Universal approximation property of a continuous neural network based on a nonlinear diffusion equation

IF 2.3 Q1 MATHEMATICS
Hirotada Honda
{"title":"Universal approximation property of a continuous neural network based on a nonlinear diffusion equation","authors":"Hirotada Honda","doi":"10.1186/s13662-023-03787-z","DOIUrl":null,"url":null,"abstract":"Abstract Recently, differential equation-based neural networks have been actively studied. This paper discusses the universal approximation property of a neural network that is based on a nonlinear partial differential equation (PDE) of the parabolic type. Based on the assumption that the activation function is non-polynomial and Lipschitz continuous, and applying the theory of the difference method, we show that an arbitrary continuous function on any compact set can be approximated using the output of the network with arbitrary precision. Additionally, we present an estimate of the order of accuracy with respect to △ t and △ x .","PeriodicalId":72091,"journal":{"name":"Advances in continuous and discrete models","volume":"22 2","pages":"0"},"PeriodicalIF":2.3000,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in continuous and discrete models","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1186/s13662-023-03787-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

Abstract Recently, differential equation-based neural networks have been actively studied. This paper discusses the universal approximation property of a neural network that is based on a nonlinear partial differential equation (PDE) of the parabolic type. Based on the assumption that the activation function is non-polynomial and Lipschitz continuous, and applying the theory of the difference method, we show that an arbitrary continuous function on any compact set can be approximated using the output of the network with arbitrary precision. Additionally, we present an estimate of the order of accuracy with respect to △ t and △ x .

Abstract Image

基于非线性扩散方程的连续神经网络的普遍逼近性质
近年来,基于微分方程的神经网络得到了积极的研究。本文讨论了一类基于抛物型非线性偏微分方程的神经网络的普遍逼近性质。基于激活函数是非多项式和Lipschitz连续的假设,应用差分法理论,证明了任意紧集上的任意连续函数可以用网络的输出以任意精度逼近。此外,我们提出了关于△t和△x的精度阶数的估计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
2.30
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信