A generalized approximate control variate framework for multifidelity uncertainty quantification

Journal Article · Tue Jan 21 00:00:00 EST 2020 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2020.109257· OSTI ID:1601260

Gorodetsky, Alex ^[1]; Geraci, Gianluca ^[2]; Eldred, Michael S. ^[2]; Jakeman, John Davis ^[2]

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1. Univ. of Michigan, Ann Arbor, MI (United States)
2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost models — which are typically lower fidelity with unknown statistics — are used to reduce the variance in statistical estimators relative to a MC estimator with equivalent cost. We derive the conditions under which our proposed approximate control variate framework recovers existing multifidelity variance reduction schemes as special cases. We demonstrate that existing recursive/nested strategies are suboptimal because they use the additional low-fidelity models only to efficiently estimate the unknown mean of the first low-fidelity model. As a result, they cannot achieve variance reduction beyond that of a control variate estimator that uses a single low-fidelity model with known mean. However, there often exists about an order-of-magnitude gap between the maximum achievable variance reduction using all low-fidelity models and that achieved by a single low-fidelity model with known mean. We show that our proposed approach can exploit this gap to achieve greater variance reduction by using non-recursive sampling schemes. The proposed strategy reduces the total cost of accurately estimating statistics, especially in cases where only low-fidelity simulation models are accessible for additional evaluations. Several analytic examples and an example with a hyperbolic PDE describing elastic wave propagation in heterogeneous media are used to illustrate the main features of the methodology.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC04-94AL85000; NA0003525
• OSTI ID: 1601260
• Alternate ID(s): OSTI ID: 1703204
• Report Number(s): SAND2020--1032J; 683277
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 408; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Control variates
Monte Carlo
Multifidelity modeling
Variance reduction