  Opinion formation and propagation are crucial phenomena in social networks
and have been extensively studied across several disciplines. Traditionally,
theoretical models of opinion dynamics have been proposed to describe the
interactions between individuals (i.e., social interaction) and their impact on
the evolution of collective opinions. Although these models can incorporate
sociological and psychological knowledge on the mechanisms of social
interaction, they demand extensive calibration with real data to make reliable
predictions, requiring much time and effort. Recently, the widespread use of
social media platforms provides new paradigms to learn deep learning models
from a large volume of social media data. However, these methods ignore any
scientific knowledge about the mechanism of social interaction. In this work,
we present the first hybrid method called Sociologically-Informed Neural
Network (SINN), which integrates theoretical models and social media data by
transporting the concepts of physics-informed neural networks (PINNs) from
natural science (i.e., physics) into social science (i.e., sociology and social
psychology). In particular, we recast theoretical models as ordinary
differential equations (ODEs). Then we train a neural network that
simultaneously approximates the data and conforms to the ODEs that represent
the social scientific knowledge. In addition, we extend PINNs by integrating
matrix factorization and a language model to incorporate rich side information
(e.g., user profiles) and structural knowledge (e.g., cluster structure of the
social interaction network). Moreover, we develop an end-to-end training
procedure for SINN, which involves Gumbel-Softmax approximation to include
stochastic mechanisms of social interaction. Extensive experiments on
real-world and synthetic datasets show SINN outperforms six baseline methods in
predicting opinion dynamics.
