eprintid: 10194909 rev_number: 12 eprint_status: archive userid: 699 dir: disk0/10/19/49/09 datestamp: 2024-07-23 12:14:54 lastmod: 2024-09-25 09:56:01 status_changed: 2024-07-23 12:14:54 type: article metadata_visibility: show sword_depositor: 699 creators_name: Elfverson, D creators_name: Scheichl, R creators_name: Weissmann, S creators_name: Diaz De La O, FA title: Adaptive Multilevel Subset Simulation with Selective Refinement ispublished: pub divisions: UCL divisions: B04 divisions: C06 divisions: F59 divisions: ZZ4 keywords: rare event probabilities, adaptive model hierarchies, high-dimensional problems, Markov chain Monte Carlo, shaking transformations note: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. abstract: 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%. date: 2024-09 date_type: published publisher: Society for Industrial and Applied Mathematics Publications official_url: https://doi.org/10.1137/22M1515240 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green verified: verified_manual elements_id: 2298611 doi: 10.1137/22M1515240 lyricists_name: Diaz De La O, Francisco lyricists_id: FADIA90 actors_name: Diaz De La O, Francisco actors_id: FADIA90 actors_role: owner full_text_status: public publication: SIAM/ASA Journal on Uncertainty Quantification volume: 12 number: 3 pagerange: 932-963 issn: 2166-2525 citation: Elfverson, D; Scheichl, R; Weissmann, S; Diaz De La O, FA; (2024) Adaptive Multilevel Subset Simulation with Selective Refinement. SIAM/ASA Journal on Uncertainty Quantification , 12 (3) pp. 932-963. 10.1137/22M1515240 <https://doi.org/10.1137/22M1515240>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10194909/1/Diaz%20De%20La%20O_22m1515240.pdf