Prediction using DMD using windowed data

[drhaserr]

The objective

I will submit a paper this month where I employ PYDMD. However, I am encountering challenges in locating documentation on predicting time series using windowed data. I need help to determine the optimal approach for fitting the model using windowed data, specifying a window size (e.g., window-size = 10), and subsequently making predictions for a specified number of data points (e.g., predicting the next 3 values).

Thank you :-)

[greinerth]

Do you want to make sure that all samples are used during the regression? Then you could directly set the svd_rank. E.g.

import numpy as np
from pydmd import DMD

# I assume you have some measurements "obs" of shape nxm which are measured with sampling time dt.
# When considering all measurements of "obs", m-1 samples can be used at maximum for your computation.
dmd = DMD(svd_rank=obs.shape[-1] - 1)
dmd.fit(obs)

For extrapolation of the timeseries you can easily use the modes, the eigenvalues and the amplitudes of the DMD class.

omegas = np.log(dmd.eigs) / dt

# define some arbitrary timestamps here
time = np.arange(10) * dt
prediction = dmd.modes  @ (np.exp(np.outer(omegas, time)) * dmd.amplitudes[:, None])

[Doublonmousse]

Well, on older versions of pydmd you had to extract modes, eigenvalues and amplitude and reconstruct everything manually.

Now this is no longer necessary using the dmd_time dictionnary. See in the tutorial 6 on hodmd

PyDMD/tutorials/tutorial6/tutorial-6-hodmd.py

Line 99 in cbd7c92

hodmd.dmd_time["tend"] = 50

And the documentation on the .dmd_time and .original_time dictionnaries

    :cvar dict original_time: dictionary that contains information about the
        time window where the system is sampled:

           - `t0` is the time of the first input snapshot;
           - `tend` is the time of the last input snapshot;
           - `dt` is the delta time between the snapshots.

    :cvar dict dmd_time: dictionary that contains information about the time
        window where the system is reconstructed:

            - `t0` is the time of the first approximated solution;
            - `tend` is the time of the last approximated solution;
            - `dt` is the delta time between the approximated solutions.

In your case just add n to .dmd_time["tend"] and calling dmd_obj.reconstructed_data will return you the reconstructed data on the windowed data + the n next timesteps. Changing .dmd_time["t0"] and you may be able to return just the prediction.

You have to double check that the dt are correct on both dictionnaries. By default dt is 1 and correspond to a single time step of your original data