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.

在当前工作中，使用人工神经网络（ANN）的功能估计能力，针对四阶多奇异非线性Emden-Fowler（FO-MS-NEF）模型的数值解，建立了一种基于神经群的启发式求解器。通过局部搜索活动集（AS）方法（即ANN-PSO-AS求解器）增强的粒子群优化（PSO）的全球应用建模。数值求解器的ANN-PSO-AS方案的设计刺激源于提出一种可行的，一致的和精确的配置，该配置在统一软计算背景的优化下将ANN的强度关联起来，以解决此类针对FO的刺激模型-MS-NEF方程。所提出的ANN-PSO-AS求解器适用于FO-MS-NEF方程的三个不同变体。