论文标题
超量参数性线性贝叶斯逆问题的顺序传感器选择策略
A sequential sensor selection strategy for hyper-parameterized linear Bayesian inverse problems
论文作者
论文摘要
我们考虑过最佳的传感器位置，用于超参数线性贝叶斯逆问题，其中超参数表征了正向模型中的非线性灵活性，并考虑了一系列可能的值。需要考虑实验设计的模型变异性，以确保贝叶斯逆溶液均匀提供信息。在这项工作中，我们将最大后点和A-最佳实验设计的数值稳定性与直接描述所选传感器的影响的可观察性系数联系起来。我们提出了一种算法，即迭代地选择传感器位置以提高该系数，从而减少后协方差矩阵的特征值。该算法通过降低的基础替代解决方案来利用溶液歧管在计算效率中的结构。我们通过稳态的热传导问题说明了结果。
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.
