  Polaron defects are ubiquitous in materials and play an important role in
many processes involving carrier mobility, charge transfer and surface
reactivity. Determining the spatial distribution of small polarons is essential
to understand materials properties and functionalities. This requires an
exploration of the configurational space, which is computationally demanding
when using standard first principles methods, and technically prohibitive for
many-polaron systems. Here, we propose a machine-learning (ML) accelerated
search that compares the energy stability of different polaron patterns and
determines the ground state configuration. The kernel-regression based ML model
is trained on databases generated by density functional theory (DFT)
calculations on a minimal set of initial polaron patterns, obtained by using
either molecular dynamics simulations or a random sampling approach. To
establish an efficient mapping between training data and configuration
stability we designed simple descriptors that model the interactions among
polarons and charged point defects. The proposed DFT+ML protocol is used here
to explore millions of polaron configurations for two different systems, oxygen
defective rutile TiO$_2$(110) and Nb-doped SrTiO$_3$(001). Our data shows that
the ML-aided search correctly individuates the ground-state polaron patterns,
proposes polaronic configurations not visited in the training and can be used
to efficiently determine the optimal distribution of polarons at any charge
concentration.
