In this work, we propose a multi-stage training strategy for the development of deep learning algorithms applied to problems with multiscale features. Each stage of the pro-posed strategy shares an (almost) identical network structure and predicts the same reduced order model of the multiscale problem. The output of the previous stage will be combined with an intermediate layer for the current stage. We numerically show that using different reduced order models as inputs of each stage can improve the training and we propose several ways of adding different information into the systems. These methods include mathematical multiscale model reductions and network approaches; but we found that the mathematical approach is a systematical way of decoupling information and gives the best result. We finally verified our training methodology on a time dependent nonlinear problem and a steady state model

中文翻译：

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一种基于多阶段深度学习的多尺度模型缩减算法

在这项工作中，我们提出了一种多阶段训练策略，用于开发适用于多尺度特征问题的深度学习算法。所提出策略的每个阶段都共享一个（几乎）相同的网络结构，并预测多尺度问题的相同降阶模型。前一阶段的输出将与当前阶段的中间层结合。我们在数值上表明使用不同的降阶模型作为每个阶段的输入可以改善训练，并且我们提出了几种将不同信息添加到系统中的方法。这些方法包括数学多尺度模型缩减和网络方法；但我们发现数学方法是一种系统的解耦信息的方法，并给出了最好的结果。