  All-atom dynamics simulations are an indispensable quantitative tool in
physics, chemistry, and materials science, but large systems and long
simulation times remain challenging due to the trade-off between computational
efficiency and predictive accuracy. To address this challenge, we combine
effective two- and three-body potentials in a cubic B-spline basis with
regularized linear regression to obtain machine-learning potentials that are
physically interpretable, sufficiently accurate for applications, as fast as
the fastest traditional empirical potentials, and two to four orders of
magnitude faster than state-of-the-art machine-learning potentials. For data
from empirical potentials, we demonstrate exact retrieval of the potential. For
data from density functional theory, the predicted energies, forces, and
derived properties, including phonon spectra, elastic constants, and melting
points, closely match those of the reference method. The introduced potentials
might contribute towards accurate all-atom dynamics simulations of large
atomistic systems over long time scales.
