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Published May 15, 2018 | Published
Journal Article Open

Multifidelity Monte Carlo Estimation of Variance and Sensitivity Indices

Abstract

Variance-based sensitivity analysis provides a quantitative measure of how uncertainty in a model input contributes to uncertainty in the model output. Such sensitivity analyses arise in a wide variety of applications and are typically computed using Monte Carlo estimation, but the many samples required for Monte Carlo to be sufficiently accurate can make these analyses intractable when the model is expensive. This work presents a multifidelity approach for estimating sensitivity indices that leverages cheaper low-fidelity models to reduce the cost of sensitivity analysis while retaining accuracy guarantees via recourse to the original, expensive model. This paper develops new multifidelity estimators for variance and for the Sobol' main and total effect sensitivity indices. We discuss strategies for dividing limited computational resources among models and specify a recommended strategy. Results are presented for the Ishigami function and a convection-diffusion-reaction model that demonstrate up to 10x speedups for fixed convergence levels. For the problems tested, the multifidelity approach allows inputs to be definitively ranked in importance when Monte Carlo alone fails to do so.

Additional Information

© 2018 Elizabeth Qian, Benjamin Peherstorfer, Daniel O'Malley, Velimir Vesselinov, and Karen Willcox. Received by the editors October 9, 2017; accepted for publication (in revised form) February 20, 2018; published electronically May 15, 2018. The work of the first author was supported by the National Science Foundation Graduate Research Fellowship and the Fannie and John Hertz Foundation. This research was supported by the Air Force Center of Excellence on Multi-Fidelity Modeling of Rocket Combustor Dynamics, Award Number FA9550-17-1-0195, as well as the U.S. Department of Energy, Office of Advanced Scientific Computing Research (ASCR), Applied Mathematics Program, awards DE-FG02-08ER2585 and DE-SC0009297, as part of the DiaMonD Multifaceted Mathematics Integrated Capability Center.

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