In recent times, I noticed that surrogates are built more from Kriging and PCE method as against using other methods SVR, ANN, simple regression in UQ. Are there clear advantages of using Kriging, PCE compared to other methods or why is Kriging and PCE more attractive in surrogate construction and reliability? Any obvious limitation in their use too?

Appreciate useful thoughts on this. In addition, thanks for the amazing uqlab software.

Fascinating question.
I personally use them both, mainly PCE, for my UQ and SA analyses. There are many reasons for this choice:

PCE gives me a direct formulation of the model, which is very handy for future analyses

PCE allows the estimation of Sobol indices straightforwardly. Regarding ANN, I was reading just this morning this article about a new way of computing sensitivity indices from neural networks. Personally, I do not know much about NN, but basically, I think that the concept of surrogate modeling for sensitivity analysis is the same

PCE is relatively easy to implement and is very flexible about the input probability distributions of the input domain.

Regarding SVR, I am not an expert, so I do not feel to say anything about
I there anything, in particular, you refer to regarding the use of PCE or Kriging? What are your thoughts?

Thank you so much for your very insightful feedback. Nothing in particular, I just noticed that a majority in the UQ world community tend to use Kriging and PCE. I thought to open a discussion on why the choice , why not a simple polynomial regression expression (quadratic or cubic) to relate input variables and responses. Thanks for your valuable input on this.

Dear @aokoro,
As I understand the PCE, it is a kind of polynomial regression, but which takes into account the input distribution, to weight each sample.
To give you a practical example, imagine you have 10 points, and among them one is unlikely to happen. The PCE wonâ€™t be influenced too much by this sample (because the probability that it is sampled is small) , but a standard linear regression will take this sample into account (with the same weight thant the other samples).
It is how I understand the PCE, but I might be mistakenâ€¦ Maybe an expert can confirm ?