We introduce and explore an approach for constructing force fields for small molecules, which combines intuitive low body order empirical force field terms with the concepts of data driven statistical fits of recent machine learned potentials. We bring these two key ideas together to bridge the gap between established empirical force fields that have a high degree of transferability on the one hand, and the machine learned potentials that are systematically improvable and can converge to very high accuracy, on the other. Our framework extends the atomic permutationally invariant polynomials (aPIP) developed for elemental materials in (2019 Mach. Learn.: Sci. Technol. 1 015004) to molecular systems. The body order decomposition allows us to keep the dimensionality of each term low, while the use of an iterative fitting scheme as well as regularisation procedures improve the extrapolation outside the training set. We investigate aPIP force fields with up to generalised 4-body terms, and examine the performance on a set of small organic molecules. We achieve a high level of accuracy when fitting individual molecules, comparable to those of the many-body machine learned force fields. Fitted to a combined training set of short linear alkanes, the accuracy of the aPIP force field still significantly exceeds what can be expected from classical empirical force fields, while retaining reasonable transferability to both configurations far from the training set and to new molecules.

我们介绍并探索了一种构建小分子力场的方法，该方法将直观的低体序经验力场术语与数据驱动的最新机器学习潜力的统计拟合概念相结合。我们将这两个关键思想结合在一起，以弥合既有经验的力场之间的差距，这些经验力场一方面具有高度的可传递性，另一方面则是机器学习的潜力，这些潜力可以系统地改进并且可以收敛到非常高的精度。我们的框架扩展了质材料研制原子弹permutationally不变多项式（APIP）在（2019马赫。了解：科学。TECHNOL。 1015004）的分子系统。身体顺序分解使我们可以将每个术语的维数保持在较低的水平，同时使用迭代拟合方案以及正则化过程可以改善训练集以外的外推。我们研究了多达4个广义项的aPIP力场，并研究了一组小的有机分子的性能。与多机体机器学习的力场相比，我们在拟合单个分子时达到了很高的准确性。适合短线性烷烃的组合训练组，aPIP力场的准确性仍大大超过了经典经验力场所期望的范围，同时保持了远离训练组和新分子的合理构型。