PCE with correlated inputs

Hi everyone,

Can we build a PCE model with correlated inputs?



Dear Hongzhou

Yes it is possible. The usual practice is to use an isoprobabilistic transform first, so as to transform the correlated input vector into, e.g., a standard normal vector (Rosenblatt or Nataf transform, depending on the copula of the joint vector), then use a polynomial chaos expansion (PCE) based on these transformed variables. This was originally introduced in [1]. This is the way it is handled in UQLab.

Recent papers construct orthonormal polynomial bases w.r.t the joint PDF of the input vector numerically [2], but this is not available in UQLab.

Best regards

[1] Blatman, G. and Sudret, B. (2010) An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis, Prob. Eng. Mech., vol. 25 (2), pp. 183–197.
[2] Jakeman, J.D., Franzelin, F., Narayan, A., Eldred, M. and Pflüger, D. (2019) Polynomial chaos expansions for dependent random variables, Comput. Methods Appl. Mech. Engrg., vol. 351, pp. 643–666.


Dear Professor Sudret,

This is really useful! Thank you very much.