A deep learning based nonlinear upscaling method for transport equations

Electronic Transactions on Numerical Analysis

article

Tak Shing Au Yeung¹  Eric T. Chung¹  Simon See² 

[1] Department of Mathematics,The Chinese University of Hong Kong;NVIDIA – NVAITC

关键词: nonlinear upscaling;    transport equations;    deep learning;   

DOI  :  10.1553/etna_vol56s187

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 摘 要 】

We will develop a nonlinear upscaling method for nonlinear transport equations. The proposed scheme gives a coarse scale equation for the cell average of the solution. In order to compute the parameters in the coarse scale equation, a local downscaling operator is constructed. This downscaling operation recovers fine scale properties using cell averages. This is achieved by solving the equation on an oversampling region with the given cell average as constraint. Due to the nonlinearity, one needs to compute these downscaling operations on the fly and cannot pre-compute these quantities. In order to give an efficient downscaling operation, we apply a deep learning approach. We will use a deep neural network to approximate the downscaling operation. Our numerical results show that the proposed scheme can achieve good accuracy and efficiency.

【 授权许可】

Unknown