  Simulations of colloidal suspensions consisting of mesoscopic particles and
smaller species such as ions or depletants are computationally challenging as
different length and time scales are involved. Here, we introduce a machine
learning (ML) approach in which the degrees of freedom of the microscopic
species are integrated out and the mesoscopic particles interact with effective
many-body potentials, which we fit as a function of all colloid coordinates
with a set of symmetry functions. We apply this approach to a colloid-polymer
mixture. Remarkably, the ML potentials can be assumed to be effectively
state-independent and can be used in direct-coexistence simulations. We show
that our ML method reduces the computational cost by several orders of
magnitude compared to a numerical evaluation and accurately describes the phase
behavior and structure, even for state points where the effective potential is
largely determined by many-body contributions.
