Sensitivity Analysis of the Information Gain in Infinite-Dimensional Bayesian Linear Inverse Problems
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909204759969792 |
|---|---|
| author | Chowdhary, Abhijit Tong, Shanyin Stadler, Georg Alexanderian, Alen |
| author_facet | Chowdhary, Abhijit Tong, Shanyin Stadler, Georg Alexanderian, Alen |
| contents | We study the sensitivity of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs) with respect to modeling uncertainties. In particular, we consider derivative-based sensitivity analysis of the information gain, as measured by the Kullback-Leibler divergence from the posterior to the prior distribution. To facilitate this, we develop a fast and accurate method for computing derivatives of the information gain with respect to auxiliary model parameters. Our approach combines low-rank approximations, adjoint-based eigenvalue sensitivity analysis, and post-optimal sensitivity analysis. The proposed approach also paves way for global sensitivity analysis by computing derivative-based global sensitivity measures. We illustrate different aspects of the proposed approach using an inverse problem governed by a scalar linear elliptic PDE, and an inverse problem governed by the three-dimensional equations of linear elasticity, which is motivated by the inversion of the fault-slip field after an earthquake. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_16906 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sensitivity Analysis of the Information Gain in Infinite-Dimensional Bayesian Linear Inverse Problems Chowdhary, Abhijit Tong, Shanyin Stadler, Georg Alexanderian, Alen Numerical Analysis 65C60, 90C31, 62F15, 35R30, 65F55 We study the sensitivity of infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs) with respect to modeling uncertainties. In particular, we consider derivative-based sensitivity analysis of the information gain, as measured by the Kullback-Leibler divergence from the posterior to the prior distribution. To facilitate this, we develop a fast and accurate method for computing derivatives of the information gain with respect to auxiliary model parameters. Our approach combines low-rank approximations, adjoint-based eigenvalue sensitivity analysis, and post-optimal sensitivity analysis. The proposed approach also paves way for global sensitivity analysis by computing derivative-based global sensitivity measures. We illustrate different aspects of the proposed approach using an inverse problem governed by a scalar linear elliptic PDE, and an inverse problem governed by the three-dimensional equations of linear elasticity, which is motivated by the inversion of the fault-slip field after an earthquake. |
| title | Sensitivity Analysis of the Information Gain in Infinite-Dimensional Bayesian Linear Inverse Problems |
| topic | Numerical Analysis 65C60, 90C31, 62F15, 35R30, 65F55 |
| url | https://arxiv.org/abs/2310.16906 |