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

TL;DR

This work addresses predicting opinion dynamics by integrating mechanistic priors with data-driven neural models. It introduces OPINN, a physics-informed neural framework that embeds a Diffusion-Convection-Reaction (DCR) system within Neural ODEs to represent local, global, and endogenous opinion interactions. By mapping DCR components to diffusion, convection, and reaction terms and implementing them with graph convolution, attention-based velocity, and flexible reaction terms, OPINN achieves state-of-the-art forecasting and strong generalization on both real-world and synthetic datasets. The approach offers interpretable dynamics, scalable neural modeling, and practical implications for analyzing cyber-physical-social systems.

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.

Figures (13)

• Figure 1: A conceptual illustration of social opinion evolution. Given an information item, users interact within the social platforms and update their opinions over time.
• Figure 2: The conceptual schematic of introducing DCR system into opinion dynamics modeling: diffusion describes the local consensus of user opinions, convection captures the drift driven by external force field, while reaction depicts the opinion evolution dictated by user internal drivers.
• Figure 3: The overall architecture of Opinn comprises three core components: (1) an encoder to map the observed user opinions into latent system states; (2) a neural dynamics module to model the trajectory of opinion dynamical system; and (3) a decoder to generate opinion predictions by integrating neural representations with dynamical priors.
• Figure 4: Visualization of synthetic datasets: we randomly sampled 1,500 users to demonstrate the overall evolutionary trends.
• Figure 5: Ablation results of opinion dynamics mechanisms.