Hello,
I have been using the UQLab for performing sensitivity analysis on my models and I have recently started using PCE. I have an analytical model and I do not have experimental data, so I have been generating samples based on the approximated distributions and sampling techniques.
I understand that there are two types of errors in PCE, the leave-out-error and the validation error, and for the validation error you need a validation set XVal like in the PCE Truss example. However, I am not able to figure out how to use the generated samples and use send some of it into validation set. Is there some options that I have to include? Can I use uq_getSample or uq_enrichSobol as define that as my XVal?
Also, is there a possibility to calculate the R^2 error/coefficient as well?
I have included the code I use for PCE using the UQLab! Kindly help! 
%% SENSITIVITY: MULTIPLE OUTPUTS
%% 1 - INITIALIZE UQLAB
%
% Clear all variables from the workspace, set the random number generator
% for reproducible results, and initialize the UQLab framework:
clearvars
rng(100, 'twister')
ops = 'winhome';
if strcmp(ops, 'mac')
addpath '/Users/shadowfangs/Library/CloudStorage/OneDrive-KTH/PhD/Research/Codes/GSA/SensitivityAnalysisECO2Lab/Construct surrogates/PCE/UQLab_Rel2.0.0/core'
elseif strcmp(ops, 'server')
addpath 'C:\Users\SaKa\OneDrive - KTH\PhD\Research\Codes\Induction motor\UQLab_Rel2.0.0\core'
addpath 'C:\Users\SaKa\OneDrive - KTH\PhD\Research\Codes\Induction motor'
else
addpath 'C:\Users\Saika\OneDrive - KTH\PhD\Research\Codes\Induction motor\UQLab_Rel2.0.0\core'
addpath 'C:\Users\Saika\OneDrive - KTH\PhD\Research\Codes\Induction motor'
end
uqlab
%% 2 - COMPUTATIONAL MODEL
%
tic
% Create a MODEL object from the function file:
ModelOpts.mFile = 'motormodelsobol';
myModel = uq_createModel(ModelOpts);
%% 3 - INPUT MARGINALS
%% Inputs for R_r_dash example
InputOpts.Marginals(1).Name = 'n'; %
InputOpts.Marginals(1).Type = 'Uniform';
InputOpts.Marginals(1).Parameters = [3 12]; % (m)
InputOpts.Marginals(2).Name = 'b'; %
InputOpts.Marginals(2).Type = 'Uniform';
InputOpts.Marginals(2).Parameters = [0.5e-2 10e-2]; %
InputOpts.Marginals(3).Name = 'A'; %
InputOpts.Marginals(3).Type = 'Uniform';
InputOpts.Marginals(3).Parameters = [40e3 50e3]; % (m)
InputOpts.Marginals(4).Name = 'P_{rated}'; %
InputOpts.Marginals(4).Type = 'Uniform';
InputOpts.Marginals(4).Parameters = [2.5e5 5e5]; % (m)
InputOpts.Marginals(5).Name = 'Jr'; %
InputOpts.Marginals(5).Type = 'Uniform';
InputOpts.Marginals(5).Parameters = [3e6 5e6]; %
InputOpts.Marginals(6).Name = 'B_{\delta_i}'; %
InputOpts.Marginals(6).Type = 'Uniform';
InputOpts.Marginals(6).Parameters = [0.4 0.9]; %
InputOpts.Marginals(7).Name = 'f'; %
InputOpts.Marginals(7).Type = 'Uniform';
InputOpts.Marginals(7).Parameters = [30 80]; %
InputOpts.Marginals(8).Name = 'U'; %
InputOpts.Marginals(8).Type = 'Uniform';
InputOpts.Marginals(8).Parameters = [400 800]; %
InputOpts.Marginals(9).Name = '\eta_{eff_{in}}'; %
InputOpts.Marginals(9).Type = 'Uniform';
InputOpts.Marginals(9).Parameters = [0.8 0.9]; %
InputOpts.Marginals(10).Name = 'cos \phi'; %
InputOpts.Marginals(10).Type = 'Uniform';
InputOpts.Marginals(10).Parameters = [0.6 0.8]; %
InputOpts.Marginals(11).Name = '\alpha_i'; %
InputOpts.Marginals(11).Type = 'Uniform';
InputOpts.Marginals(11).Parameters = [0.6 0.9]; %
InputOpts.Marginals(12).Name = 'cos \zeta'; %
InputOpts.Marginals(12).Type = 'Uniform';
InputOpts.Marginals(12).Parameters = [0.5 0.9]; %
InputOpts.Marginals(13).Name = 'J_{ring}'; %
InputOpts.Marginals(13).Type = 'Uniform';
InputOpts.Marginals(13).Parameters = [3.5e6 4.5e6]; %
InputOpts.Marginals(14).Name = 'h_{1r}'; %
InputOpts.Marginals(14).Type = 'Uniform';
InputOpts.Marginals(14).Parameters = [0.3e-3 0.8e-3]; %
InputOpts.Marginals(15).Name = 'h_{2r}'; %
InputOpts.Marginals(15).Type = 'Uniform';
InputOpts.Marginals(15).Parameters = [0.3e-3 0.8e-3];
InputOpts.Marginals(16).Name = 'n_{req}'; %
InputOpts.Marginals(16).Type = 'Uniform';
InputOpts.Marginals(16).Parameters = [1250 2000]; %
%%
% Create an INPUT object based on the specified marginals:
myInput = uq_createInput(InputOpts);
%% 4 - SENSITIVITY ANALYSIS
%
% Sobol' indices are calculated first with a direct MC simulation
% of the model and subsequently through post-processing of the
% coefficients of its PCE and LRA approximation.
%% 4.1 PCE-based Sobol' indices
%
% Select the metamodeling tool in UQLab
% and the polynomial chaos expansion (PCE) type:
PCEOpts.Type = 'Metamodel';
PCEOpts.MetaType = 'PCE';
PCEOpts.Input = myInput;
%%
% Assign the full computational model:
PCEOpts.FullModel = myModel;
%%
% The full model is used to generate an experimental design for the PCE.
%%
% Specify the maximum polynomial degree (*default*: sparse PCE):
PCEOpts.Degree = 7;
%%
% Specify the size of the experimental design
% (i.e., the total computational cost of constructing the metamodel):
PCEOpts.ExpDesign.NSamples = 1000;
PCEOpts.ExpDesign.Sampling = 'sobol';
%%
% Calculate the PCE:
myPCE = uq_createModel(PCEOpts);
%%
% The same options structure |SobolOpts| can be re-used
% to create a new analysis on the PCE model:
% mySobolAnalysisPCE = uq_createAnalysis(SobolOpts);
PCESobol.Type = 'Sensitivity';
PCESobol.Method = 'Sobol';
PCESobol.Sobol.Order = 3;
PCESobolAnalysis = uq_createAnalysis(PCESobol);
PCESobolAnalysis.Results