  Machine learned force fields typically require manual construction of
training sets consisting of thousands of first principles calculations, which
can result in low training efficiency and unpredictable errors when applied to
structures not represented in the training set of the model. This severely
limits the practical application of these models in systems with dynamics
governed by important rare events, such as chemical reactions and diffusion. We
present an adaptive Bayesian inference method for automating the training of
interpretable, low-dimensional, and multi-element interatomic force fields
using structures drawn on the fly from molecular dynamics simulations. Within
an active learning framework, the internal uncertainty of a Gaussian process
regression model is used to decide whether to accept the model prediction or to
perform a first principles calculation to augment the training set of the
model. The method is applied to a range of single- and multi-element systems
and shown to achieve a favorable balance of accuracy and computational
efficiency, while requiring a minimal amount of ab initio training data. We
provide a fully open-source implementation of our method, as well as a
procedure to map trained models to computationally efficient tabulated force
fields.
