The dynamics of Artificial Neural Networks (ANNs) have emerged as a cornerstone of computational intelligence, providing transformative insights into learning behaviors, stability properties, and predictive modeling in complex systems. In this study, we proposed a dynamic neural network framework designed to model and forecast competency development trajectories in socio-educational environments, situated within the "New liberal arts" paradigm. By synthesizing multi-source behavioral data into longitudinal competency profiles, we characterize evolving collaboration networks through dynamic centrality indicators. Unsupervised learning techniques, specifically DBSCAN and K-means clustering, were implemented to identify and categorize divergent developmental pathways. To encapsulate these temporal fluctuations, a Long Short-Term Memory (LSTM) recurrent neural network was developed, with a rigorous focus on convergence behavior, trajectory forecasting stability, and cross-domain generalization. The results demonstrated robust performance, evidenced by Mean Absolute Errors (MAE) ranging from 0.203 to 0.247 and high correlation coefficients (0.85–0.87), thereby validating the efficacy of ANN dynamics in modeling evolving human competencies. Beyond the educational domain, this framework underscores the broader utility of neural network dynamics for analyzing complex, human-centered systems, furthering the interdisciplinary expansion of ANN applications.