A Fully Parallelized and Budgeted Multilevel Monte Carlo Method and the Application to Acoustic Waves

IF 2.1 3区工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Siam-Asa Journal on Uncertainty Quantification Pub Date : 2024-08-19 DOI:10.1137/23m1588354

Niklas Baumgarten, Sebastian Krumscheid, Christian Wieners

引用次数: 0

Abstract

SIAM/ASA Journal on Uncertainty Quantification, Volume 12, Issue 3, Page 901-931, September 2024.
Abstract.We present a novel variant of the multilevel Monte Carlo method that effectively utilizes a reserved computational budget on a high-performance computing system to minimize the mean squared error. Our approach combines concepts of the continuation multilevel Monte Carlo method with dynamic programming techniques following Bellman’s optimality principle and a new parallelization strategy based on a single distributed data structure. Additionally, we establish a theoretical bound on the error reduction on a parallel computing cluster and provide empirical evidence that the proposed method adheres to this bound. We implement, test, and benchmark the approach on computationally demanding problems, focusing on its application to acoustic wave propagation in high-dimensional random media.

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完全并行化和预算多级蒙特卡洛方法及其在声波中的应用

SIAM/ASA《不确定性量化期刊》，第12卷第3期，第901-931页，2024年9月。摘要.我们提出了多级蒙特卡洛方法的一种新变体，它能有效利用高性能计算系统的预留计算预算，最大限度地减小均方误差。我们的方法结合了延续多级蒙特卡洛法的概念、遵循贝尔曼最优性原理的动态编程技术以及基于单一分布式数据结构的新型并行化策略。此外，我们还建立了在并行计算集群上减少误差的理论界限，并提供了经验证据证明所提出的方法符合这一界限。我们在计算要求很高的问题上实施、测试和基准测试了该方法，重点是其在高维随机介质中声波传播的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Siam-Asa Journal on Uncertainty Quantification Mathematics-Statistics and Probability

CiteScore

3.70

自引率

0.00%

发文量

期刊介绍： SIAM/ASA Journal on Uncertainty Quantification (JUQ) publishes research articles presenting significant mathematical, statistical, algorithmic, and application advances in uncertainty quantification, defined as the interface of complex modeling of processes and data, especially characterizations of the uncertainties inherent in the use of such models. The journal also focuses on related fields such as sensitivity analysis, model validation, model calibration, data assimilation, and code verification. The journal also solicits papers describing new ideas that could lead to significant progress in methodology for uncertainty quantification as well as review articles on particular aspects. The journal is dedicated to nurturing synergistic interactions between the mathematical, statistical, computational, and applications communities involved in uncertainty quantification and related areas. JUQ is jointly offered by SIAM and the American Statistical Association.