基于ELM算法的Chebyshev神经网络在常微分方程数值解中的应用  

Application of Chebyshev Neural Network Based on ELM Algorithm to Numerical Solutions of Ordinary Differential Equations

作　　者：张继超 ZHANG Ji-chao(Yangzhou University,Yangzhou 225009,Jiangsu)

机构地区：[1]扬州大学数学科学学院,江苏扬州225009

出　　处：《电脑与电信》2022年第6期58-61,共4页Computer & Telecommunication

基　　金：2021年扬州大学大学生科创基金项目“基于神经网络算法求解微分方程”,项目编号:X20210230;江苏高校品牌专业建设工程资助项目(数学与应用数学),项目编号:PPZY2015B109。

摘　　要：提出了一种快速的、新颖的、高精度的用于求解常微分方程数值解的方法:考虑了极限学习机(ELM)算法对参数调整的简便性和适合单层网络的特点,结合Chebyshev多项式的正交特性带来的少参数而高逼近的作用。该联合算法只需要少量的神经元和单层的神经网络,再通过最小二乘法,解出矩阵广义逆进行参数调整便可获得具有较高精度且无穷可微的常微分方程数值解。This paper presents a fast, novel and high-precision method for solving ordinary differential equations. The ELM algorithm is easy to adjust parameters and suitable for single-layer networks, combined with the orthogonal characteristics of Chebyshev polynomials. This joint algorithm only requires a few neurons and a single layer of neural network, and then, by means of the least square method, the generalized inverse of the matrix is solved and the parameters are adjusted to obtain the numerical solutions of ordinary differential equations with high precision and infinite differentiability.

关 键 词：常微分方程 数值解 CHEBYSHEV 神经网络 极限学习机 深层优化 

分 类 号：O241.81[理学—计算数学]