Ensemble approximate control variate estimators: Applications to multi-fidelity importance sampling.

Pham, Trung; Gorodetsky, Alex

doi:10.1137/21M1390426

Ensemble approximate control variate estimators: Applications to multi-fidelity importance sampling.

Journal Article · Wed Sep 28 00:00:00 EDT 2022 · SIAM/ASA Journal on Uncertainty Quantification

DOI:https://doi.org/10.1137/21M1390426· OSTI ID:1894597

Pham, Trung ^[1]; Gorodetsky, Alex ^[1]

University of Michigan, Ann Arbor, MI (United States)

The recent growth in multifidelity uncertainty quantification has given rise to a large set of variance reduction techniques that leverage information from model ensembles to provide variance reduction for estimates of the statistics of a high-fidelity model. In this paper we provide two contributions: (1) we utilize an ensemble estimator to account for uncertainties in the optimal weights of approximate control variate (ACV) approaches and derive lower bounds on the number of samples required to guarantee variance reduction; and (2) we extend an existing multifidelity importance sampling (MFIS) scheme to leverage control variates. Our approach directly addresses a limitation of many multifidelity sampling strategies that require the usage of pilot samples to estimate covariances. As such we make significant progress towards both increasing the practicality of approximate control variates—for instance, by accounting for the effect of pilot samples—and using multifidelity approaches more effectively for estimating low-probability events. The numerical results indicate our hybrid MFIS-ACV estimator achieves up to 50% improvement in variance reduction over the existing state-of-the-art MFIS estimator, which had already shown an outstanding convergence rate compared to the Monte Carlo method, on several problems of computational mechanics.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); University of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003525

OSTI ID:: 1894597

Report Number(s):: SAND2022-3390J; 704327

Journal Information:: SIAM/ASA Journal on Uncertainty Quantification, Journal Name: SIAM/ASA Journal on Uncertainty Quantification Journal Issue: 3 Vol. 10; ISSN 2166-2525

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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