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jonathf / chaospy

Chaospy - Toolbox for performing uncertainty quantification.
https://chaospy.readthedocs.io/
MIT License
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Data driven PCE to conduct uncertainty quantification and sensitivity analysis #316

Open AmosJoseph opened 3 years ago

AmosJoseph commented 3 years ago

Y=F(Xi),i=1.2.3.4.5 pdf of Xi is known.Then how to construct PCE through samples of Xi and Y?

I have seen the Data Driven PCE in tourial of Kernel Density Estimation,is this accessiable?

The generalized polynomial expansion can be employed to perform Data Driven PCE? Then how?

Congratulations!Nice job for the update of chaospy indeed!

Best wishes!

jonathf commented 3 years ago

Do you mean Y = F(X1, .., X5), or Y1 = F(X1), ..., Y5 = F(X5)? A varying X wihtout varying Y does not make sense to me.

Data driven PCE should be fine using chaospy.GaussianKDE as the distribution and chaospy.generate_expansion(order, dist, rule="cholesky") to generate the orthogonal expansion.

And thanks. :)

jonathf commented 3 years ago

Note that dd-pce is a big topic and depending on your reference, method might vary.

AmosJoseph commented 3 years ago

Y = F(X1, .., X9), 9 independent variables(dimensions), varying X and varying Y.

then is it efficient to employ sparse dd-pce?