Comparison of three unsupervised neural network models for first Painlevé Transcendent

被引：0

作者：

Muhammad Asif Zahoor Raja

Junaid Ali Khan

Syed Muslim Shah

Raza Samar

Djilali Behloul

机构：

[1] COMSATS Institute of Information Technology,Department of Electrical Engineering

[2] Hamdard University,Faculty of Engineering Science and Technology, Islamabad Campus

[3] Mohammad Ali Jinnah University,Department of Electrical Engineering

[4] USTHB,Department of Computer Science

来源：

Neural Computing and Applications | 2015年 / 26卷

关键词：

Painlevé Transcendents; Artificial neural network; Sequential quadratic programming; Nonlinear differential equations; Activation functions; Unsupervised learning;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper, a reliable soft computing framework is presented for the approximate solution of initial value problem (IVP) of first Painlevé equation using three unsupervised neural network models optimized with sequential quadratic programming (SQP). These mathematical models are constructed in the form of feed-forward architecture including log-sigmoid, radial base and tan-sigmoid activation functions in the hidden layers. The optimization of designed parameters for each model is performed with SQP, an efficient constraint optimization problem-solving algorithm. The designed methodology is tested on the IVP, and comparative study is carried out with standard solution based on numerical and analytical solvers. The accuracy, convergence and effectiveness of the schemes are validated on the given benchmark problem by large number of simulations and their comprehensive analysis.

引用

页码：1055 / 1071

页数：16

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