caa a22 4500 606160116 CHVBK 20210128100628.0 cr unu---uuuuu 210128e20150701xx s 000 0 eng 10.1007/s00521-014-1774-y doi (NATIONALLICENCE)springer-10.1007/s00521-014-1774-y Comparison of three unsupervised neural network models for first Painlevé Transcendent [Elektronische Daten] [Muhammad Raja, Junaid Khan, Syed Shah, Raza Samar, Djilali Behloul] 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. The Natural Computing Applications Forum, 2014 Painlevé Transcendents nationallicence Artificial neural network nationallicence Sequential quadratic programming nationallicence Nonlinear differential equations nationallicence Activation functions nationallicence Unsupervised learning nationallicence Raja Muhammad Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock, Pakistan aut Khan Junaid Faculty of Engineering Science and Technology, Islamabad Campus, Hamdard University, Karachi, Pakistan aut Shah Syed Department of Electrical Engineering, Mohammad Ali Jinnah University, Islamabad, Pakistan aut Samar Raza Department of Electrical Engineering, Mohammad Ali Jinnah University, Islamabad, Pakistan aut Behloul Djilali Department of Computer Science, USTHB, BP32 El Alia, 16111, Bab Ezzouar, Algiers, Algeria aut Neural Computing and Applications Springer London 26/5(2015-07-01), 1055-1071 0941-0643 26:5<1055 2015 26 521 https://doi.org/10.1007/s00521-014-1774-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00521-014-1774-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Raja Muhammad Department of Electrical Engineering, COMSATS Institute of Information Technology, Attock, Pakistan aut NATIONALLICENCE 700 1- Khan Junaid Faculty of Engineering Science and Technology, Islamabad Campus, Hamdard University, Karachi, Pakistan aut NATIONALLICENCE 700 1- Shah Syed Department of Electrical Engineering, Mohammad Ali Jinnah University, Islamabad, Pakistan aut NATIONALLICENCE 700 1- Samar Raza Department of Electrical Engineering, Mohammad Ali Jinnah University, Islamabad, Pakistan aut NATIONALLICENCE 700 1- Behloul Djilali Department of Computer Science, USTHB, BP32 El Alia, 16111, Bab Ezzouar, Algiers, Algeria aut NATIONALLICENCE 773 0- Neural Computing and Applications Springer London 26/5(2015-07-01), 1055-1071 0941-0643 26:5<1055 2015 26 521