Skip to Main content Skip to Navigation
Journal articles

Polynomial chaos representation of databases on manifolds

Abstract : Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. The method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.
Complete list of metadata

Cited literature [45 references]  Display  Hide  Download
Contributor : Christian Soize Connect in order to contact the contributor
Submitted on : Friday, January 27, 2017 - 8:30:56 PM
Last modification on : Saturday, January 15, 2022 - 4:13:24 AM
Long-term archiving on: : Saturday, April 29, 2017 - 1:56:59 AM


Files produced by the author(s)




Christian Soize, Roger Ghanem. Polynomial chaos representation of databases on manifolds. Journal of Computational Physics, Elsevier, 2017, 335, pp.201-221. ⟨10.1016/⟩. ⟨hal-01448413⟩



Record views


Files downloads