A novel heuristic Morlet wavelet neural network design for the painlevé equation-II arising in nonlinear optics.

Journal: Scientific reports
Published Date: Jul 9, 2025

Abstract

The current investigations present the novel structure of Morlet wavelet neural network (MWNN) for the numerical solutions of Painlevé equation-II arising in nonlinear optics. An error based fitness function is constructed using the sense of differential model and its initial or boundary conditions, which is further optimized through the hybrid computing terminologies of the global search genetic algorithm (GA) and local search interior-point algorithm (IPA), i.e., GA-IPA. The precision of the process is observed through the overlapping of the proposed and reference results, and negligible absolute error. Moreover, the statistical analysis using the multiple independent runs is performed by different tests including Theil's inequality coefficient, variance account for and semi inter-quartile range, which shows the dependability of the proposed MWNN-GA-IPA in order to Painlevé equation-II arising in nonlinear optics. The proposed MWNN-GA-IPA optics is discussed for the first time for solving the Painlevé equation-II arising in nonlinear.

Authors

  • Sundas Faisal
    Department of Graphics, Computer Vision and Digital Systems, Silesian University of Technology, Gliwice, Poland. sundas.faisal@polsl.pl.
  • Zulqurnain Sabir
    Department of Mathematics and Statistics, Hazara University, Mansehra, Pakistan.
  • Samra Urooj Khan
    Faculty of Electrical and Electronic Engineering, Universiti Malaysia Pahang Al-Sultan Abdullah, Pekan, Pahang, 26600, Malaysia.
  • Muhammad Aamir
    Department of Computer Science, Sahiwal Campus, COMSATS University Islamabad, Sahiwal 57000, Pakistan.
  • Krzysztof A Cyran
    Institute of Computer Sciences, Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice, Poland.

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