A multi-stage deep learning based algorithm for multiscale modelreduction
arXiv:2009.11341
Abstract
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
References in corpus (8)
- Very Deep Convolutional Networks for Large-Scale Image Recognition
- Generalized Multiscale Finite Element Methods (GMsFEM)
- Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods
- Constraint Energy Minimizing Generalized Multiscale Finite Element Method
- Constraint-Aware Neural Networks for Riemann Problems
- Generalized Multiscale Finite Element Method. Symmetric Interior Penalty Coupling
- Learning macroscopic parameters in nonlinear multiscale simulations using nonlocal multicontinua upscaling techniques
- Learning Algorithms for Coarsening Uncertainty Space and Applications to Multiscale Simulations