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Multilevel Estimation of Rare Events
16 references·15 citing·39 second hop
Multilevel Estimation of Rare Events (2015)Multilevel Estimation of Rare EventsMCMC algorithms for Subset Simulation (2015)MCMC algorithms for Subset Si…Engineering Risk Assessment with Subset Simulation (2014)Engineering Risk Assessment w…Metamodel-based importance sampling for structural reliability analysis (2013)Metamodel-based importance sa…Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients (2011)Multilevel Monte Carlo method…Assessing small failure probabilities by combined subset simulation and Support Vector Machines (2011)Assessing small failure proba…The stochastic finite element method: Past, present and future (2008)The stochastic finite element…Multilevel Monte Carlo Path Simulation (2008)Multilevel Monte Carlo Path S…Reliability of structures in high dimensions, part I: algorithms and applications (2004)Reliability of structures in …Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations (2004)Galerkin methods for linear a…Important sampling in high dimensions (2002)Important sampling in high di…Reliability analysis—a review and some perspectives (2001)Reliability analysis—a review…Estimation of small failure probabilities in high dimensions by subset simulation (2001)Estimation of small failure p…A new adaptive importance sampling scheme for reliability calculations (1999)A new adaptive importance sam…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Adaptive sampling — an iterative fast Monte Carlo procedure (1988)Adaptive sampling — an iterat…A critical appraisal of methods to determine failure probabilities (1987)A critical appraisal of metho…Large Deviation Theory-based Adaptive Importance Sampling for Rare Events in High Dimensions (2023)Large Deviation Theory-based …The Ensemble Kalman Filter for Rare Event Estimation (2022)The Ensemble Kalman Filter fo…Sequential Active Learning of Low-Dimensional Model Representations for Reliability Analysis (2022)Sequential Active Learning of…On information fusion for reliability estimation with multifidelity models (2022)On information fusion for rel…Error Analysis for Probabilities of Rare Events with Approximate Models (2021)Error Analysis for Probabilit…A scenario optimization approach to reliability-based and risk-based design: Soft-constrained modulation of failure probability bounds (2021)A scenario optimization appro…Subset simulation method including fitness-based seed selection for reliability analysis (2020)Subset simulation method incl…Multilevel Sequential Importance Sampling for Rare Event Estimation (2020)Multilevel Sequential Importa…Estimation of distributions via multilevel Monte Carlo with stratified sampling (2020)Estimation of distributions v…Accelerated Multilevel Monte Carlo With Kernel‐Based Smoothing and Latinized Stratification (2020)Accelerated Multilevel Monte …Multifidelity probability estimation via fusion of estimators (2019)Multifidelity probability est…Multifidelity approaches for uncertainty quantification (2019)Multifidelity approaches for …Multifidelity Preconditioning of the Cross-Entropy Method for Rare Event Simulation and Failure Probability Estimation (2018)Multifidelity Preconditioning…Convergence analysis of multifidelity Monte Carlo estimation (2018)Convergence analysis of multi…Combining multiple surrogate models to accelerate failure probability estimation with expensive high-fidelity models (2017)Combining multiple surrogate …Exact and Invariant Second-Moment Code Format (1974)A critical appraisal of reliability estimation procedures for high dimensions (2004)Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles (2011)The Logic of Scientific Discovery (2013)Structural Reliability Analysis and Prediction (2017)Simulation and the Monte Carlo Method (1981)A combined Importance Sampling and Kriging reliability method for small failure 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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2001Estimation of small failure probabilities in high dimensions by subset simulation2,419 cited
  • 2008Multilevel Monte Carlo Path Simulation1,436 cited
  • 2008The stochastic finite element method: Past, present and future999 cited
  • 2001Reliability analysis—a review and some perspectives775 cited
  • 1999A new adaptive importance sampling scheme for reliability calculations564 cited
  • 2004Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations556 cited
  • 2013Metamodel-based importance sampling for structural reliability analysis535 cited
  • 2011Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients490 cited
  • 1988Adaptive sampling — an iterative fast Monte Carlo procedure464 cited
  • 1987A critical appraisal of methods to determine failure probabilities436 cited
  • 2011Assessing small failure probabilities by combined subset simulation and Support Vector Machines419 cited
  • 2015MCMC algorithms for Subset Simulation413 cited
  • 2002Important sampling in high dimensions375 cited
  • 2004Reliability of structures in high dimensions, part I: algorithms and applications

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370 cited
  • 2014Engineering Risk Assessment with Subset Simulation315 cited
  • Cited by

    • 2017Combining multiple surrogate models to accelerate failure probability estimation with expensive high-fidelity models47 cited
    • 2018Multifidelity Preconditioning of the Cross-Entropy Method for Rare Event Simulation and Failure Probability Estimation44 cited
    • 2021A scenario optimization approach to reliability-based and risk-based design: Soft-constrained modulation of failure probability bounds40 cited
    • 2020Estimation of distributions via multilevel Monte Carlo with stratified sampling30 cited
    • 2020Subset simulation method including fitness-based seed selection for reliability analysis28 cited
    • 2019Multifidelity probability estimation via fusion of estimators27 cited
    • 2020Multilevel Sequential Importance Sampling for Rare Event Estimation25 cited
    • 2018Convergence analysis of multifidelity Monte Carlo estimation24 cited
    • 2019Multifidelity approaches for uncertainty quantification15 cited
    • 2020Accelerated Multilevel Monte Carlo With Kernel‐Based Smoothing and Latinized Stratification15 cited
    • 2023Large Deviation Theory-based Adaptive Importance Sampling for Rare Events in High Dimensions13 cited
    • 2022Sequential Active Learning of Low-Dimensional Model Representations for Reliability Analysis13 cited
    • 2022The Ensemble Kalman Filter for Rare Event Estimation11 cited
    • 2022On information fusion for reliability estimation with multifidelity models9 cited
    • 2021Error Analysis for Probabilities of Rare Events with Approximate Models8 cited