  We present an atomic cluster expansion (ACE) for carbon that improves over
available classical and machine learning potentials. The ACE is parameterized
from an exhaustive set of important carbon structures at extended volume and
energy range, computed using density functional theory (DFT). Rigorous
validation reveals that ACE predicts accurately a broad range of properties of
both crystalline and amorphous carbon phases while being several orders of
magnitude more computationally efficient than available machine learning
models. We demonstrate the predictive power of ACE on three distinct
applications, brittle crack propagation in diamond, evolution of amorphous
carbon structures at different densities and quench rates and nucleation and
growth of fullerene clusters under high pressure and temperature conditions.
