|本期目录/Table of Contents|

[1]张殿焜,靳聪明.基于残差神经网络模型的Fredholm积分方程数值解法[J].浙江理工大学学报,2020,43-44(自科五):706-721.
　ZHANG Diankun,JIN Congming.Numerical method of Fredholm integral equation based on residual neural network model[J].Journal of Zhejiang Sci-Tech University,2020,43-44(自科五):706-721.
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基于残差神经网络模型的Fredholm积分方程数值解法()
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浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第43-44卷
期数:
2020年自科五期
页码:
706-721
栏目:
出版日期:
2020-09-18

文章信息/Info

Title:
Numerical method of Fredholm integral equation based on residual neural network model
文章编号:
1673-3851 (2020) 05-0706-08
作者:
张殿焜; 靳聪明
浙江理工大学理学院，杭州 310018
Author(s):
ZHANG Diankun; JIN Congming
School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China
关键词:
残差神经网络; Fredholm积分方程; 高维积分方程; 最小二乘法
分类号:
O175-5;TP183
文献标志码:
A
摘要:
为了求解Fredholm积分方程，特别是高维Fredholm积分方程，提出了一种采用残差神经网络求解Fredholm积分方程的数值方法。首先在求解区域随机产生训练数据集，通过前向传播残差神经网络得到训练集上的预测值；然后代入Fredholm积分方程得到离散格式，并定义损失函数，将解Fredholm积分方程转化为一个最小二乘问题；最后利用残差神经网络进行优化求解。该方法形式简单，对高维Fredholm积分方程求解问题计算量无显著增加。数值实验表明：该方法能有效求解Fredholm积分方程，且能取得很好的收敛精度；所训练的残差神经网络不会出现网络退化现象，表现出稳定性好、泛化能力强等优点。

参考文献/References:

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相似文献/References:

[1]管钰,丁玖,靳聪明.基于分片线性最大Renyi熵的Fredholm积分方程数值解法[J].浙江理工大学学报,2022,47-48(自科六):950.
　GUAN Yu,DING Jiu,JIN Congming.Numerical solution of Fredholm integral equations via  piecewise linear maximum Rényi entropy method[J].Journal of Zhejiang Sci-Tech University,2022,47-48(自科五):950.

备注/Memo

备注/Memo:
收稿日期：2020-01-10
网络出版日期：2020-05-08
基金项目：国家自然科学基金项目(11571314)
作者简介：张殿焜(1993-)，男，河南平顶山人，硕士研究生，主要从事机器学习方面的研究
通信作者：靳聪明，E-mail：jincm@lsec.cc.ac.cn
更新日期/Last Update: 2020-09-15