  State-of-the-art planet formation models are now capable of accounting for
the full spectrum of known planet types. This comes at the cost of increasing
complexity of the models, which calls into question whether established links
between their initial conditions and the calculated planetary observables are
preserved. In this paper, we take a data-driven approach to investigate the
relations between clusters of synthetic planets with similar properties and
their formation history. We trained a Gaussian Mixture Model on typical
exoplanet observables computed by a global model of planet formation to
identify clusters of similar planets. We then traced back the formation
histories of the planets associated with them. Using cluster affiliation as
labels, we trained a Random Forest classifier to predict planet species from
properties of the originating protoplanetary disk. Without presupposing any
planet types, we identified four distinct classes in our synthetic population.
They roughly correspond to the observed populations of (sub-)Neptunes, giant
planets, and (super-)Earths, plus an additional unobserved class we denote as
"icy cores". These groups emerge already within the first 0.1 Myr of the
formation phase and are predicted from disk properties with an overall accuracy
of >90%. The most reliable predictors are the initial orbital distance of
planetary nuclei and the total planetesimal mass available. Giant planets form
only in a particular region of this parameter space that is in agreement with
purely analytical predictions. Including N-body interactions between the
planets decreases the predictability, especially for sub-Neptunes that
frequently undergo giant collisions and turn into super-Earths. The impact of
gravitational interactions highlights the need for N-body integrators for
realistic predictions of systems of low-mass planets. (abridged)
