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Artificial neural network (ANN) potentials enable the efficient large-scaleatomistic modeling of complex materials with near first-principles accuracy.For molecular dynamics simulations, accurate energies and interatomic forcesare a prerequisite, but training ANN potentials simultaneously on energies andforces from electronic structure calculations is computationally demanding.Here, we introduce an efficient alternative method for the training of ANNpotentials on energy and force information based on an extrapolation of thetotal energy via a Taylor expansion. By translating the force information toapproximate energies, the quadratic scaling with the number of atoms exhibitedby conventional force-training methods can be avoided, which enables thetraining on reference data sets containing complex atomic structures. Wedemonstrate for different materials systems, clusters of water molecules, bulkliquid water, and a lithium transition-metal oxide, that the proposedforce-training approach provides substantial improvements over schemes thattrain on energies only. Including force information for training reduces thesize of the reference data sets required for ANN potential construction,increases the transferability of the potential, and generally improves theforce prediction accuracy. For a set of water clusters, the Taylor-expansionapproach achieves around 50% of the force error improvement compared to theexplicit training on all force components, at a much smaller computationalcost. The alternative force training approach thus simplifies the constructionof general ANN potentials for the prediction of accurate energies andinteratomic forces for diverse types of materials, as demonstrated here forwater and a transition-metal oxide.

Efficient Training of ANN Potentials by Including Atomic Forces via Taylor Expansion and Application to Water and a Transition-Metal Oxide