Advanced heuristic computing with Gudermannian neural networks for mathematical modeling of divorced dynamics in social networks

This study investigates the transmission dynamics of divorce within social networks through the innovative application of Gudermannian neural networks (GNNs), combined with a hybrid optimization framework that integrates heuristic genetic algorithms (HGAs) and sequential quadratic programming (SQP). The proposed methodology, referred to as HGA-SQP-GNN, is employed to analyze the intricacies of marital dissolution, encapsulated within the Married-Divorced-Separated (MDS) mathematical framework. This framework categorizes individuals into three distinct groups: Married (M), Divorced (D), and Separated (S). The findings show that about 80 % of marriages end in separation by the end of the observed period. This statistic highlights how divorced individuals can significantly influence the likelihood of separation among married couples, emphasizing the need for targeted interventions to address the rise of broken families. Furthermore, the study demonstrates the robustness and effectiveness of the proposed HGA-SQP-GNN algorithm, as shown by the optimal solutions achieved compared to the traditional Adam method. Our study highlights the urgent need for focused interventions to curb the proliferation of broken families. A hybrid technique, HGA-SQP-GNN, enables rapid convergence optimization by minimizing the mean square error (MSE), which acts as the fitness function for optimization. The robustness and efficacy of the proposed algorithm are confirmed by comparing the optimal solutions of the hybrid approach with the numerical results obtained from the Adam method. The precise measurements of absolute error findings, ranging from 10−2 to 10−12, demonstrate the value and effectiveness of the proposed algorithm. The reliability, stability, and convergence characteristics of the integrated techniques are further verified through statistical analyses, including mean absolute deviation, root mean square error, and Theil's inequality coefficient. Additionally, the lower values of minimum, median, and SIR, ranging from 10−5 to 10−12, further validate the accuracy, robustness, and efficacy of the proposed solver.