Efficient Bayesian inference of subsurface flow models using nested sampling and sparse polynomial chaos surrogates

Ahmed H. Elsheikh, Ibrahim Hoteit, Mary Fanett Wheeler

Research output: Contribution to journalArticlepeer-review

74 Scopus citations

Abstract

An efficient Bayesian calibration method based on the nested sampling (NS) algorithm and non-intrusive polynomial chaos method is presented. Nested sampling is a Bayesian sampling algorithm that builds a discrete representation of the posterior distributions by iteratively re-focusing a set of samples to high likelihood regions. NS allows representing the posterior probability density function (PDF) with a smaller number of samples and reduces the curse of dimensionality effects. The main difficulty of the NS algorithm is in the constrained sampling step which is commonly performed using a random walk Markov Chain Monte-Carlo (MCMC) algorithm. In this work, we perform a two-stage sampling using a polynomial chaos response surface to filter out rejected samples in the Markov Chain Monte-Carlo method. The combined use of nested sampling and the two-stage MCMC based on approximate response surfaces provides significant computational gains in terms of the number of simulation runs. The proposed algorithm is applied for calibration and model selection of subsurface flow models. © 2013.
Original languageEnglish (US)
Pages (from-to)515-537
Number of pages23
JournalComputer Methods in Applied Mechanics and Engineering
Volume269
DOIs
StatePublished - Feb 2014

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Mechanics of Materials
  • Mechanical Engineering
  • Computational Mechanics
  • Computer Science Applications

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