  Is it possible to understand the intricacies of a dynamical system not solely
from its input/output pattern, but also by observing the behavior of other
systems within the same class? This central question drives the study presented
in this paper.
  In response to this query, we introduce a novel paradigm for system
identification, addressing two primary tasks: one-step-ahead prediction and
multi-step simulation. Unlike conventional methods, we do not directly estimate
a model for the specific system. Instead, we learn a meta model that represents
a class of dynamical systems. This meta model is trained on a potentially
infinite stream of synthetic data, generated by simulators whose settings are
randomly extracted from a probability distribution. When provided with a
context from a new system-specifically, an input/output sequence-the meta model
implicitly discerns its dynamics, enabling predictions of its behavior.
  The proposed approach harnesses the power of Transformers, renowned for their
\emph{in-context learning} capabilities. For one-step prediction, a GPT-like
decoder-only architecture is utilized, whereas the simulation problem employs
an encoder-decoder structure. Initial experimental results affirmatively answer
our foundational question, opening doors to fresh research avenues in system
identification.

Systems and Control;Machine Learning;Systems and Control