Neural Computing and Applications

, Volume 26, Issue 5, pp 1055–1071 | Cite as

Comparison of three unsupervised neural network models for first Painlevé Transcendent

  • Muhammad Asif Zahoor Raja
  • Junaid Ali Khan
  • Syed Muslim Shah
  • Raza Samar
  • Djilali Behloul
Original Article

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.

Keywords

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

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Copyright information

© The Natural Computing Applications Forum 2014

Authors and Affiliations

  • Muhammad Asif Zahoor Raja
    • 1
  • Junaid Ali Khan
    • 2
  • Syed Muslim Shah
    • 3
  • Raza Samar
    • 3
  • Djilali Behloul
    • 4
  1. 1.Department of Electrical EngineeringCOMSATS Institute of Information TechnologyAttockPakistan
  2. 2.Faculty of Engineering Science and Technology, Islamabad CampusHamdard UniversityKarachiPakistan
  3. 3.Department of Electrical EngineeringMohammad Ali Jinnah UniversityIslamabadPakistan
  4. 4.Department of Computer ScienceUSTHBBab Ezzouar, AlgiersAlgeria

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