In this work we introduce a new multiscale artificial neural network based on
the structure of $H$-matrices. This network generalizes the latter to
the nonlinear case by introducing a local deep neural network at each spatial
scale. Numerical results indicate that the network is able to efficiently
approximate discrete nonlinear maps obtained from discretized nonlinear partial
differential equations, such as those arising from nonlinear Schrödinger
equations and the Kohn-Sham density functional theory.
%0 Generic
%1 fan2018multiscale
%A Fan, Yuwei
%A Lin, Lin
%A Ying, Lexing
%A Zepeda-Nunez, Leonardo
%D 2018
%K multiresolution spatial todo:read
%T A multiscale neural network based on hierarchical matrices
%U http://arxiv.org/abs/1807.01883
%X In this work we introduce a new multiscale artificial neural network based on
the structure of $H$-matrices. This network generalizes the latter to
the nonlinear case by introducing a local deep neural network at each spatial
scale. Numerical results indicate that the network is able to efficiently
approximate discrete nonlinear maps obtained from discretized nonlinear partial
differential equations, such as those arising from nonlinear Schrödinger
equations and the Kohn-Sham density functional theory.
@misc{fan2018multiscale,
abstract = {In this work we introduce a new multiscale artificial neural network based on
the structure of $\mathcal{H}$-matrices. This network generalizes the latter to
the nonlinear case by introducing a local deep neural network at each spatial
scale. Numerical results indicate that the network is able to efficiently
approximate discrete nonlinear maps obtained from discretized nonlinear partial
differential equations, such as those arising from nonlinear Schr\"odinger
equations and the Kohn-Sham density functional theory.},
added-at = {2022-06-20T11:16:07.000+0200},
author = {Fan, Yuwei and Lin, Lin and Ying, Lexing and Zepeda-Nunez, Leonardo},
biburl = {https://www.bibsonomy.org/bibtex/2b4ae3d0b04527716d6865e830b0c22db/annakrause},
description = {1807.01883.pdf},
interhash = {ffd9940f9cccd6bd2c6c571a77f39d62},
intrahash = {b4ae3d0b04527716d6865e830b0c22db},
keywords = {multiresolution spatial todo:read},
note = {cite arxiv:1807.01883Comment: 26 pages, 11 figures},
timestamp = {2022-06-20T11:16:07.000+0200},
title = {A multiscale neural network based on hierarchical matrices},
url = {http://arxiv.org/abs/1807.01883},
year = 2018
}