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 datasets 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 datasets 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.

人工神经网络（ANN）势能使复杂材料的高效大规模原子建模具有接近第一原理的准确性。对于分子动力学模拟，准确的能量和原子间力是前提，但同时需要对电子结构计算中的能量和力同时训练ANN势。在此，我们基于通过泰勒展开法对总能量进行外推，介绍了一种用于在能量和力信息上训练ANN势的有效替代方法。通过将力信息转换为近似能量，可以避免常规力训练方法所显示的原子数量的二次缩放，从而可以对包含复杂原子结构的参考数据集进行训练。我们证明了对于不同的材料系统，水分子簇，大量液态水和锂过渡金属氧化物，所提出的力训练方法相对于仅依靠能量训练的方案提供了实质性的改进。包含用于训练的力信息可减少ANN电位构建所需的参考数据集的大小，增加电位的可传递性，并通常提高力预测的准确性。对于一组水簇，与对所有力分量进行显式训练相比，泰勒展开方法可实现约50％的力误差改善，而计算成本却要低得多。