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.

本文提出了使用经验插值法（EIM）算法在监督机器学习中高效降低训练数据维度的方法（称为DNN-EIM），并对数据科学和参数化（和时变）偏微分方程（PDE）的应用进行了考虑。在分类情况下，为每个类训练并行的DNN，这种方法是顺序的，即可以添加新类而无需重新训练网络。在PDE情况下，为每个EIM点设计一个DNN。在所有情况下，平行网络需要少于十倍的训练权重，观察到在不牺牲准确性的情况下，训练时间的显着提高。

关于使用经验插值方法对深度神经网络进行降维的说明