https://doi.org/10.1140/epjp/s13360-025-06497-5
Regular Article
A novel heuristic-based physics-informed neural networks (H-PINNs)-based analysis of boundary stresses on magnetohydrodynamic convective flow in a convergent/divergent channel
1
Department of Physics and Applied Mathematics (DPAM), Pakistan Institute of Engineering and Applied Sciences, 45650, Nilore, Islamabad, Pakistan
2
Center for Mathematical Sciences (CMS), Pakistan Institute of Engineering and Applied Sciences, 45650, Nilore, Islamabad, Pakistan
3
Department of Mathematics, Lahore Garrison University, Lahore, Pakistan
a naeemaslam_20@pieas.edu.pk, muhammadnaeemaslam10@gmail.com
Received:
4
November
2024
Accepted:
29
May
2025
Published online:
23
June
2025
In the present study, the influence of mixed boundary stresses on magnetohydrodynamic (MHD) flow in convergent/divergent channels is investigated. The analysis is performed using a machine learning approach using Morlet-wavelet neural networks hybrid with particle swarm optimization and water cycle algorithm as optimizers. This article aims to analysis the impact of Reynolds number, Hartmann number and convergence/divergence angles on flow behavior with associated boundary stresses. The proposed algorithm’s performance is evaluated through (100) one hundred independent runs to determine its effectiveness with the mean squared error ranging from 
. The numerical results obtained from proposed technique is compared with those obtained using the Runge–Kutta method (RK4). It is observed that the absolute errors are ranging from 
for velocity. For the efficiency and the validation of the Morlet-wavelet neural networks algorithm, hundred independent trials (runs) tested to statistical metrics. The proposed algorithm Morlet-wavelet neural networks performs better with reasonable accuracy, and observed to be robust and computational efficient, when compared to analytical and other numerical reference solution. Overall, this study presents an innovative and effective approach for simulating magnetohydrodynamic (MHD) flow in convergent/divergent channels, which could have significant implications for various industrial applications.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
