This paper presents an ongoing project about the implementation of digital twins (DT) for simulating cognitive-affective behaviours in social networks. Our approach relies on a pure data-driven solution, which takes existing public data from social networks to learn cognitive models according to the profile, posts and interactions of the social network users. The final aim is that the learned cognitive models can be parameterised according to existing classifications of traits and emotions so that different behaviours can be eventually simulated with the resulting DTs. In this work, we propose the use of the Transformers neural-network architectures to both interpret incoming messages according to cognitive contexts, and to generate responses to these messages. The first experiments are aimed at integrating and measuring existing approaches for emotion recognition from texts.