The prediction of chemical properties using machine learning techniques calls for a set of appropriate descriptors that accurately describe atomic and, on a larger scale, molecular environments. A mapping of conformational information on a space spanned by atom-centred symmetry functions (SF) has become a standard technique for energy and force predictions using high-dimensional neural network potentials (HDNNP). An appropriate choice of SFs is particularly crucial for accurate force predictions. Established atom-centred SFs, however, are limited in their flexibility, since their functional form restricts the angular domain that can be sampled without introducing problematic derivative discontinuities. Here, we introduce a class of atom-centred SFs based on polynomials with compact support called polynomial symmetry functions (PSF), which enable a free choice of both, the angular and the radial domain covered. We demonstrate that the accuracy of PSFs is either on par or considerably better than that of conventional, atom-centred SFs. In particular, a generic set of PSFs with an intuitive choice of the angular domain inspired by organic chemistry considerably improves prediction accuracy for organic molecules in the gaseous and liquid phase, with reductions in force prediction errors over a test set approaching 50% for certain systems. Contrary to established atom-centred SFs, computation of PSF does not involve any exponentials, and their intrinsic compact support supersedes use of separate cutoff functions, facilitating the choice of their free parameters. Most importantly, the number of floating point operations required to compute polynomial SFs introduced here is considerably lower than that of other state-of-the-art SFs, enabling their efficient implementation without the need of highly optimised code structures or caching, with speedups with respect to other state-of-the-art SFs reaching a factor of 4.5 to 5. This low-effort performance benefit substantially simplifies their use in new programs and emerging platforms such as graphical processing units. Overall, polynomial SFs with compact support improve accuracy of both, energy and force predictions with HDNNPs while enabling significant speedups compared to their well-established counterparts.

使用机器学习技术预测化学性质需要一组适当的描述符，以准确地描述原子环境，并在更大范围内描述分子环境。在以原子中心对称函数 (SF) 跨越的空间上映射构象信息已成为使用高维神经网络势 (HDNNP) 进行能量和力预测的标准技术。An appropriate choice of SFs is particularly crucial for accurate force predictions. 然而，已建立的以原子为中心的 SF 的灵活性受到限制，因为它们的函数形式限制了可以在不引入有问题的导数不连续性的情况下采样的角域。在这里，我们介绍了一类基于多项式的以原子为中心的 SFs，具有紧凑的支持，称为多项式对称函数 (PSF)，这使得可以自由选择覆盖的角度域和径向域。我们证明了 PSF 的准确性与传统的以原子为中心的 SF 的准确性相当或明显更好。特别是，受有机化学启发，具有直观选择角域的通用 PSF 集显着提高了气相和液相中有机分子的预测精度，在某些系统的测试集上，力预测误差降低了接近 50% . 与已建立的以原子为中心的 SFs 相反，PSF 的计算不涉及任何指数，并且它们内在的紧凑支持取代了单独的截止函数的使用，促进了它们的自由参数的选择。最重要的是，此处介绍的计算多项式 SF 所需的浮点运算数量远低于其他最先进的 SF，从而无需高度优化的代码结构或缓存即可高效实现，并且相对于其他技术有加速最先进的 SF 达到 4.5 到 5 倍。这种省力的性能优势大大简化了它们在新程序和新兴平台（例如图形处理单元）中的使用。总体而言，具有紧凑支持的多项式 SF 提高了 HDNNP 的能量和力预测的准确性，同时与成熟的对应项相比实现了显着的加速。与其他最先进的 SF 相比，速度提高了 4.5 到 5 倍。这种省力的性能优势大大简化了它们在新程序和新兴平台（例如图形处理单元）中的使用。总体而言，具有紧凑支持的多项式 SF 提高了 HDNNP 的能量和力预测的准确性，同时与成熟的对应项相比实现了显着的加速。与其他最先进的 SF 相比，速度提高了 4.5 到 5 倍。这种省力的性能优势大大简化了它们在新程序和新兴平台（例如图形处理单元）中的使用。总体而言，具有紧凑支持的多项式 SF 提高了 HDNNP 的能量和力预测的准确性，同时与成熟的对应项相比实现了显着的加速。