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A sequential sensor selection strategy for hyper-parameterized linear Bayesian inverse problems
arXiv - CS - Numerical Analysis Pub Date : 2020-11-23 , DOI: arxiv-2011.11391
Nicole Aretz-Nellesen, Peng Chen, Martin A. Grepl, Karen Veroy

We consider optimal sensor placement for hyper-parameterized linear Bayesian inverse problems, where the hyper-parameter characterizes nonlinear flexibilities in the forward model, and is considered for a range of possible values. This model variability needs to be taken into account for the experimental design to guarantee that the Bayesian inverse solution is uniformly informative. In this work we link the numerical stability of the maximum a posterior point and A-optimal experimental design to an observability coefficient that directly describes the influence of the chosen sensors. We propose an algorithm that iteratively chooses the sensor locations to improve this coefficient and thereby decrease the eigenvalues of the posterior covariance matrix. This algorithm exploits the structure of the solution manifold in the hyper-parameter domain via a reduced basis surrogate solution for computational efficiency. We illustrate our results with a steady-state thermal conduction problem.

中文翻译:

超参数线性贝叶斯逆问题的顺序传感器选择策略

我们考虑针对超参数化线性贝叶斯逆问题的最佳传感器位置,其中超参数表征前向模型中的非线性柔性,并考虑了一系列可能的值。实验设计需要考虑该模型的可变性,以确保贝叶斯逆解具有统一的信息量。在这项工作中,我们将最大后验点的数值稳定性和A最优实验设计与可观察性系数联系起来,该系数直接描述了所选传感器的影响。我们提出了一种算法,该算法迭代地选择传感器位置以提高该系数,从而减小后协方差矩阵的特征值。该算法通过简化的基础替代解决方案在超参数域中利用了解决方案流形的结构,从而提高了计算效率。我们用稳态导热问题来说明我们的结果。
更新日期:2020-11-25
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