Message spreading modeling from the perspective of social psychology, differential equation dynamics, and deep learning technique

To gain a deeper understanding of the characteristics of message spreading, it is crucial to explore various methods of modeling this phenomenon. Given that message spreading is significantly influenced by social media, we propose a modified spreading model informed by social psychology analysis. This approach also incorporates differential equation dynamics and deep learning technique. The proposed model accounts for a cross-transmission mechanism between individuals and social media platforms, as well as a nonlinear spreading rate, to effectively characterize the saturation effect of messages. Utilizing Lyapunov functionals, we carry out a dynamical analysis of the message spreading model. Furthermore, we develop physics-informed neural networks based on deep learning technique that merges the efficiency inherent in data-driven modeling with the precision offered by mathematical modeling. Numerical simulations demonstrate that our prediction method can accurately capture real-time changes in data while correcting deviations observed in data-driven predictions, which highlights the robust potential for multidisciplinary integration among social psychology, differential equation dynamics, and deep learning technique.