Journal
SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION
Volume 6, Issue 2, Pages 737-761Publisher
SIAM PUBLICATIONS
DOI: 10.1137/17M1122992
Keywords
multifidelity; Monte Carlo; rare event simulation; failure probability estimation; surrogate models; reduced models; importance sampling; multilevel; cross-entropy method; variance reduction
Funding
- DARPA EQUiPS Program [UTA15-001067]
- AFOSR MURI on multi-information sources of multi-physics systems [FA9550-15-1-0038]
- Air Force Center of Excellence on Multi-Fidelity Modeling of Rocket Combustor Dynamics [FA9550-17-1-0195]
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Accurately estimating rare event probabilities with Monte Carlo can become costly if for each sample a computationally expensive high-fidelity model evaluation is necessary to approximate the system response. Variance reduction with importance sampling significantly reduces the number of required samples if a suitable biasing density is used. This work introduces a multifidelity approach that leverages a hierarchy of low-cost surrogate models to efficiently construct biasing densities for importance sampling. Our multifidelity approach is based on the cross-entropy method that derives a biasing density via an optimization problem. We approximate the solution of the optimization problem at each level of the surrogate-model hierarchy, reusing the densities found on the previous levels to precondition the optimization problem on the subsequent levels. With the preconditioning, an accurate approximation of the solution of the optimization problem at each level can be obtained from a few model evaluations only. In particular, at the highest level, only a few evaluations of the computationally expensive high-fidelity model are necessary. Our numerical results demonstrate that our multifidelity approach achieves speedups of several orders of magnitude in a thermal and a reacting-flow example compared to the single-fidelity cross-entropy method that uses a single model alone.
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