The purpose of this research is to construct an integrated neuro swarming scheme using the procedures of the artificial neural networks (ANNs) with the use of global search particle swarm optimization (PSO) along with the competent local search interior-point programming (IPP) called as ANN-PSOIPP. The proposed computational scheme is implemented for the numerical simulations of the third order nonlinear delay differential Emden-Fowler model (TON-DD-EFM). The TON-DD-EFM is based on two types along with the particulars of shape factor, delayed terms, and singular points. A merit function is performed using the optimization of PSOIPP to find the solutions to the TON-DD-EFM. The effectiveness of the ANN-PSOIPP is certified through the comparison with the exact results for solving four examples of the TON-DD-EFM. The scheme’s efficiency is observed by performing the absolute error in suitable measures found around 10−04 to 10−07. Furthermore, the statistical-based assessments for 100 trials are provided to compute the accuracy, stability, and constancy of the ANN-PSOIPP for solving the TON-DD-EFM.