A Multilevel Monte Carlo Method for Computing Failure Probabilities
Artikel i vetenskaplig tidskrift, 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.

multilevel Monte Carlo

uncertainty quantification

failure probability

error analysis


D. Elfverson

F. Hellman

Axel Målqvist

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

SIAM-ASA Journal on Uncertainty Quantification

2166-2525 (ISSN)

Vol. 4 312-330