In the present work, a novel neuro-swarming based heuristic solver is established for the numerical solutions of fourth-order multi-singular nonlinear Emden–Fowler (FO-MS-NEF) model using the function estimate capability of artificial neural networks (ANNs) modelling together with the global application of particle swarm optimization (PSO) enhanced by local search active set (AS) approach, i.e., ANN-PSO-AS solver. The design stimulation for the ANN-PSO-AS scheme for a numerical solver originates with an intention to present a viable, consistent and precise configuration that associates the ANNs strength under the optimization of unified soft computing backgrounds to tackle with such stimulating models for the FO-MS-NEF equation. The proposed ANN-PSO-AS solver is applied for three different variants of FO-MS-NEF equations. The comparison of the obtained results with the true solutions calmed its correctness, effectiveness, and robustness that is further validated with in-depth statistical investigations.