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

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.