The efficacy of mathematical models heavily depends on the quality of the training data, yet collecting sufficient data is often expensive and challenging. Many modeling applications require inferring parameters only as a means to predict other quantities of interest (QoI). Because models often contain many unidentifiable (sloppy) parameters, QoIs often depend on a relatively small number of parameter combinations. Therefore, we introduce an information-matching criterion based on the Fisher Information Matrix to select the most informative training data from a candidate pool. This method ensures that the selected data contain sufficient information to learn only those parameters that are needed to constrain downstream QoIs. It is formulated as a convex optimization problem, making it scalable to large models and datasets. We demonstrate the effectiveness of this approach across various modeling problems in diverse scientific fields, including power systems and underwater acoustics. Finally, we use information-matching as a query function within an Active Learning loop for material science applications. In all these applications, we find that a relatively small set of optimal training data can provide the necessary information for achieving precise predictions. These results are encouraging for diverse future applications, particularly active learning in large machine learning models.

本研究解决了数据收集困难且昂贵的问题，提出了一种基于费舍尔信息矩阵的信息匹配标准，以从候选数据池中选择最具信息性的训练数据。研究发现，使用这一方法可以在多个科学领域中，通过相对较小的最优训练数据集，实现精确的预测，为未来在大型机器学习模型中的主动学习应用提供了重要的参考。 

信息匹配方法在最优实验设计和主动学习中的应用