Empirical interpolation method (EIM) is a well-known technique to efficiently approximate parameterized functions. This paper proposes to use EIM algorithm to efficiently reduce the dimension of the training data within supervised machine learning. This is termed as DNN-EIM. Applications in data science (e.g., MNIST) and parameterized (and time-dependent) partial differential equations (PDEs) are considered. The proposed DNNs in case of classification are trained in parallel for each class. This approach is sequential, i.e., new classes can be added without having to retrain the network. In case of PDEs, a DNN is designed corresponding to each EIM point. Again, these networks can be trained in parallel, for each EIM point. In all cases, the parallel networks require fewer than ten times the number of training weights. Significant gains are observed in terms of training times, without sacrificing accuracy.

翻译：经验插值方法（EIM）是一种高效逼近参数化函数的经典技术。本文提出利用EIM算法对监督机器学习中的训练数据进行有效降维，称为DNN-EIM。研究考虑了数据科学（如MNIST）及参数化（含时间相关）偏微分方程（PDE）的应用场景。所提出的分类任务中，DNN按类别进行并行训练，该策略具有序列性，即新增类别无需重新训练网络。针对PDE问题，每个EIM点对应设计一个DNN，这些网络同样可按EIM点并行训练。所有案例中，并行网络的训练参数数量均不足基准方法的十分之一。在保证精度的前提下，训练效率获得显著提升。