A multi-stage deep learning based algorithm for multiscale model reduction

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 proposed shares an (almost) identical network structure and predicts same reduced order model problem. The output previous will be combined intermediate layer current stage. We numerically show that using different models as inputs each can improve several ways adding information into systems. These methods include mathematical reductions approaches; but found approach is systematical way decoupling gives best result. finally verified our methodology on time dependent nonlinear problem steady state model.