A Multiscale Strategy for Bayesian Inference Using Transport Maps
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15m1032478.pdf
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Author(s)
Parno, Matthew
Moselhy, Tarek
Marzouk, Youssef M
Date Issued
October 2016
Journal
SIAM/ASA Journal on Uncertainty Quantification
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Citation
Parno, Matthew et al. “A Multiscale Strategy for Bayesian Inference Using Transport Maps.” SIAM/ASA Journal on Uncertainty Quantification 4, 1 (January 2016): 1160–1190 © 2016 Society for Industrial & Applied Mathematics (SIAM)
Version
Final published version
Abstract
In many inverse problems, model parameters cannot be precisely determined from observational data. Bayesian inference provides a mechanism for capturing the resulting parameter uncertainty, but typically at a high computational cost. This work introduces a multiscale decomposition that exploits conditional independence across scales, when present in certain classes of inverse problems, to decouple Bayesian inference into two stages: (1) a computationally tractable coarse-scale inference problem, and (2) a mapping of the low-dimensional coarse-scale posterior distribution into the original high-dimensional parameter space. This decomposition relies on a characterization of the non-Gaussian joint distribution of coarse- and fine-scale quantities via optimal transport maps. We demonstrate our approach on a sequence of inverse problems arising in subsurface flow, using the multiscale finite element method to discretize the steady state pressure equation. We compare the multiscale strategy with full-dimensional Markov chain Monte Carlo on a problem of moderate dimension (100 parameters) and then use it to infer a conductivity field described by over 10000 parameters. Keywords: Bayesian inference; inverse problems; multiscale modeling; multiscale finite element method; optimal transportation; Markov chain Monte Carlo
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.
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DOI of Published Version
https://doi.org/10.1137/15M1032478
