A possible complication might arise from the fact that there are two layers of output in a Principal component model.

The first is the principal component score metamodeling error using the usual metric, Q2 and RMSE.
The second is the reconstruction error from using a truncated principal component coupled with the score predicted by the metamodel. The error here will be more intuitive.

Three different regression formulas for constructing a GP metamodel for the Sandia Thermal problem are considered:

1. Constant
2. Linear
3. Linear + Interaction

Four types of design of computer experiment are considered:

1. Simple Random Sampling (SRS)
2. Latin Hypercube Sampling (LHS)
3. Optimized Latin Hypercube Sampling (LHS-OPT)
4. Sobol' Sequence

Considered 4 different replications for the two-dimensional problem: 4, 8, 16, 32

The effects using on using 5 different covariance/correlation functions are investigated for the Sandia Thermal Challenge problem. The covariance function includes:

1. Exponential
2. Gaussian
3. Power Exponential
4. Matern 3/2
5. Matern 5/2

Check if there is differences.
Three transformations are considered:

1. original
2. log
3. sqrt

Don't forget to shift the output because they are not strictly positive.