Estimation of distributions via multilevel Monte Carlo with stratified sampling

Taverniers, Søren; Tartakovsky, Daniel M.

doi:10.1016/j.jcp.2020.109572

Estimation of distributions via multilevel Monte Carlo with stratified sampling

Journal Article · Thu Jul 09 00:00:00 EDT 2020 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2020.109572· OSTI ID:1852855

Taverniers, Søren ^[1]; ^[2]

Stanford Univ., CA (United States). Dept. of Energy Resources Engineering; Stanford Univ., CA (United States)
Stanford Univ., CA (United States). Dept. of Energy Resources Engineering

We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the joint cumulative distribution function (CDF) of a vector-valued quantity of interest in problems with random input parameters and initial conditions. Our approach combines MLMC with stratified sampling of the input sample space by replacing standard Monte Carlo at each level with stratified Monte Carlo initialized with proportionally allocated samples. We show that the resulting stratified MLMC (sMLMC) algorithm is more efficient than its standard MLMC counterpart due to the additional variance reduction provided by the stratification of the random parameter's domain, especially at the coarsest levels. Additional computational cost savings are obtained by smoothing the indicator function with a Gaussian kernel, which proves to be an efficient and robust alternative to recently developed polynomial-based techniques.

View Accepted Manuscript (DOE)

Research Organization:: Stanford Univ., CA (United States)

Sponsoring Organization:: Defense Advanced Research Project Agency (DARPA); US Air Force Office of Scientific Research (AFOSR); USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0019130

OSTI ID:: 1852855

Alternate ID(s):: OSTI ID: 1638394

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 419; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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GINNs: Graph-Informed Neural Networks for multiscale physics Hall, Eric J.; Taverniers, Søren; Katsoulakis, Markos A. Journal of Computational Physics, Vol. 433 https://doi.org/10.1016/j.jcp.2021.110192	journal	May 2021
UNSW-NB15 Computer Security Dataset: Analysis through Visualization Zoghi, Zeinab; Serpen, Gursel arXiv https://doi.org/10.48550/arxiv.2101.05067	preprint	January 2021

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