基于组合神经网络的时间分数阶扩散方程计算方法

王江; 陈文

doi:10.21656/1000-0887.390288

基于组合神经网络的时间分数阶扩散方程计算方法

doi: 10.21656/1000-0887.390288

王江,
陈文

河海大学力学与材料学院软物质力学研究所, 南京 211100

基金项目: 111引智计划（B12032）；中央高校基本科研业务费（2017B01114）

详细信息

作者简介:
王江（1993—），男，硕士生（E-mail: 1150904137@qq.com）;陈文（1967—2018），男，教授，博士，博士生导师（通讯作者. E-mail: chenwen@hhu.edu.cn).

中图分类号: O232; O172
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- 文章访问数: 1547
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- PDF下载量: 643
- 被引次数: 0
出版历程
- 收稿日期: 2018-11-16
- 修回日期: 2018-11-20
- 刊出日期: 2019-07-01

A Combined Artificial Neural Network Method for Solving Time Fractional Diffusion Equations

Institute of Soft Matter Mechanics, College of Mechanics and Materials, Hohai University, Nanjing 211100, P.R.China

摘要

摘要: 该文首次采用一种组合神经网络的方法，求解了一维时间分数阶扩散方程.组合神经网络是由径向基函数（RBF）神经网络与幂激励前向神经网络相结合所构造出的一种新型网络结构.首先，利用该网络结构构造出符合时间分数阶扩散方程条件的数值求解格式，同时设置误差函数，使原问题转化为求解误差函数极小值问题；然后，结合神经网络模型中的梯度下降学习算法进行循环迭代，从而获得神经网络的最优权值以及各项最优参数，最终得到问题的数值解.数值算例验证了该方法的可行性、有效性和数值精度.该文工作为时间分数阶扩散方程的求解开辟了一条新的途径.
- 一维时间分数阶扩散方程 /
- 组合神经网络 /
- 误差函数 /
- 梯度下降学习算法
Abstract: A combined artificial neural network method was proposed to solve 1D time fractional diffusion equations. The combined artificial neural network is a new network structure constructed through combination of the radial basis function (RBF) neural network and the power series feed-forward neural network. First, the proposed new model was applied to create a numerical solution conforming to the conditions of the time fractional diffusion equation. Meanwhile, an error function was defined and the original differential equation was transformed into a minimization problem. Afterwards, the gradient descent learning algorithm was used to obtain the optimal weights of the neural network and other optimal parameters. Finally, a numerical example was given to illustrate the validity of the proposed method. The work makes a new way to the solution of 1D time fractional diffusion equations.
- 1D time fractional diffusion equation /
- combined artificial neural network /
- error function /
- gradient descent learning algorithm

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参考文献(15)

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基于组合神经网络的时间分数阶扩散方程计算方法

doi: 10.21656/1000-0887.390288

作者简介:
王江（1993—），男，硕士生（E-mail: 1150904137@qq.com）;陈文（1967—2018），男，教授，博士，博士生导师（通讯作者. E-mail: chenwen@hhu.edu.cn).

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A Combined Artificial Neural Network Method for Solving Time Fractional Diffusion Equations

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留言板

基于组合神经网络的时间分数阶扩散方程计算方法

doi: 10.21656/1000-0887.390288

作者简介: 王江（1993—），男，硕士生（E-mail: 1150904137@qq.com）;陈文（1967—2018），男，教授，博士，博士生导师（通讯作者. E-mail: chenwen@hhu.edu.cn).

计量

出版历程

A Combined Artificial Neural Network Method for Solving Time Fractional Diffusion Equations

计量

出版历程

目录

作者简介:
王江（1993—），男，硕士生（E-mail: 1150904137@qq.com）;陈文（1967—2018），男，教授，博士，博士生导师（通讯作者. E-mail: chenwen@hhu.edu.cn).