I am trying to build an explicit expression based on the obtained PCE model. My random inputs are all standard uniform variables. However, when I built up the PCE expression as shown in point 2 of this post and tested several samples, I found that the output results were not the same as the results obtained from uq_evalModel.

Specifically, I was using the PCE.Basis.Indices, PCE.Coefficients in the PCE model, and standard Legendre polynomials to build explicit expressions. I am now wondering what basis function I should use. I understand that for standard uniform distributions, the orthogonal polynomials are the standard Legendre polynomials defined on [−1,1]. However, there is also Hilbertian basis in Table 1 of PCE manual. And when I build up the expression with the Hilbertian basis instead of Legendre polynomials, the test results will be the same as those from the function uq_evalModel.

Can you help to clarify this point for me? Thank you.

When weighting the integral with the probability distribution function of the uniform distribution over [-1, 1], i.e., \displaystyle{\frac{1}{2}}, one gets: