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基于多层前馈神经网络的扩散系数求解

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如何利用浓度分布的测量数据(间接采样)来确定扩散系数,并建立有效快速的数值求解方法是目前亟待解决的问题.由于扩散系数的求解属于反问题中的参数识别问题,通常具有不适定、非线性和计算量大等特点,所以在仅考虑给定温度下扩散对物质输运的影响的情况下,研究扩散系数与浓度、浓度梯度的关系,并利用物质扩散浓度的动态采样值和多层前馈神经网络对扩散系数进行求解,数值实验表明该方法十分有效.
Solution of Diffusion Coefficient Based on Multilayer Feed-forward Neural Network
The utilization of concentration distribution measurement data(indirect sampling)to determine the diffusion coefficient and develop an efficient numerical method is an urgent problem in contemporary research.Identifying the diffusion coefficient is inherently an inverse parameter identification problem,typically characterized by ill-posedness,nonlinearity,and high computational complexity.This study investigates the relationship between the diffusion coefficient,concentration,and concentration gradient,while considering the effects of diffusion on material transport at a specified temperature.The diffusion coefficient is computed numerically using dynamic sampling values of material diffusion concentration alongside a multilayer feed-forward neural network.Finally,numerical experiments demonstrate the effectiveness of our proposed method.

diffusion coefficientdynamic samplingmultilayer feed-forward neural networkdiffusion equation

刘金凤、李松华

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湖南理工学院 数学学院,湖南 岳阳 414006

扩散系数 动态采样 多层前馈神经网络 扩散方程

湖南省自然科学基金项目湖南省教育厅重点项目

2020JJ433019A196

2024

湖南理工学院学报(自然科学版)
湖南理工学院

湖南理工学院学报(自然科学版)

影响因子:0.259
ISSN:1672-5298
年,卷(期):2024.37(3)