Abhijit Chowdhary, Shanyin Tong, Georg Stadler, Alen Alexanderian
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引用次数: 0
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 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.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.