Will PCE work with transformed inputs (ensuring one-to-one mapping)

Hello everyone

I have a model with 36 input parameters and an output vector of size 80. I have about 10,000 samples.
Suppose I apply a one to one mapping from my 36 dimensional input parameter space to a reduced order space of say 5 dimensions. I will use different groups of the 36 parameters to construct each of the parameters in my 5 dimensional space so that they are all independent. For example,
parameters 1 to 8 → param 1 of the new space
parameters 9 to 15 → param 2 of the new space
parameters 16 to 22 → param 3 of the new space
parameters 23 to 29 → param 4 of the new space
parameters 30 to 36 → param 5 of the new space

So now I have my 10,000 samples where the inputs have only 5 dimensions and output dimension remains the same as before, 80.

Can I expect to get a good pce model for the outputs using this new 5 dimensional input space?

Thank you very much.