三阶常微分方程的神经网络模型分析
Comparison of Several Neural Network Methods for a Class of Third Order Ordinary Differential Equations
DOI: 10.12677/AAM.2022.114204, PDF,    科研立项经费支持
作者: 伍 阳, 杨云磊*：贵州大学，贵州 贵阳
关键词: ODE；神经网络模型；正交多项式；ODE； Neural Network Model； Orthogonal Polynomial
摘要: 本文研究神经网络模型对一类三阶常微分方程数值解的影响。首先，分析网络结构在神经网络模型求解常微分方程中的重要性，接着，探究单隐层前馈神经网络的网络隐层激活函数，选择几类正交多项式来消除隐层，构造不同类型的神经网络模型，利用极限习机(ELM)算法求解网络权值，最后利用数值实验模拟展示不同的神经网络模型形成的影响。
Abstract: In this paper, the influence of neural network model on the numerical solution of a class of third-order ordinary differential equations is studied. First, the importance of network structure in solving ordinary differential equations by neural network model is analyzed. Then, the network hidden layer activation function of single hidden layer feed forward neural network is explored. Several orthogonal polynomials are selected to eliminate hiding, and different types of neural network models are constructed. The limit learning machine (ELM) algorithm is used to solve the network weights. Finally, numerical experiments are used to simulate the influence of different neural network models.
文章引用：伍阳, 杨云磊. 三阶常微分方程的神经网络模型分析[J]. 应用数学进展, 2022, 11(4): 1870-1875. https://doi.org/10.12677/AAM.2022.114204

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