几类微分-代数方程的神经网络求解法

杨钊; 兰钧; 吴勇军

doi:10.21656/1000-0887.390122

几类微分-代数方程的神经网络求解法

doi: 10.21656/1000-0887.390122

¹上海交通大学工程力学系, 上海 200240;²卫宁健康科技集团股份有限公司, 上海 200072

基金项目: 国家自然科学基金（11772293；11272201）

详细信息

作者简介:
吴勇军（1978—），男，副研究员(通讯作者. E-mail: yj.wu@sjtu.edu.cn).

中图分类号: O193;O322
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- 被引次数: 0
出版历程
- 收稿日期: 2018-04-18
- 修回日期: 2018-11-11
- 刊出日期: 2019-02-01

On Solutions to Several Classes of Differential-Algebraic Equations Based on Artificial Neural Networks

¹Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, P.R.China;²Winning Health Technology Group Co., Ltd.,Shanghai 200072, P.R.China

Funds: The National Natural Science Foundation of China（11772293；11272201）

摘要

摘要: 在非线性科学中，寻求微分方程的近似解析解一直是重要的研究课题和研究热点.利用人工神经网络原理，结合最优化方法，研究了几类微分-代数方程的近似解析解，包括指标1，2，3型Hessenberg方程及指标3型Euler-Lagrange方程，得到了方程近似解析解的表达式.通过与精确解或Runge-Kutta(龙格-库塔)数值计算结果对比，表明神经网络方法的结果有很高的精度.
- 人工神经网络 /
- 微分代数方程 /
- 近似解析解 /
- 最优化方法
Abstract: In nonlinear science, it is always an important subject and research focus to find the approximate analytical solutions to differential equations. The artificial neural network and the optimization method were combined to solve 2 special classes of differentialalgebraic equations (DAEs). The 1st 3 numerical examples, namely, the Hessenberg DAEs with indices 1, 2, 3, fell into a category of pure mathematical problems. Then the 2nd example related to EulerLagrange DAEs with indices 3, i.e. a pendulum without external force, arising from the background of nonholonomic mechanics. The approximate analytical solutions to the above 4 examples were obtained and compared with the exact solutions and the results from the RungeKutta method. High accuracy of the proposed method was demonstrated.
- artificial neural network /
- differential-algebraic equation /
- approximate analytical solution /
- optimization method

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