  We develop a model to establish the interconnection between galaxies and
their dark matter halos. We use Principal Component Analysis (PCA) to reduce
the dimensionality of both the mass assembly histories of halos/subhalos and
the star formation histories of galaxies, and Gradient Boosted Decision Trees
(GBDT) to transform halo/subhalo properties into galaxy properties. We use two
sets of hydrodynamic simulations to motivate our model architecture and to
train the transformation. We then apply the two sets of trained models to dark
matter only (DMO) simulations to show that the transformation is reliable and
statistically accurate. The model trained by a high-resolution hydrodynamic
simulation, or by a set of such simulations implementing the same physics of
galaxy formation, can thus be applied to large DMO simulations to make "mock"
copies of the hydrodynamic simulation. The model is both flexible and
interpretable, which paves the way for future applications in which we will
constrain the model using observations at different redshifts simultaneously
and explore how galaxies form and evolve in dark matter halos empirically.
