when it changes from 1 to 2 variables. The snapshots matrix is not changed and only the training_params changes.