{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/langevin-bi-fidelity-importance-sampling-for","title":"Langevin Bi-fidelity Importance Sampling for Failure Probability Estimation","arxiv_id":"2503.17796","date":"2025-03-22","proceeding":null,"authors":["Nuojin Cheng","Alireza Doostan"],"abstract":"Estimating failure probability is a key task in the field of uncertainty quantification. In this domain, importance sampling has proven to be an effective estimation strategy; however, its efficiency heavily depends on the choice of the biasing distribution. An improperly selected biasing distribution can significantly increase estimation error. One approach to address this challenge is to leverage a less expensive, lower-fidelity surrogate. Building on the accessibility to such a model and its derivative on the random uncertain inputs, we introduce an importance sampling-based estimator, termed the Langevin bi-fidelity importance sampling (L-BF-IS), which uses score-function-based sampling algorithms to generate new samples and substantially reduces the mean square error (MSE) of failure probability estimation. The proposed method demonstrates lower estimation error, especially in high-dimensional input spaces and when limited high-fidelity evaluations are available. The L-BF-IS estimator's effectiveness is validated through experiments with two synthetic functions and two real-world applications governed by partial differential equations. These real-world applications involve a composite beam, which is represented using a simplified Euler-Bernoulli equation as a low-fidelity surrogate, and a steady-state stochastic heat equation, for which a pre-trained neural operator serves as the low-fidelity surrogate.","url_abs":"https://arxiv.org/abs/2503.17796v2","url_pdf":"https://arxiv.org/pdf/2503.17796v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"langevin-bi-fidelity-importance-sampling-for","repo_url":"https://github.com/cu-uq/l-bf-is","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}