Abstract
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.
Highlights
The increasing necessity of handling data uncertainties in many different science and engineering scenarios and the development of computational capabilities of supercomputers are leading to the necessity of having a strict integration between Uncertainty Quantification (UQ) techniques and efficient algorithms
We propose an asynchronous version of the algorithms belonging to the Monte Carlo (MC) family, together with a reference implementation based on the Kratos Multiphysics software [13,14] and the XMC library [3], exploiting the PyCOMPSs programming model [2,25,34]
In the tables presenting the results, B identifies the initial number of batches, defined by the initial hierarchy, it the number of iterations, that is the amount of convergence checks executed, N the total number of realizations computed per level at the end of the of the execution, EMC[Q H ] and EMLMC[Q H ] the expected value estimate, SE the statistical error, time to solution the total time the simulation required to finish, measured in seconds, and C the computational cost of the algorithm run, expressed in CPU hours
Summary
The increasing necessity of handling data uncertainties in many different science and engineering scenarios and the development of computational capabilities of supercomputers are leading to the necessity of having a strict integration between Uncertainty Quantification (UQ) techniques and efficient algorithms. UQ studies how uncertainties propagate in the. The authors thankfully acknowledge the computer resources at MareNostrum and the technical support provided by Barcelona Supercomputing Center (IM-2020-1-0016)
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