https://doi.org/10.1140/epjp/i2018-12013-3
Regular Article
Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics
1
Department of Mathematics, University of Gujrat, 50700, Punjab, Pakistan
2
Department of Mathematics, COMSATS Institute of Information Technology, 43600, Attock, Pakistan
3
Department of Physics, COMSATS Institute of Information Technology, Islamabad, Pakistan
4
Department of Electrical Engineering, COMSATS Institute of Information Technology, 43600, Attock, Pakistan
* e-mail: muhammad.asif@ciit-attock.edu.pk
Received:
28
January
2018
Accepted:
12
April
2018
Published online:
16
May
2018
The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018