  In-context system identification aims at constructing meta-models to describe
classes of systems, differently from traditional approaches that model single
systems. This paradigm facilitates the leveraging of knowledge acquired from
observing the behaviour of different, yet related dynamics. This paper
discusses the role of meta-model adaptation. Through numerical examples, we
demonstrate how meta-model adaptation can enhance predictive performance in
three realistic scenarios: tailoring the meta-model to describe a specific
system rather than a class; extending the meta-model to capture the behaviour
of systems beyond the initial training class; and recalibrating the model for
new prediction tasks. Results highlight the effectiveness of meta-model
adaptation to achieve a more robust and versatile meta-learning framework for
system identification.
