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.

翻译：我们提出了一种多层蒙特卡洛方法的新型变体，该方法能在高性能计算系统上有效利用预留的计算预算，以最小化均方误差。该方法融合了延续型多层蒙特卡洛方法的概念、基于贝尔曼最优性原理的动态规划技术，以及一种基于单一分布式数据结构的新并行化策略。此外，我们在并行计算集群上建立了误差缩减的理论界，并通过实验证明所提出的方法严格遵循该理论界。我们针对计算密集型问题对方法进行了实现、测试与性能评估，重点研究了该方法在高维随机介质声波传播问题中的应用。