Advancing Opinion Dynamics Modeling with Neural Diffusion-Convection-Reaction Equation

Abstract: Advanced opinion dynamics modeling is vital for deciphering social behavior, emphasizing its role in mitigating polarization and securing cyberspace. To synergize mechanistic interpretability with data-driven flexibility, recent studies have explored the integration of Physics-Informed Neural Networks (PINNs) for opinion modeling. Despite this promise, existing methods are tailored to incomplete priors, lacking a comprehensive physical system to integrate dynamics from local, global, and endogenous levels. Moreover, penalty-based constraints adopted in existing methods struggle to deeply encode physical priors, leading to optimization pathologies and discrepancy between latent representations and physical transparency. To this end, we offer a physical view to interpret opinion dynamics via Diffusion-Convection-Reaction (DCR) system inspired by interacting particle theory. Building upon the Neural ODEs, we define the neural opinion dynamics to coordinate neural networks with physical priors, and further present the OPINN, a physics-informed neural framework for opinion dynamics modeling. Evaluated on real-world and synthetic datasets, OPINN achieves state-of-the-art performance in opinion evolution forecasting, offering a promising paradigm for the nexus of cyber, physical, and social systems.