A multi-stage deep learning based algorithm for multiscale modelreduction

TL;DR

This paper introduces a multi-stage deep learning approach for multiscale model reduction, improving training efficiency and accuracy by incorporating various reduced models and mathematical decoupling techniques.

Contribution

It presents a novel multi-stage training strategy that leverages mathematical multiscale reductions to enhance deep learning-based model reduction.

Findings

Mathematical multiscale reductions outperform other methods.

Multi-stage training improves model accuracy.

Method verified on nonlinear and steady-state problems.

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