Forward and inverse uncertainty quantification using multilevel Monte Carlo algorithms for an elliptic non-local equation

Journal Article · Thu Dec 31 23:00:00 EST 2015 · International Journal for Uncertainty Quantification

DOI:https://doi.org/10.1615/Int.J.UncertaintyQuantification.2016018661· OSTI ID:1342665

Jasra, Ajay ^[1]; Law, Kody J. H. ^[2]; Zhou, Yan ^[1]

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1. National Univ. of Singapore (Singapore). Dept. of Statistics and Applied Probability
2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science and Mathematics Division

Our paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a probability measure. It is shown that the induced probability measure on some quantities of interest arising from functionals of the solution to the equation with random inputs is well-defined,s as is the posterior distribution on parameters given observations. As the elliptic nonlocal equation cannot be solved approximate posteriors are constructed. The multilevel Monte Carlo (MLMC) and multilevel sequential Monte Carlo (MLSMC) sampling algorithms are used for a priori and a posteriori estimation, respectively, of quantities of interest. Furthermore, these algorithms reduce the amount of work to estimate posterior expectations, for a given level of error, relative to Monte Carlo and i.i.d. sampling from the posterior at a given level of approximation of the solution of the elliptic nonlocal equation.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC05-00OR22725
• OSTI ID: 1342665
• Journal Information: International Journal for Uncertainty Quantification, Journal Name: International Journal for Uncertainty Quantification Journal Issue: 6 Vol. 6; ISSN 2152-5080
• Publisher: Begell House
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING