Sabir, ZulqurnainRaja, Muhammad Asif ZahoorUmar, MuhammadSalahshour, SoheilAwan, Saeed EhsanAsghar, Malik Summair2025-07-152025-07-1520252520-81602520-817910.1007/s41939-025-00961-6https://doi.org/10.1007/s41939-025-00961-6https://hdl.handle.net/20.500.14517/8079The purpose of the current study is to design a feed forward Gudermannian neural networks for a singular Lane-Emden model based Neumann, Neumann-Robin and Dirichlet boundary conditions arising in numerous physical systems. The procedure based on the GNNs is exploited through the optimization of global and local search methods, i.e., genetic algorithm and active-set technique. A fitness function is constructed using the model and its boundary conditions, while the efficiency of the scheme is observed through the optimization with the hybridization of global and local search schemes. Four different nonlinear variants of the singular Lane-Emden model based Neumann, Neumann-Robin and Dirichlet boundary conditions have been numerically presented to validate the efficiency and accuracy of the model. The comparison of the obtained and exact results is used to verify the validity of the designed procedure. Moreover, different statistical measures have been implemented to certify the reliability of the proposed technique.eninfo:eu-repo/semantics/closedAccessLane-EmdenGudermannian Neural NetworksNeumann-Robin And DirichletHybrid SchemeActive-Set TechniqueGenetic AlgorithmArticleN/AQ388WOS:001521883700002