Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients

By K. Andrew Cliffe, M. Giles, Robert Scheichl, Aretha L. Teckentrup. Computing and Visualization in Science, 2011

556 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/720c1e1920b209eb6bc58e566ef0c9c9d5e0d825

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In Computational Theory and Mathematics

In Numerical Analysis

In Statistics and Probability

Citations in the corpus

Towards efficient uncertainty quantification in complex and large-scale biomechanical problems based on a Bayesian multi-fidelity scheme (2014, background): “The second broad class of algorithms is based on sampling approaches like Monte Carlo (MC) and all its variants (Metropolis and Ulam 1949; McKay et al. 1979; Bourgund and Bucher 1986; Cliffe et al. 2011; Pellissetti and Schuëller 2009; Pradlwarter et al. 2007; Olsson and Sandberg 2002; Neal 2001; Hu”
Reduced basis methods for partial differential equations with stochastic influences (2013, methodology): “It can be shown that the computational costs compared to the straightforward MC application can be reduced [21].”
Multifidelity importance sampling (2016, methodology): “One approach based on the control variate method is the multi-level Monte Carlo method [15, 16], which combines the outputs of a hierarchy of coarse grid solutions using control variates.”
Optimal Model Management for Multifidelity Monte Carlo Estimation (2016, methodology): “The multilevel Monte Carlo method [27, 22, 15, 46] uses coarse-grid approximations as surrogate models and distributes the work among the models using known error and cost rates.”
Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks (2019, methodology): “Consequently, the MC method and it’s advanced variants have been extensively applied to a variety of UQ problems [6, 7, 8, 9, 10].”
Survey of multifidelity methods in uncertainty propagation, inference, and optimization (2018, background): “, [45, 199], the recent advances on multi-index Monte Carlo [95], and the nesting of multilevel Monte Carlo and control variates [155] for detailed studies and further references.”