  The success of first principles electronic structure calculation for
predictive modeling in chemistry, solid state physics, and materials science is
constrained by the limitations on simulated length and time scales due to
computational cost and its scaling. Techniques based on machine learning ideas
for interpolating the Born-Oppenheimer potential energy surface without
explicitly describing electrons have recently shown great promise, but
accurately and efficiently fitting the physically relevant space of
configurations has remained a challenging goal. Here we present a Gaussian
Approximation Potential for silicon that achieves this milestone, accurately
reproducing density functional theory reference results for a wide range of
observable properties, including crystal, liquid, and amorphous bulk phases, as
well as point, line, and plane defects. We demonstrate that this new potential
enables calculations that would be extremely expensive with a first principles
electronic structure method, such as finite temperature phase boundary lines,
self-diffusivity in the liquid, formation of the amorphous by slow quench, and
dynamic brittle fracture. We show that the uncertainty quantification inherent
to the Gaussian process regression framework gives a qualitative estimate of
the potential's accuracy for a given atomic configuration. The success of this
model shows that it is indeed possible to create a useful
machine-learning-based interatomic potential that comprehensively describes a
material, and serves as a template for the development of such models in the
future.
