Legendre Neural Network for Solving Linear Variable Coefficients Delay Differential-Algebraic Equations with Weak Discontinuities
Legendre Neural Network for Solving Linear Variable Coefficients Delay Differential-Algebraic Equations with Weak Discontinuities
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DOI：
10.4208/aamm.oa-2019-0281
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发表时间：
2021-02-01
影响因子：
1.4
通讯作者：
Li, Lijuan
中科院分区：
文献类型：
--
作者：
Liu, Hongliang;Song, Jingwen;Li, Lijuan
本文提出了一种新的Legendre神经网络与极限学习机算法相结合来求解具有弱间断的变系数线性延迟微分代数方程。首先，解区间被弱间断点划分为多个子区间。然后，勒让德神经网络被用来消除隐藏层，扩大输入模式使用勒让德多项式在每个子区间。最后用极限学习机对神经网络进行训练，得到网络参数。数值算例表明，该方法能有效地解决不连续性给数值模拟带来的困难。
In this paper, we propose a novel Legendre neural network combined with the extreme learning machine algorithm to solve variable coefficients linear delay differential-algebraic equations with weak discontinuities. First, the solution interval is divided into multiple subintervals by weak discontinuity points. Then, Legendre neural network is used to eliminate the hidden layer by expanding the input pattern using Legendre polynomials on each subinterval. Finally, the parameters of the neural network are obtained by training with the extreme learning machine. The numerical examples show that the proposed method can effectively deal with the difficulty of numerical simulation caused by the discontinuities.