Optimal experimental design (OED) plays an important role in the problem of identifying uncertainty with limited experimental data. In many applications, we seek to minimize the uncertainty of a predicted quantity of interest (QoI) based on the solution of the inverse problem, rather than the inversion model parameter itself. In these scenarios, we develop an efficient method for goal-oriented optimal experimental design (GOOED) for large-scale Bayesian linear inverse problem that finds sensor locations to maximize the expected information gain (EIG) for a predicted QoI. By deriving a new formula to compute the EIG, exploiting low-rank structures of two appropriate operators, we are able to employ an online-offline decomposition scheme and a swapping greedy algorithm to maximize the EIG at a cost measured in model solutions that is independent of the problem dimensions. We provide detailed error analysis of the approximated EIG, and 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)在用有限的实验数据识别不确定性问题上起着重要作用。在许多应用中,我们力求根据倒数问题的解决办法,而不是倒数模型参数本身,尽量减少预期利息数量的不确定性。在这些假设中,我们为大规模巴伊西亚线性反向问题制定了一种有效的方法,以目标为导向的最佳实验设计(GOOED),找到传感器位置,使预测的QoI的预期信息收益最大化(EIG)。通过产生一种新的公式来计算EIG,利用两个合适的操作员的低级结构,我们能够采用在线离线拆解方案和贪婪的算法,以独立于问题维度的模型解决办法所衡量的成本使EIG最大化。我们提供了近似于EIG的模型详细错误分析,并展示了无穷度参数参数字段的污染物反向传输的拟议算法的效率、准确性以及数据和参数分解独立性。