skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

Abstract

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even with gradient information provided. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this work, we propose a novel Bayesian stochastic inversion methodology, characterized by a tight coupling between a gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). This approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated spatial random field. Moreover, non-Gaussian full posterior probability distribution functions are estimated via an efficient LMCMC method on both the projected low-dimensional feature space and the recovered high-dimensional parameter space. We demonstrate this computational framework by integrating and adapting recent developments such as data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to solve inverse problems in linear elasticity.

Authors:
 [1];  [1];  [1];  [2];  [2];  [3];  [3];  [3]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Atmospheric, Earth and Energy Division
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Engineering
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1481063
Report Number(s):
LLNL-TR-760558
949317
DOE Contract Number:  
AC52-07NA27344
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Chen, Xiao, Thimmisetty, Charanraj A., Tong, Charles H., White, Joshua A., Morency, Christina, Huang, Can, Korkali, Mert, and Min, Liang. Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA. United States: N. p., 2018. Web. doi:10.2172/1481063.
Chen, Xiao, Thimmisetty, Charanraj A., Tong, Charles H., White, Joshua A., Morency, Christina, Huang, Can, Korkali, Mert, & Min, Liang. Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA. United States. doi:10.2172/1481063.
Chen, Xiao, Thimmisetty, Charanraj A., Tong, Charles H., White, Joshua A., Morency, Christina, Huang, Can, Korkali, Mert, and Min, Liang. Fri . "Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA". United States. doi:10.2172/1481063. https://www.osti.gov/servlets/purl/1481063.
@article{osti_1481063,
title = {Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA},
author = {Chen, Xiao and Thimmisetty, Charanraj A. and Tong, Charles H. and White, Joshua A. and Morency, Christina and Huang, Can and Korkali, Mert and Min, Liang},
abstractNote = {Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even with gradient information provided. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this work, we propose a novel Bayesian stochastic inversion methodology, characterized by a tight coupling between a gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). This approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated spatial random field. Moreover, non-Gaussian full posterior probability distribution functions are estimated via an efficient LMCMC method on both the projected low-dimensional feature space and the recovered high-dimensional parameter space. We demonstrate this computational framework by integrating and adapting recent developments such as data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to solve inverse problems in linear elasticity.},
doi = {10.2172/1481063},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2018},
month = {10}
}