The purpose of the present work is to solve a third kind of multi-singular nonlinear system using the neuro-swarm computing solver based on the artificial neural networks (ANNs) optimized with the effectiveness of particle swarm optimization (PSO) maintained by a local search proficiency of interior-point algorithm (IPA), i.e., ANN-PSO-IPA. An objective function is designed using the continuous mapping of ANN for nonlinear multi-singular third order system of Emden-Fowler equations and optimization of fitness function carried out with the integrated strength of PSO-IPA. The motivation to design the ANN-PSO-IPA is to present a feasible, reliable and feasible framework to handle with such complicated nonlinear multi-singular third order system of Emden-Fowler model. The designed ANN-PSO-IPA is tested for three different nonlinear variants of the multi-singular third kind of Emden-Fowler system. The obtained numerical results on single/multiple executions of the designed ANN-PSO-IPA are used to endorse the precision, viability and reliability.