[论文解读] Atomic Permutationally Invariant Polynomials for Fitting Molecular Force Fields

Alice E. A. Allen, Gábor Cśanyi+2 more|arXiv (Cornell University)|Oct 23, 2020

Machine Learning in Materials Science参考文献 77被引用 52

一句话总结

该论文将原子可置换不变多项式(aPIP)扩展到分子系统，结合低阶项的经验式成分与数据驱动拟合，获得可迁移且对小型有机分子具有高准确性的力场。

ABSTRACT

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 [Mach. Learn.: Sci. Technol. 2019 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.

研究动机与目标

• 通过开发基于 aPIP 的分子力场来弥合传统可迁移经验力场与数据驱动的机器学习势能之间的差距。
• 通过分解体自由度保持较低的项维数，同时实现可系统地提升至四体相互作用。
• 通过正则化和迭代数据拟合，确保光滑的势能面外推并避免过拟合。

提出的方法

• 将总能量分解为最多到四体贡献的体序项，并包含元素特定分量。
• 将笛卡尔坐标转换为旋转不变的距离和角度坐标，并通过初级与次级不变量构造置换不变多项式。
• 实现基于距离的截断以控制计算成本，并使用平滑截断以避免势能面中的洞。
• 使用正则化线性最小二乘拟合基函数线性组合以拟合能量与力。
• 应用拉普拉斯正则化和双边截断以促进光滑性并防止势能面进入非物理区域。
• 使用迭代数据收集与拟合方案来改进势能面覆盖与外推。

实验结果

研究问题

• RQ1 基于 aPIP 的势能在受控的体序下是否能够在相关分子之间实现可转移性，同时保持高精度？
• RQ2 限制体序和应用正则化对力场的精度与外推行为有何影响？
• RQ3 距离-角度坐标与置换不变多项式在小分子势能拟合中，与全高维 ML 方法相比有何差异？

主要发现

• 基于 aPIP 的力场，至多一般化的四体项作用下，在小型有机分子上实现高精度，且在每个分子层面与多体 ML 力场相当。
• 拟合于短链烷烃的联合训练集，aPIP 的精度显著超过经典经验力场，同时保持对训练集外的构型以及新分子的可转移性。
• 正则化和迭代拟合方案提高势能面的平滑性与外推能力，帮助避免洞。
• 基于距离-角度不变表示与对称性自适应多项式，能够在不显式离散原子类型的情况下实现对多元素系统的可扩展处理。