重庆工商大学学报（自然科学版）2024，Vol.41Issue(1)：106-112,7.DOI:10.16055/j.issn.1672-058X.2024.0001.014
比例延迟微分方程的极限学习机算法
Extreme Learning Machine Algorithm for Pantograph Delay Differential Equations
李佳颖 1陈浩1
作者信息
- 1. 重庆师范大学 数学科学学院,重庆 401331
- 折叠
摘要
Abstract
Objective A single hidden layer feed-forward neural network training method based on extreme learning machine(ELM)was proposed for pantograph delay differential equations,and the method was extended to deal with the system of pantograph equations with two delays.Methods Firstly,a feed-forward neural network with a single hidden layer was constructed and the input weights and hidden layer bias were randomly generated.Then,by calculating the coefficient matrix to satisfy the pantograph delay differential equation and its initial value conditions,the equation was transformed into a least squares problem,and the output weight was obtained by using the Moor-Penrose generalized inverse solution.Finally,the numerical solution of the pantograph delay differential equation with high precision could be obtained by inputting the output weights into the constructed neural network.Results By comparing the results of numerical experiments with those of existing methods,the effectiveness of the proposed method in dealing with pantograph delay differential equations and the system of pantograph equations with two delays was verified.With the increase in the number of selected training points and hidden layer nodes,the accuracy and convergence rate of the numerical solutions were also increased.Conclusion The ELM algorithm is effective in dealing with pantograph delay differential equations and the system of pantograph equations with two delays.关键词
前馈神经网络/比例延迟微分方程/极限学习机/双比例延迟微分系统Key words
feed-forward neural networks/pantograph delay differential equation/extreme learning machine/pantograph equation with two delays分类
数理科学引用本文复制引用
李佳颖,陈浩..比例延迟微分方程的极限学习机算法[J].重庆工商大学学报（自然科学版）,2024,41(1):106-112,7.
