Meta-learning pseudo-differential operators with deep neural networks

JOURNAL OF COMPUTATIONAL PHYSICS

卷:408

Article

Feliu-Faba, Jordi¹  Fan, Yuwei²  Ying, Lexing^1,2 

[1] Stanford Univ, ICME, Stanford, CA 94305 USA

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

关键词: Deep neural networks;    Convolutional neural networks;    Nonstandard wavelet form;    Meta-learning;    Green's functions;    Radiative transfer equation;   

DOI  :  10.1016/j.jcp.2020.109309

来源: Elsevier

【 摘 要 】

This paper introduces a meta-learning approach for parameterized pseudo-differential operators with deep neural networks. With the help of the nonstandard wavelet form, the pseudo-differential operators can be approximated in a compressed form with a collection of vectors. The nonlinear map from the parameter to this collection of vectors and the wavelet transform are learned together from a small number of matrix-vector multiplications of the pseudo-differential operator. Numerical results for Green's functions of elliptic partial differential equations and the radiative transfer equations demonstrate the efficiency and accuracy of the proposed approach. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free