I just gave a lecture to our UQ class on response surfaces, and I went over the attached slide containing a “decision tree” for choosing a response surface. The purpose for the class was to get the students asking questions about their “uncertain quantity of interest” before blindly applying a method — since I don’t expect them to know the details of all the methods, yet.

I might develop this further with more branches and hyperlinks to relevant research papers. Feel free to leave any comments!

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Thank your for the post, Paul! It was really helpful. I sincerely believe such “big-picture” diagrams are of immense importance when it comes to studying such a complex topic as UQ, especially when there are so many ways of achieving the same goal, and it is not that obvious which one is worth being tried. If I am not mistaken, polynomial chaos is not covered by this diagram as it is typically not considered to be a type of response surface analysis. What wound be the range of variables and other criteria for using PC? Also, were/are you recording your lectures this time? Thank you.

Thanks, Ivan! In practice, polynomial chaos methods differ very little from standard polynomial regression methods used in statistics. (This may be a contentious statement, and I’m happy to discuss it further.) I use “Kriging/RBF plus polynomial mean,” which is essentially polynomial regression with a Gaussian process approximation for the residual. I also use polynomial interpolation on a Chebyshev grid if the dimension is 1 or 2, which is sometimes called “stochastic collocation” in UQ (although there’s nothing stochastic about the approximation). That’s also closely related to polynomial chaos methods. Remember: there’s nothing chaotic about polynomial chaos.

Oh, and we did not record the lectures this year.