Hyper-differential sensitivity analysis with respect to model discrepancy: Prior distributions
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908580036214784 |
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| author | Hart, Joseph Waanders, Bart van Bloemen Li, Jixian Ouermi, Timbwaoga A. J. Johnson, Chris R. |
| author_facet | Hart, Joseph Waanders, Bart van Bloemen Li, Jixian Ouermi, Timbwaoga A. J. Johnson, Chris R. |
| contents | Hyper-differential sensitivity analysis with respect to model discrepancy was recently developed to enable uncertainty quantification for optimization problems. The approach consists of two primary steps: (i) Bayesian calibration of the discrepancy between high- and low-fidelity models, and (ii) propagating the model discrepancy uncertainty through the optimization problem. When high-fidelity model evaluations are limited, as is common in practice, the prior discrepancy distribution plays a crucial role in the uncertainty analysis. However, specification of this prior is challenging due to its mathematical complexity and many hyper-parameters. This article presents a novel approach to specify the prior distribution. Our approach consists of two parts: (1) an algorithmic initialization of the prior hyper-parameters that uses existing data to initialize a hyper-parameter estimate, and (2) a visualization framework to systematically explore properties of the prior and guide tuning of the hyper-parameters to ensure that the prior captures the appropriate range of uncertainty. We provide detailed mathematical analysis and a collection of numerical examples that elucidate properties of the prior that are crucial to ensure uncertainty quantification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19812 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyper-differential sensitivity analysis with respect to model discrepancy: Prior distributions Hart, Joseph Waanders, Bart van Bloemen Li, Jixian Ouermi, Timbwaoga A. J. Johnson, Chris R. Numerical Analysis Hyper-differential sensitivity analysis with respect to model discrepancy was recently developed to enable uncertainty quantification for optimization problems. The approach consists of two primary steps: (i) Bayesian calibration of the discrepancy between high- and low-fidelity models, and (ii) propagating the model discrepancy uncertainty through the optimization problem. When high-fidelity model evaluations are limited, as is common in practice, the prior discrepancy distribution plays a crucial role in the uncertainty analysis. However, specification of this prior is challenging due to its mathematical complexity and many hyper-parameters. This article presents a novel approach to specify the prior distribution. Our approach consists of two parts: (1) an algorithmic initialization of the prior hyper-parameters that uses existing data to initialize a hyper-parameter estimate, and (2) a visualization framework to systematically explore properties of the prior and guide tuning of the hyper-parameters to ensure that the prior captures the appropriate range of uncertainty. We provide detailed mathematical analysis and a collection of numerical examples that elucidate properties of the prior that are crucial to ensure uncertainty quantification. |
| title | Hyper-differential sensitivity analysis with respect to model discrepancy: Prior distributions |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2504.19812 |