Regularised Atomic Body-Ordered Permutation-Invariant Polynomials for the Construction of Interatomic Potentials

TL;DR

This paper introduces a systematic, permutation-invariant polynomial basis called aPIPs for constructing interatomic potentials, offering improved transferability and interpretability over kernel and neural network models.

Contribution

The authors develop a new atomic body-ordered polynomial basis that preserves symmetry and enables low-dimensional, interpretable, and transferable interatomic potentials.

Findings

aPIPs achieve better transferability than kernel-based models.

The polynomial basis allows interpretability of atomic contributions.

Low body-order terms are sufficient for accurate modeling.

Abstract

We investigate the use of invariant polynomials in the construction of data-driven interatomic potentials for material systems. The "atomic body-ordered permutation-invariant polynomials" (aPIPs) comprise a systematic basis and are constructed to preserve the symmetry of the potential energy function with respect to rotations and permutations. In contrast to kernel based and artificial neural network models, the explicit decomposition of the total energy as a sum of atomic body-ordered terms allows to keep the dimensionality of the fit reasonably low, up to just 10 for the 5-body terms. The explainability of the potential is aided by this decomposition, as the low body-order components can be studied and interpreted independently. Moreover, although polynomial basis functions are thought to extrapolate poorly, we show that the low dimensionality combined with careful regularisation actually leads to better transferability than the high dimensional, kernel based Gaussian Approximation Potential.