利用Legendre小波神经网络求解Lane-Emden方程的机器学习模型
A Machine Learning Model for Solving Lane-Emden Equation using Legendre Wavelet Neural Network
AI总结：
本文提出利用Legendre小波神经网络求解非线性微分方程，特别是二阶Lane-Emden方程，通过引入Legendre小波函数和误差反向传播方法提升求解效果。
摘要：
众所周知，微分方程对电气工程师来说非常有用，可以解决各种问题，例如电容器两端的电压、输入与输出电压等。因此，本文的目标是基于二阶Lane-Emden方程，利用Legendre小波神经网络（LWNN）方法来求解非线性微分方程的解。所有考虑的方程都是奇点初值问题。为管理奇点挑战，我们采用了人工神经网络方法。该方法使用单层神经网络，通过扩大输入使用Legendre小波函数来省略隐藏层。我们还对所提出的问题应用了前馈神经网络方法，并结合误差反向传播原理。Legendre小波神经网络方法的有效性通过Lane-Emden方程得到了验证。
英文摘要：
As we know differential equations are very useful for electrical engineers to solve a variety of problems like: voltage across a capacitor, input versus output voltage, etc. Therefore, the goal of this paper is to find the solutions of non-linear differential equations based on the Lane Emden equation of second order using the Legendre wavelet neural network (LWNN) method. Here all the considered equations are singular initial value problems. To manage the singularity challenge, we have employed an artificial neural network method. This approach utilizes a neural network of a single layer, where the hidden layer is omitted by enlarging the input using Legendre wavelets functions. We have applied a feed-forward neural network method to the proposed problem along with the principle of error backpropagation. The effectiveness of the Legendre wavelet Neural Network method is validated through Lane Emden equations..
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
