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.

在许多不同的科学和工程领域，处理不确定性的必要性正在增长。由于计算能力的不断发展，当前的求解器必须同时满足统计精度和计算效率。这项工作的目的是为 Monte Carlo 和 Multilevel Monte Carlo 方法引入一个异步框架来实现这样的结果。所提出的方法提供了与现有技术相同的可靠性，并旨在通过相对于现有算法添加新的并行级别来提高计算效率：批次之间，其中每个批次拥有其层次结构并且相互独立。在超级计算机中考虑并解决了两个不同的数值问题，以显示所提出方法的行为。