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A fully parallelized and budgeted multi-level Monte Carlo method and the application to acoustic waves

Baumgarten, Niklas 1; Krumscheid, Sebastian ORCID iD icon 2; Wieners, Christian 1
1 Institut für Angewandte und Numerische Mathematik (IANM), Karlsruher Institut für Technologie (KIT)
2 Scientific Computing Center (SCC), Karlsruher Institut für Technologie (KIT)


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.

Volltext §
DOI: 10.5445/IR/1000161083
Veröffentlicht am 31.07.2023
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 07.2023
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000161083
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 28 S.
Serie CRC 1173 Preprint ; 2023/18
Projektinformation SFB 1173/3 (DFG, DFG KOORD, SFB 1173/3)
Externe Relationen Siehe auch
Schlagwörter Uncertainty quantification, high performance computing, multi-level Monte Carlo method, Knapsack problem, dynamic programming, parallelization, wave propagation
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