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Multilevel Monte Carlo applied for uncertainty quantification in stochastic multiscale systems
16 references·1 citing·47 second hop
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References

  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2003Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems2,707 cited
  • 2008Multilevel Monte Carlo Path Simulation1,436 cited
  • 2004Verification, validation, and predictive capability in computational engineering and physics721 cited
  • 2009Fast Numerical Methods for Stochastic Computations: A Review608 cited
  • 1990Polynomial Chaos in Stochastic Finite Elements416 cited
  • 2009Recent Advances in Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Analysis and Design371 cited
  • 2007Distributional uncertainty analysis using power series and polynomial chaos expansions195 cited
  • 2012Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions113 cited
  • 2005Perspectives on the design and control of multiscale systems88 cited
  • 2015Multilevel Monte Carlo Approximation of Distribution Functions and Densities70 cited
  • 2014Uncertainty analysis and robust optimization of multiscale process systems with application to epitaxial thin film growth61 cited
  • 2013Multilevel Monte Carlo for two phase flow and Buckley–Leverett transport in random heterogeneous porous media61 cited
  • 2016Approximation of probability density functions by the Multilevel Monte Carlo Maximum Entropy method

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52 cited
  • 2013Mean Exit Times and the Multilevel Monte Carlo Method42 cited
  • 2016Distributional uncertainty analysis and robust optimization in spatially heterogeneous multiscale process systems33 cited
  • Cited by

    • 2023Learning and optimization under epistemic uncertainty with Bayesian hybrid models18 cited