摘要
本文讨论了一种单隐层神经网络算法在数值常微分方程求解中的应用.设定具有神经网络结构的近似解满足常微分方程的初边值条件,将原方程中关于神经网络权重的离散优化问题转化为近似解中神经网络的训练问题,使得近似解逼近真实解.通过网络推演观察到神经网络结构、权值、阈值的变化情况.基于python语言求解的数值算例证明了该算法的有效性.
This paper discusses a single hidden layer neural network algorithm in the application of numerical differential equation in this paper.Supposed that the approximate solution with neural network structure is set to satisfy the initial boundary value condition of ordinary differential equation and the discrete optimization problem about the weight of neural network in the original equation is transformed into the training problem of neural network in the approximate solution,so that the approximate solution approaches the real solution.The change of the weight threshold of neural network structure is observed through network deduction.Numerical examples based on python language show the effectiveness of the algorithm.
作者
杨震
陈豫眉
李霜
YANG Zhen;CHEN Yumei;LI Shuang(School of Mathematics and Information, China West Normal University,Nanchong, Sichuan 637009;School of Mathematics Education, China West Normal University,Nanchong, Sichuan 637009;Institute of Computing Method and Application Software, China West Normal University, Nanchong, Sichuan 637009)
出处
《绵阳师范学院学报》
2020年第5期78-84,共7页
Journal of Mianyang Teachers＇ College
基金
国家自然科学基金面上项目(11971094)
四川省科技厅项目(2017JY0186)
四川省教育厅科研项目重点项目(15ZA0149)
西华师范大学英才基金项目(17YC371).
关键词
神经网络
常微分方程
初值问题
PYTHON语言
neural network
ordinary differential equations
initial value problems
python language
