We present a review of methods for optimal experimental design (OED) for Bayesian inverse problems governed by partial differential equations with infinite-dimensional parameters. The focus is on problems where one seeks to optimize the placement of measurement points, at which data are collected, such that the uncertainty in the estimated parameters is minimized. We present the mathematical foundations of OED in this context and survey the computational methods for the class of OED problems under study. We also outline some directions for future research in this area.

中文翻译：

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偏微分方程支配的无穷维贝叶斯逆问题的最优实验设计：综述

我们对由具有无限维参数的偏微分方程控制的贝叶斯逆问题的最佳实验设计（OED）方法进行了综述。重点是那些试图优化测量点位置的问题，在这些位置上收集数据，以使估计参数的不确定性最小化。我们介绍了这种情况下OED的数学基础，并调查了所研究的OED类问题的计算方法。我们还概述了该领域未来研究的一些方向。