  Individuals modify their opinions towards a topic based on their social
interactions. Opinion evolution models conceptualize the change of opinion as a
uni-dimensional continuum, and the effect of influence is built by the group
size, the network structures, or the relations among opinions within the group.
However, how to model the personal opinion evolution process under the effect
of the online social influence as a function remains unclear. Here, we show
that the uni-dimensional continuous user opinions can be represented by
compressed high-dimensional word embeddings, and its evolution can be
accurately modelled by an ordinary differential equation (ODE) that reflects
the social network influencer interactions. Our three major contributions are:
(1) introduce a data-driven pipeline representing the personal evolution of
opinions with a time kernel, (2) based on previous psychology models, we model
the opinion evolution process as a function of online social influence using an
ordinary differential equation, and (3) applied Our opinion evolution model to
the real-time Twitter data. We perform our analysis on 87 active users with
corresponding influencers on the COVID-19 topic from 2020 to 2022. The
regression results demonstrate that 99% of the variation in the quantified
opinions can be explained by the way we model the connected opinions from their
influencers. Our research on the COVID-19 topic and for the account analysed
shows that social media users primarily shift their opinion based on
influencers they follow (e.g., model explains for 99% variation) and
self-evolution of opinion over a long time scale is limited.
