BCR-Net: A neural network based on the nonstandard wavelet form

JOURNAL OF COMPUTATIONAL PHYSICS

卷:384

Article

Fan, Yuwei¹  Bohorquez, Cindy Orozco²  Ying, Lexing^1,2,3 

[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[2] Stanford Univ, Inst Computat & Math Engn, Stanford, CA 94305 USA

[3] Facebook AI Res, Menlo Pk, CA 94025 USA

关键词: Wavelet transform;    Nonstandard form;    Artificial neural network;    Convolutional network;    Locally connected network;   

DOI  :  10.1016/j.jcp.2019.02.002

来源: Elsevier

【 摘 要 】

This paper proposes a novel neural network architecture inspired by the nonstandard form proposed by Beylkin et al. (1991) [7]. The nonstandard form is a highly effective wavelet-based compression scheme for linear integral operators. In this work, we first represent the matrix-vector product algorithm of the nonstandard form as a linear neural network where every scale of the multiresolution computation is carried out by a locally connected linear sub-network. In order to address nonlinear problems, we propose an extension, called BCR-Net, by replacing each linear sub-network with a deeper and more powerful nonlinear one. Numerical results demonstrate the efficiency of the new architecture by approximating nonlinear maps that arise in homogenization theory and stochastic computation. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free