A parallel dynamic asynchronous framework for uncertainty quantification by hierarchical Monte Carlo algorithms

The necessity of dealing with uncertainties is growing in many different fields of science and engineering. Due to the constant development of computational capabilities, current solvers must satisfy both statistical accuracy and computational efficiency. The aim of this work is to introduce an asynchronous framework for Monte Carlo and Multilevel Monte Carlo methods to achieve such a result. The proposed approach presents the same reliability of state of the art techniques, and aims at improving the computational efficiency by adding a new level of parallelism with respect to existing algorithms: between batches, where each batch owns its hierarchy and is independent from the others. Two different numerical problems are considered and solved in a supercomputer to show the behavior of the proposed approach.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 800898. This work has been supported by the Spanish Government (contracts SEV2015- 0493 and TIN2015-65316-P), by the Generalitat de Catalunya (contract 2014-SGR-1051). The authors thankfully acknowledge the computer resources at MareNostrum and the technical support provided by Barcelona Supercomputing Center (IM-2020-1-0016).Peer ReviewedPostprint (published version