A Multilevel Monte Carlo Method for Computing Failure Probabilities
Journal article, 2016

We propose and analyze a method for computing failure probabilities of systems modeled as numerical deterministic models (e.g., PDEs) with uncertain input data. A failure occurs when a functional of the solution to the model is below (or above) some critical value. By combining recent results on quantile estimation and the multilevel Monte Carlo method, we develop a method that reduces computational cost without loss of accuracy. We show how the computational cost of the method relates to error tolerance of the failure probability. For a wide and common class of problems, the computational cost is asymptotically proportional to solving a single accurate realization of the numerical model, i.e., independent of the number of samples. Significant reductions in computational cost are also observed in numerical experiments.

uncertainty quantification

multilevel Monte Carlo

failure probability

error analysis

Author

D. Elfverson

F. Hellman

Axel Målqvist

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

SIAM-ASA Journal on Uncertainty Quantification

21662525 (eISSN)

Vol. 4 1 312-330

Subject Categories

Mathematics

DOI

10.1137/140984294

More information

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1/3/2024 9