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

2026-02-05

AI Summary

Existing opinion dynamics models struggle to jointly capture local, global, and endogenous interactions, while penalty-based enforcement of physical constraints often leads to optimization difficulties and representational distortions. This work proposes OPINN, a novel framework that, for the first time, integrates the diffusion–convection–reaction (DCR) physical system into opinion evolution modeling. By leveraging neural ordinary differential equations (neural ODEs), OPINN deeply fuses physical priors with data-driven learning, overcoming key limitations of traditional physics-informed neural networks (PINNs) in constraint representation and optimization. The method achieves state-of-the-art performance in predicting opinion dynamics on both real-world and synthetic datasets, offering an interpretable and high-fidelity paradigm for socio-physical-cyber integrated systems.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Search and Optimization: Mixed Discrete/Continuous Search
• Knowledge Representation and Reasoning: Preferences

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• opinion dynamics
• physics-informed neural networks
• Diffusion-Convection-Reaction system
• physical priors
• modeling polarization

Innovation

• Physics-Informed Neural Networks
• Opinion Dynamics
• Diffusion-Convection-Reaction
• Neural ODEs
• OPINN