On multilevel Monte Carlo methods for deterministic and uncertain hyperbolic systems

@article{Hu2022OnMM,
  title={On multilevel Monte Carlo methods for deterministic and uncertain hyperbolic systems},
  author={Junpeng Hu and Shi Jin and Jinglai Li and Lei Zhang},
  journal={ArXiv},
  year={2022},
  volume={abs/2205.06424}
}
. In this paper, we evaluate the performance of the multilevel Monte Carlo method (MLMC) for deterministic and uncertain hyperbolic systems, where randomness is introduced either in the modeling parameters or in the approximation algorithms. MLMC is a well known variance reduction method widely used to accelerate Monte Carlo (MC) sampling. However, we demonstrate in this paper that for hyperbolic systems, whether MLMC can achieve a real boost turns out to be delicate. The computational costs of… 

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