期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 230, 期 19, 页码 7311-7331出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2011.05.037
关键词
Stochastic partial differential equations; Data-driven models; Kernel principal component analysis; Non-linear model reduction; Flow in random porous media
资金
- US Department of Energy, Office of Science, Advanced Scientific Computing Research
- National Science Foundation (NSF) [DMS- 0809062]
- OSD/AFOSR
- NSF through NCSA [TG-DMS090007]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0809062] Funding Source: National Science Foundation
Stochastic analysis of random heterogeneous media provides useful information only if realistic input models of the material property variations are used. These input models are often constructed from a set of experimental samples of the underlying random field. To this end, the Karhunen-Loeve (K-L) expansion, also known as principal component analysis (PCA), is the most popular model reduction method due to its uniform mean-square convergence. However, it only projects the samples onto an optimal linear subspace, which results in an unreasonable representation of the original data if they are non-linearly related to each other. In other words, it only preserves the first-order (mean) and second-order statistics (covariance) of a random field, which is insufficient for reproducing complex structures. This paper applies kernel principal component analysis (KPCA) to construct a reduced-order stochastic input model for the material property variation in heterogeneous media. KPCA can be considered as a nonlinear version of PCA. Through use of kernel functions, KPCA further enables the preservation of higher-order statistics of the random field, instead of just two-point statistics as in the standard Karhunen-Loeve (K-L) expansion. Thus, this method can model non-Gaussian, non-stationary random fields. In this work, we also propose a new approach to solve the pre-image problem involved in KPCA. In addition, polynomial chaos (PC) expansion is used to represent the random coefficients in KPCA which provides a parametric stochastic input model. Thus, realizations, which are statistically consistent with the experimental data, can be generated in an efficient way. We showcase the methodology by constructing a low-dimensional stochastic input model to represent channelized permeability in porous media. (C) 2011 Elsevier Inc. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据