TY - JOUR N1 - This version is the version of record. For information on re-use, please refer to the publisher?s terms and conditions. KW - rare event probabilities KW - adaptive model hierarchies KW - high-dimensional problems KW - Markov chain Monte Carlo KW - shaking transformations AV - public SN - 2166-2525 TI - Adaptive Multilevel Subset Simulation with Selective Refinement EP - 963 IS - 3 SP - 932 VL - 12 JF - SIAM/ASA Journal on Uncertainty Quantification A1 - Elfverson, D A1 - Scheichl, R A1 - Weissmann, S A1 - Diaz De La O, FA PB - Society for Industrial and Applied Mathematics Publications Y1 - 2024/09// UR - https://doi.org/10.1137/22M1515240 ID - discovery10194909 N2 - In this work we propose an adaptive multilevel version of subset simulation to estimate the probability of rare events for complex physical systems. Given a sequence of nested failure domains of increasing size, the rare event probability is expressed as a product of conditional probabilities. The proposed new estimator uses different model resolutions and varying numbers of samples across the hierarchy of nested failure sets. In order to dramatically reduce the computational cost, we construct the intermediate failure sets such that only a small number of expensive high-resolution model evaluations are needed, whilst the majority of samples can be taken from inexpensive low-resolution simulations. A key idea in our new estimator is the use of a posteriori error estimators combined with a selective mesh refinement strategy to guarantee the critical subset property that may be violated when changing model resolution from one failure set to the next. The efficiency gains and the statistical properties of the estimator are investigated both theoretically via shaking transformations, as well as numerically. On a model problem from subsurface flow, the new multilevel estimator achieves gains of more than a factor 60 over standard subset simulation for a practically relevant relative error of 25%. ER -