Difficulty to reach Kriging accuracy

Methodology
1

Dear OT users,

I am working right now on a UQ workflow with a numerical model taking into inputs 19 uncertain variables and computing out 3 quantities of interest.

For the UQ analysis (sobol sensitivity, forward propagation, etc.) I construct a Kriging model.
The trouble is that for 2 of the QOIs, the validation of the surrogate (computed on an independent validation set of 60 points) is still very bad, even as I increase the size of the DOE.

For instance i attach here the figures of the qq plots for each QOI (Y0,Y1,Y2), considering a Kriging constructed on a DOE of 4000 points sampled with LHS, according to uniform distribution. Note that the Q2 scores are worst with smaller DOE sizes. It means that when I increase the size the of the DOE, the validation is getting better but it is very weak enhancement.

qqPlotKriging_qoi_0.pdf (196.7 KB)

qqPlotKriging_qoi_1.pdf (196.7 KB)

qqPlotKriging_qoi_2.pdf (196.8 KB)

Would you have any advice or tips to enhance the surrogate model accuracy with respect with the real model ? Or am I just stuck in the curse of dimensionality with so many inputs ?

An other question is about the Kriging algorithm complexity, it takes very long time to construct the Kriging with so much points, but I assume it is expected considering the size of the DOE.

Thanks by advance for your help in this topic, and I look forward to discuss these issues with the community.

Best regards,

Elie

2

hi,

It could be useful to set the scale parameters in the range of the data, for example if you have no other active parameters than scales parameters in your covariance model:

algo_fit = otexp.GaussianProcessFitter(X_train, Y_train, covariance_model, basis)
scaleOptimizationBounds = ot.Interval(0.1 * X_train.computeRange(), 4.0 * X_train.computeRange())
algo_fit.setOptimizationBounds(scaleOptimizationBounds)
algo_fit.run()`

otherwise we realized the hyperparameters optimization is much better performed in a normalized space, but for this to be available you will have to wait for version 1.26.

j