分数多变气体球的人工神经网络模拟
Modeling Fractional Polytropic Gas Spheres Using Artificial Neural Network
摘要：
Lane-Emden微分方程描述了不同的物理和天体物理现象，包括恒星结构、等温气体球、气体球云热历史和电子流的形式。提出了一种基于神经网络的求解分数阶Lane-Emden微分方程的计算方法。这样的解将有助于解决在物理学、天体物理学、工程学和现实生活中有不同应用的分数多方气体球问题。我们使用人工神经网络（ANN）的框架，在其前馈反向传播学习计划。通过对4个分数阶Lane-Emden方程的计算，验证了算法的有效性和准确性，并与多面体指数n= 0，1，5的精确解和多变指数n=3的级数展开式的精确解进行了比较.结果表明，人工神经网络方法是可行的，准确的，并可能优于其他方法。
英文摘要：
Lane-Emden differential equations describe different physical and astrophysical phenomena that include forms of stellar structure, isothermal gas spheres, gas spherical cloud thermal history, and thermionic currents. This paper presents a computational approach to solve the problems related to fractional Lane-Emden differential equations based on neural networks. Such a solution will help solve the fractional polytropic gas spheres problems which have different applications in physics, astrophysics, engineering, and several real-life issues. We used Artificial Neural Network (ANN) framework in its feedforward back propagation learning scheme. The efficiency and accuracy of the presented algorithm are checked by testing it on four fractional Lane-Emden equations and compared with the exact solutions for the polytopic indices n=0,1,5 and those of the series expansions for the polytropic index n=3. The results we obtained prove that using the ANN method is feasible, accurate, and may outperform other methods.
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。
