  In the current paradigm of planet formation research, it is believed that the
first step to forming massive bodies (such as asteroids and planets) requires
that small interstellar dust grains floating through space collide with each
other and grow to larger sizes. The initial formation of these pebbles is
governed by an integro-differential equation known as the Smoluchowski
coagulation equation, to which analytical solutions are intractable for all but
the simplest possible scenarios. While brute-force methods of approximation
have been developed, they are computationally costly, currently making it
infeasible to simulate this process including other physical processes relevant
to planet formation, and across the very large range of scales on which it
occurs. In this paper, we take a machine learning approach to designing a
system for a much faster approximation. We develop a multi-output random forest
regression model trained on brute-force simulation data to approximate
distributions of dust particle sizes in protoplanetary disks at different
points in time. The performance of our random forest model is measured against
the existing brute-force models, which are the standard for realistic
simulations. Results indicate that the random forest model can generate highly
accurate predictions relative to the brute-force simulation results, with an
$R^{2}$ of 0.97, and do so significantly faster than brute-force methods.
