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

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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.

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Dear @mridula ,

I am sorry for the delay in replying! In case you have not solved your problem, here is my answer:

It is challenging to know in advance whether the PCE model would provide reasonable estimations. It strongly depends on whether the relationship between the parameters of this new space and the outputs is smooth. If so, then most likely, PCE will approximate it well. In your particular case, I suggest you perform the mapping of your inputs and then pre-process it. Additionally, some plots might help you understand how it behaves. If smoothly, then, as I said, I believe the chances of getting a good surrogate are high.

Good luck with it, and please let us know if you have further questions!

Best regards,
Anderson