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国际不确定性的量化期刊
影响因子: 4.911 5年影响因子: 3.179 SJR: 1.008 SNIP: 0.983 CiteScore™: 5.2

ISSN 打印: 2152-5080
ISSN 在线: 2152-5099

Open Access

国际不确定性的量化期刊

DOI: 10.1615/Int.J.UncertaintyQuantification.2020030092
pages 399-424

DATA-CONSISTENT SOLUTIONS TO STOCHASTIC INVERSE PROBLEMS USING A PROBABILISTIC MULTI-FIDELITY METHOD BASED ON CONDITIONAL DENSITIES

L. Bruder
Mechanics and High Performance Computing Group, Technical University of Munich, Parkring 35, 85748 Garching, Germany
M. W. Gee
Mechanics & High Performance Computing Group, Technical University of Munich, Parkring 35, 85748 Garching, Germany
Timothy Wildey
Optimization and Uncertainty Quantification Department, Center for Computing Research, Sandia National Laboratories, Albuquerque, NM 87185

ABSTRACT

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.

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