Polynomial chaos representation of databases on manifolds

JOURNAL OF COMPUTATIONAL PHYSICS

卷:335

Article

Soize, C.¹  Ghanem, R.² 

[1] Univ Paris Est, Lab Modelisat & Simulat Multi Echelle, CNRS, MSME,UMR 8208, 5 Bd Descartes, F-77454 Marne La Vallee 2, France

[2] Univ Southern Calif, 210 KAP Hall, Los Angeles, CA 90089 USA

关键词: Polynomial chaos expansion;    Arbitrary probability measure;    Concentration of probability;    Measure concentration;    Generator;    Probability distribution on manifolds;    Random sampling generator;    MCMC generator;    Diffusion maps;    Statistics on manifolds;   

DOI  :  10.1016/j.jcp.2017.01.031

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free