Dear UQlab team,

Thank you for developing such an amazing software for us to use.

I want to use the PCE module to get a surrogate where the experimental design is specified manually (as in the attached files, with three inputs and on output; train_data for training, test_data for validation; train_data(:,1:3) the inputs and train_data(:,4) the output, same goes for test_data). Since the distributions of the input random variables are unknown, and the use of PCE requires the information of distributions. So the statistical inference module available in UQlab is used to get the distribution info from the data set, the result is: input 1~uniform (0.1 2), input 2~Beta (0.6983 1.951 0 1), input 3~Gamma (0.3048 666.879).

To this end, I can use the PCE to construct the surrogate model. And based on my own experience, the PCE can generally yield a good approximation to the original model. But I donât know why it doesnât work in this way for this example, i.e. the PCE is poorly behaved with quite high LOO error and validation error, and can hardly get a good prediction of the new samples in the domain, even with high polynomial degree. And the histogram plot does not seem to be correct since the value in vertical is decimal, which should be an integer (as shown in fig). I wonder if anyone can help me check with that and find the reason why the PCE doesnât work for my case. Really appreciate your kind help.

BTW, after get the PCE using UQlab, how can I get an explicit expression of the PCE surrogate (the relation between the coefficients and the multivariate orthonormal polynomials)? how to interpret the myPCE.PCE.Basis.Indices sparse array in the result?

Attached is the data set (training and testing), and the code I used.

Iâm a new user and cannot upload attachments, could you please give me access to do that? Many thanks!