Langevin Bi-fidelity Importance Sampling for Failure Probability Estimation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915219116130304 |
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| author | Cheng, Nuojin Doostan, Alireza |
| author_facet | Cheng, Nuojin Doostan, Alireza |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17796 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Langevin Bi-fidelity Importance Sampling for Failure Probability Estimation Cheng, Nuojin Doostan, Alireza Computation 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. |
| title | Langevin Bi-fidelity Importance Sampling for Failure Probability Estimation |
| topic | Computation |
| url | https://arxiv.org/abs/2503.17796 |