  In the late stages of terrestrial planet formation, pairwise collisions
between planetary-sized bodies act as the fundamental agent of planet growth.
These collisions can lead to either growth or disruption of the bodies involved
and are largely responsible for shaping the final characteristics of the
planets. Despite their critical role in planet formation, an accurate treatment
of collisions has yet to be realized. While semi-analytic methods have been
proposed, they remain limited to a narrow set of post-impact properties and
have only achieved relatively low accuracies. However, the rise of machine
learning and access to increased computing power have enabled novel data-driven
approaches. In this work, we show that data-driven emulation techniques are
capable of predicting the outcome of collisions with high accuracy and are
generalizable to any quantifiable post-impact quantity. In particular, we focus
on the dataset requirements, training pipeline, and regression performance for
four distinct data-driven techniques from machine learning (ensemble methods
and neural networks) and uncertainty quantification (Gaussian processes and
polynomial chaos expansion). We compare these methods to existing analytic and
semi-analytic methods. Such data-driven emulators are poised to replace the
methods currently used in N-body simulations. This work is based on a new set
of 10,700 SPH simulations of pairwise collisions between rotating,
differentiated bodies at all possible mutual orientations.
