ParametricDMD for scalar time-series

[alirezakarimi82]

I'm trying to model a parametric dynamical system which is not a function of space. So, basically for each value of the parameter we have a scalar time series. However, it seems that the current implementation of the ParametricDMD is not able to handle the case when the training snapshots are not a function of space. I guess implementing that feature as a special case should be straightforward and I'd appreciate if you could help me in this regard.

[fandreuz]

Hi @alirezakarimi82, I propose pairing HankelDMD with ParametricDMD:

from pydmd import ParametricDMD, HankelDMD
from ezyrb import POD, RBF

pdmd = ParametricDMD(dmds, POD(svd_rank=-1), RBF())

# params x space x time
X = np.arange(100*len(params)).reshape(len(params), 1, 100)
params = np.array([0.5 * i for i in range(20)])

pdmd.fit(X, params)
pdmd.parameters = np.array([0.25, 0.75])
pdmd.reconstructed_data

Let me know if you need more clarification. What I think is the problem in your case is that you did not provide an appropriate shape for X, which should always have 3 dimensions: params, space and time. Otherwise, please provide a code sample such that we can discuss further the problem.

[alirezakarimi82]

Thanks @fAndreuzzi for your prompt reply. The shape of X in my code was right. However, after fitting the ParametricDMD to my training data all the reconstructed data rows are zeros. I'm wondering what causes this issue. This is my code:

dmds = [HankelDMD(svd_rank=-1) for _ in range(len(params))]
pdmd = ParametricDMD(dmds, POD(rank=-1), RBF())
pdmd.fit(x_train, params)
pdmd.parameters = params
pdmd.reconstructed_data

By the way, as a side note, for each time series I have two parameters, so my params array has a shape of (10, 2), for example. I just to want to make sure it doesn't cause any issue.

[fandreuz]

By the way, as a side note, for each time series I have two parameters, so my params array has a shape of (10, 2), for example. I just to want to make sure it doesn't cause any issue.

This should work @alirezakarimi82, if you notice any problem it means there's a bug to fix :)

This is my code:

You should set the parameter d for HankelDMD, which controls the space dimension of HankelDMD modes (the default value is d=1, so a standard DMD). Could you please try HankelDMD(d=n, ...) with n > 1?

[alirezakarimi82]

Thanks again. Using your advice and also setting exact and opt to True, I was able to train and obtain good reconstructed data. There is another question which I very much appreciate to know your recommendation. I'm trying to model multiple types of variables as time series. For smooth signals, the combination of HankelDMD and ParametricDMD works perfectly. However, for signals which we have different modes of variation, the prediction is pretty poor. Ignoring the parameters, I was able to get prediction of those signals using a combination of HankelDMD and MrDMD (see attached picture). But when I try to use this combination within ParametricDMD, I get an error indicating that LinAlgError: Array must not contain infs or NaNs. I really appreciate if you give me some hints in this regard too. Following you may find my code.

sub_dmd = HankelDMD(svd_rank=-1, exact=True, opt=True, d=5)
dmds = [MrDMD(sub_dmd, max_level=7, max_cycles=1) for _ in range(len(training_params))]
pdmd = ParametricDMD(dmds, POD(rank=-1), RBF())
pdmd.fit(training_snapshots, training_params)

[fandreuz]

Hi @alirezakarimi82, I'm happy that my solution did the work.

[...] But when I try to use this combination within ParametricDMD, I get an error [...]

You're using a kind of triple nested DMD, which is something we never tested internally (even MrDMD+(*DMD) different than the standard one is quite new in PyDMD, #260). This is an interesting behavior and might be related to #251.

Does this happen in fit or reconstructed_data?

[alirezakarimi82]

This happens in fit.

[fandreuz]

I'll check, thanks for the report.

[fandreuz]

Hi @alirezakarimi82, sorry for the long wait but I couldn't work on this for a few weeks.

Could you please provide your dataset? I tried a few examples, but it looks like the problem occurs only when pathological data is provided (e.g. all-zero matrix).

[alirezakarimi82]

Thanks @fAndreuzzi for following up. Since it is proprietary data, unfortunately I cannot share it. But my data is not ill-posed as far as I know.