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