Improved description of atomic environments using low-cost polynomial functions with compact support
Improved description of atomic environments using low-cost polynomial functions with compact support
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DOI：
10.1088/2632-2153/abf817
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发表时间：
2021-09-01
影响因子：
6.8
通讯作者：
Dellago, Christoph
中科院分区：
文献类型：
--
作者：
Bircher, Martin P.;Singraber, Andreas;Dellago, Christoph
使用机器学习技术预测化学性质需要一组适当的描述符，这些描述符可以准确地描述原子环境，并且在更大的范围内，可以描述分子环境。在原子中心对称函数（SF）所跨越的空间上的构象信息的映射已经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。适当选择SF对于精确的力预测特别重要。建立原子为中心的SF，但是，在他们的灵活性是有限的，因为他们的功能形式限制了角域，可以不引入有问题的衍生物不连续采样。在这里，我们介绍了一类原子为中心的SF的基础上多项式与紧凑的支持称为多项式对称函数（PSF），这使得一个自由选择的角度和径向域覆盖。我们证明，PSFS的准确性是在标准杆上或大大优于传统的，原子为中心的SF。特别是，一个通用的一组PSF的角度域的直观选择灵感来自有机化学显着提高预测准确性的有机分子在气相和液相中，与力的预测误差减少超过一个测试集接近50%的某些系统。相反，建立原子为中心的SF，PSF的计算不涉及任何指数，其内在的紧凑的支持取代使用单独的截止函数，方便选择其自由参数。最重要的是，这里介绍的计算多项式SF所需的浮点运算的数量大大低于其他最先进的SF，使其有效的实现，而不需要高度优化的代码结构或高速缓存，与其他最先进的SF的加速比达到4.5至5倍。这种低工作量的性能优势大大简化了它们在新程序和新兴平台（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HDNNPs的能量和力预测的准确性，同时与其成熟的同行相比实现了显着的加速。
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.