2023/07/20 by Niklas Baumgarten, Baumgarten, Niklas, Sebastian Krumscheid +3 · 2 citations
Mathematics · Physics and Astronomy · #Distributed #FOS: Computer and information sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Numerical Analysis (math.NA) #Parallel #Theoretical and Computational Physics #and Cluster Computing (cs.DC)
paper · pdf · doi:10.48550/arxiv.2307.10767
openalex publication_date 2023/07/20 · openalex created_date 2023/07/22 · openalex updated_date 2026/07/28
We present a novel variant of the multi-level 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 multi-level 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.