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Title: An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions

Abstract

Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes’ rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle these challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limitedmore » number of forward simulations.« less

Authors:
 [1];  [2]
  1. Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
  2. Purdue University, West Lafayette, IN (United States)
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1182897
Alternate Identifier(s):
OSTI ID: 1367756
Report Number(s):
PNNL-SA-105408
Journal ID: ISSN 0021-9991; KJ0401000
Grant/Contract Number:  
DMS-1115887; AC05-76RL01830
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 294; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; inverse modeling, uncertainty reduction, adaptive sampling, Gaussian mixture, mixture of polynomial chaos expansions

Citation Formats

Li, Weixuan, and Lin, Guang. An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions. United States: N. p., 2015. Web. doi:10.1016/j.jcp.2015.03.047.
Li, Weixuan, & Lin, Guang. An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions. United States. doi:10.1016/j.jcp.2015.03.047.
Li, Weixuan, and Lin, Guang. Sat . "An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions". United States. doi:10.1016/j.jcp.2015.03.047. https://www.osti.gov/servlets/purl/1182897.
@article{osti_1182897,
title = {An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions},
author = {Li, Weixuan and Lin, Guang},
abstractNote = {Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes’ rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle these challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.},
doi = {10.1016/j.jcp.2015.03.047},
journal = {Journal of Computational Physics},
number = C,
volume = 294,
place = {United States},
year = {Sat Mar 21 00:00:00 EDT 2015},
month = {Sat Mar 21 00:00:00 EDT 2015}
}

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