A multilevel Monte Carlo method for computing failure probabilities
Abstract
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 which 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.
Cite
@article{arxiv.1408.6856,
title = {A multilevel Monte Carlo method for computing failure probabilities},
author = {Daniel Elfverson and Fredrik Hellman and Axel Målqvist},
journal= {arXiv preprint arXiv:1408.6856},
year = {2016}
}