论文标题
多阶段的多阶段深度学习算法
A multi-stage deep learning based algorithm for multiscale modelreduction
论文作者
论文摘要
在这项工作中，我们提出了一种多阶段培训策略，以开发用于多尺度功能问题的深度学习算法。亲规范策略的每个阶段都具有（几乎）相同的网络结构，并预测了多尺度问题的相同降低订单模型。上一个阶段的输出将与当前阶段的中间层结合使用。我们从数值上表明，使用不同的减少订单模型作为每个阶段的输入可以改善培训，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减少和网络方法；但是我们发现，数学方法是分解信息并给出最佳结果的系统性方法。我们终于在依赖时间的非线性问题和稳态模型上验证了我们的培训方法
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
