Incorporating long-range physics in atomic-scale machine learning

The most successful and popular machine learning models of atomic-scale properties derive their transferability from a locality ansatz. The properties of a large molecule or a bulk material are written as a sum over contributions that depend on the configurations within finite atom-centered environments. The obvious downside of this approach is that it cannot capture nonlocal, nonadditive effects such as those arising due to long-range electrostatics or quantum interference. We propose a solution to this problem by introducing nonlocal representations of the system, which are remapped as feature vectors that are defined locally and are equivariant in O(3). We consider, in particular, one form that has the same asymptotic behavior as the electrostatic potential. We demonstrate that this framework can capture nonlocal, long-range physics by building a model for the electrostatic energy of randomly distributed point-charges, for the unrelaxed binding curves of charged organic molecular dimers, and for the electronic dielectric response of liquid water. By combining a representation of the system that is sensitive to long-range correlations with the transferability of an atom-centered additive model, this method outperforms current state-of-the-art machine-learning schemes and provides a conceptual framework to incorporate nonlocal physics into atomistic machine learning.

当前用于原子尺度性质（atomic-scale properties）预测的最成功且流行的机器学习模型，其可迁移性源于局域假设（locality ansatz）。大型分子或块体材料的性质可表示为若干贡献项的求和，各贡献项仅依赖于有限个以原子为中心的局域环境内的原子构型。该方法的明显局限性在于，无法捕捉非局域、非加和性效应，例如由长程静电作用（long-range electrostatics）或量子干涉（quantum interference）所引发的此类效应。我们通过引入体系的非局域表征来解决这一问题，该表征被重映射为局域定义且具有O(3)群等变性的特征向量。我们特别考量了一种与静电势（electrostatic potential）具有相同渐近行为的表征形式。我们通过构建随机分布点电荷体系的静电能模型、带电有机分子二聚体的未弛豫结合曲线模型，以及液态水的电子介电响应（electronic dielectric response）模型，验证了该框架能够捕捉非局域长程物理效应。通过将对长程关联敏感的体系表征，与以原子为中心的加和模型的可迁移性相结合，该方法优于当前最先进的机器学习方法，并为将非局域物理效应融入原子尺度机器学习（atomistic machine learning）提供了一套概念性框架。