  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
