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We present a novel variant of the multi-level Monte Carlo method thateffectively utilizes a reserved computational budget on a high-performancecomputing system to minimize the mean squared error. Our approach combinesconcepts of the continuation multi-level Monte Carlo method with dynamicprogramming techniques following Bellman's optimality principle, and a newparallelization strategy based on a single distributed data structure.Additionally, we establish a theoretical bound on the error reduction on aparallel computing cluster and provide empirical evidence that the proposedmethod adheres to this bound. We implement, test, and benchmark the approach oncomputationally demanding problems, focusing on its application to acousticwave propagation in high-dimensional random media.

A Fully Parallelized and Budgeted Multi-Level Monte Carlo Method and the Application to Acoustic Waves