Optimal experimental design (OED) is a principled framework for maximizing information gained from limited data in inverse problems. Unfortunately, conventional methods for OED are prohibitive when applied to expensive models with high-dimensional parameters, as we target here. We develop a fast and scalable computational framework for goal-oriented OED of large-scale Bayesian linear inverse problems that finds sensor locations to maximize the expected information gain (EIG) for a predicted quantity of interest. By employing low-rank approximations of appropriate operators, an online-offline decomposition, and a new swapping greedy algorithm, we are able to maximize EIG at a cost measured in model solutions that is independent of the problem dimensions. We demonstrate the efficiency, accuracy, and both data- and parameter-dimension independence of the proposed algorithm for a contaminant transport inverse problem with infinite-dimensional parameter field.

翻译：最佳实验设计(OED)是最大限度地利用从反面问题有限数据中获得的信息的一个原则框架。 不幸的是,我们在这里瞄准的是高维参数的昂贵模型,而常规的OED方法在应用到高维参数的昂贵模型时却令人望而却步。我们为面向目标的大规模巴伊西亚线性反向问题开发了一个快速和可缩放的计算框架,以找到传感器位置,使预期获得的信息最大化(EIG ), 以达到一定的预期利益。通过使用适当操作员的低级别近似值、在线离线分解和新的贪婪算法,我们能够以独立于问题维度的模型解决方案所衡量的成本最大限度地使用EIG。我们展示了与无限参数字段相反的污染物转移问题的拟议算法的效率、准确性以及数据和参数分解独立性。