Large input data condition number problem

[zonexo]

The objective
Hi, I got the warning on Large input data condition number - consider preprocessing data, passing in augmented data.

So what should I do exactly? How should I pre-process it. and what does it mean by passing in augmented data?

My data comes from the surface pressure of a moving body in CFD.

Already tried tests

I have a total of 10,000 snapshots. I tried to increase and decrease the amount of data as input but I still get the error msg.

[mtezzele]

Hi @zonexo,

I suggest trying to rescale the data by subtracting the temporal mean or the initial condition, for example. This operation will change the spectrum of the snapshots matrix and hopefully reduce the condition number.

[azzeddinetiba]

Hello,
You can also use the tikhonov parameter, (See

PyDMD/pydmd/dmdbase.py

Line 175 in 261dba9

tikhonov_regularization=None,

,

PyDMD/pydmd/dmdbase.py

Lines 145 to 148 in 261dba9

	:param tikhonov_regularization: Tikhonov parameter for the regularization.
	If `None`, no regularization is applied, if `float`, it is used as the
	:math:`\\lambda` tikhonov parameter.
	:type tikhonov_regularization: int or float

)
i.e use a small value like 1e-6 (the value is problem-dependent) to regularize the minimization problem and avoid spurious modes due to ill-conditioning.
See this tutorial

[zonexo]

Hi all, thanks for the suggestions. I forgot to mention that I have tried the tikhonov_regularization, using 1e-8 as suggested in the tutorial. I will experiment with more values since I still get the error. I will also try to rescale the data. Thanks!