Abstract
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 postoptimal sensitivity analysis. The proposed approach also paves the 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.
Original language | English (US) |
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Pages (from-to) | 17-35 |
Number of pages | 19 |
Journal | International Journal for Uncertainty Quantification |
Volume | 14 |
Issue number | 6 |
DOIs | |
State | Published - 2024 |
Keywords
- Bayesian inverse problems
- Kullback-Leibler divergence
- adjoint-based gradient computation
- numerical PDE
- uncertainty quantification
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Discrete Mathematics and Combinatorics
- Control and Optimization