Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems
Name
MarzoukNajm_JCP2009.pdf
Description
Main article
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1.13 MB
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Adobe PDF
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df1ebbcaaf9bfe55a893f7876a422320
Author(s)
Marzouk, Youssef M.
Najm, Habib N.
Date Issued
December 2008
Journal
Journal of Computational Physics
Publisher
Elsevier
Citation
Marzouk, Youssef M., and Habib N. Najm. “Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems.” Journal of Computational Physics 228.6 (2009): 1862-1902.
Version
Author's final manuscript
Abstract
We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a spatial or temporal field, endowed with a hierarchical Gaussian process prior. Computational challenges in this construction arise from the need for repeated evaluations of the forward model (e.g., in the context of Markov chain Monte Carlo) and are compounded by high dimensionality of the posterior. We address these challenges by introducing truncated Karhunen–Loève expansions, based on the prior distribution, to efficiently parameterize the unknown field and to specify a stochastic forward problem whose solution captures that of the deterministic forward model over the support of the prior. We seek a solution of this problem using Galerkin projection on a polynomial chaos basis, and use the solution to construct a reduced-dimensionality surrogate posterior density that is inexpensive to evaluate. We demonstrate the formulation on a transient diffusion equation with prescribed source terms, inferring the spatially-varying diffusivity of the medium from limited and noisy data.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.jcp.2008.11.024
