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Comparison of three unsupervised neural network models for first Painlevé Transcendent

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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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Authors and Affiliations

  1. Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock, Pakistan

    Muhammad Asif Zahoor Raja

  2. Faculty of Engineering Science and Technology, Islamabad Campus, Hamdard University, Karachi, Pakistan

    Junaid Ali Khan

  3. Department of Electrical Engineering, Mohammad Ali Jinnah University, Islamabad, Pakistan

    Syed Muslim Shah & Raza Samar

  4. Department of Computer Science, USTHB, BP32 El Alia, 16111, Bab Ezzouar, Algiers, Algeria

    Djilali Behloul

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  1. Muhammad Asif Zahoor Raja
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  2. Junaid Ali Khan
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  3. Syed Muslim Shah
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  4. Raza Samar
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  5. Djilali Behloul
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Correspondence to Muhammad Asif Zahoor Raja.

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Raja, M.A.Z., Khan, J.A., Shah, S.M. et al. Comparison of three unsupervised neural network models for first Painlevé Transcendent. Neural Comput & Applic 26, 1055–1071 (2015). https://doi.org/10.1007/s00521-014-1774-y

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