  Artificial neural network (ANN) potentials enable the efficient large-scale
atomistic modeling of complex materials with near first-principles accuracy.
For molecular dynamics simulations, accurate energies and interatomic forces
are a prerequisite, but training ANN potentials simultaneously on energies and
forces from electronic structure calculations is computationally demanding.
Here, we introduce an efficient alternative method for the training of ANN
potentials on energy and force information based on an extrapolation of the
total energy via a Taylor expansion. By translating the force information to
approximate energies, the quadratic scaling with the number of atoms exhibited
by conventional force-training methods can be avoided, which enables the
training on reference data sets containing complex atomic structures. We
demonstrate for different materials systems, clusters of water molecules, bulk
liquid water, and a lithium transition-metal oxide, that the proposed
force-training approach provides substantial improvements over schemes that
train on energies only. Including force information for training reduces the
size of the reference data sets required for ANN potential construction,
increases the transferability of the potential, and generally improves the
force prediction accuracy. For a set of water clusters, the Taylor-expansion
approach achieves around 50% of the force error improvement compared to the
explicit training on all force components, at a much smaller computational
cost. The alternative force training approach thus simplifies the construction
of general ANN potentials for the prediction of accurate energies and
interatomic forces for diverse types of materials, as demonstrated here for
water and a transition-metal oxide.
