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Neural Computing and Applications

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01-07-2015 | Original Article

Comparison of three unsupervised neural network models for first Painlevé Transcendent

Authors: Muhammad Asif Zahoor Raja, Junaid Ali Khan, Syed Muslim Shah, Raza Samar, Djilali Behloul

Published in: Neural Computing and Applications | Issue 5/2015

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Abstract

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.

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Title: Comparison of three unsupervised neural network models for first Painlevé Transcendent
Authors: Muhammad Asif Zahoor Raja
Junaid Ali Khan
Syed Muslim Shah
Raza Samar
Djilali Behloul
Publication date: 01-07-2015
Publisher: Springer London
Published in: Neural Computing and Applications / Issue 5/2015
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-014-1774-y

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