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International Journal for Uncertainty Quantification
Импакт фактор: 4.911 5-летний Импакт фактор: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

ISSN Печать: 2152-5080
ISSN Онлайн: 2152-5099

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International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2020030092
Forthcoming Article

Solving Stochastic Inverse Problems using Approximate Push-forward Densities based on a Multi-fidelity Monte Carlo Method

Lukas Bruder
Michael Gee
Timothy Wildey
Sandia National Labs

Краткое описание

We build upon a recently developed approach for solving stochastic inverse problems based on a combination of measure-theoretic principles and Bayes' rule. We propose a multi-fidelity method to reduce the computational burden of performing uncertainty quantification using high-fidelity models. This approach is based on a Monte Carlo framework for uncertainty quantification that combines information from solvers of various fidelities to obtain statistics on the quantities of interest of the problem. In particular, our goal is to generate samples from a high-fidelity push-forward density at a fraction of the costs of standard Monte Carlo methods, while maintaining flexibility in the number of random model input parameters. Key to this methodology is the construction of a regression model to represent the stochastic mapping between the low- and high-fidelity models, such that most of the computations can be leveraged to the low-fidelity model. To that end, we employ Gaussian process regression and present extensions to multi-level-type hierarchies as well as to the case of multiple quantities of interest. Finally, we demonstrate the feasibility of the framework in several numerical examples.}