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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 when gradient information can be computed efficiently. 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 paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the 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 parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.

Authors:
 [1];  [2];  [1];  [1];  [3]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
  2. Florida State Univ., Tallahassee, FL (United States). Dept. of Scientific Computing
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Atmospheric, Earth and Energy Division
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1404854
Report Number(s):
LLNL-TR-740300
DOE Contract Number:  
AC52-07NA27344
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE

Citation Formats

Thimmisetty, Charanraj A., Zhao, Wenju, Chen, Xiao, Tong, Charles H., and White, Joshua A.. Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA. United States: N. p., 2017. Web. doi:10.2172/1404854.
Thimmisetty, Charanraj A., Zhao, Wenju, Chen, Xiao, Tong, Charles H., & White, Joshua A.. Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA. United States. doi:10.2172/1404854.
Thimmisetty, Charanraj A., Zhao, Wenju, Chen, Xiao, Tong, Charles H., and White, Joshua A.. Wed . "Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA". United States. doi:10.2172/1404854. https://www.osti.gov/servlets/purl/1404854.
@article{osti_1404854,
title = {Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA},
author = {Thimmisetty, Charanraj A. and Zhao, Wenju and Chen, Xiao and Tong, Charles H. and White, Joshua A.},
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 when gradient information can be computed efficiently. 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 paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the 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 parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.},
doi = {10.2172/1404854},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2017},
month = {10}
}

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