Proper Orthogonal Descriptors for Efficient and Accurate Interatomic Potentials

TL;DR

This paper introduces proper orthogonal descriptors (PODs) for representing atomic potential energy surfaces efficiently, enabling accurate interatomic potentials comparable to advanced machine learning methods.

Contribution

The paper develops a new set of descriptors based on the Karhunen-Loève expansion for improved efficiency and accuracy in interatomic potential modeling.

Findings

POD potentials achieve accuracy comparable to state-of-the-art ML potentials.

Rapid convergence of KL expansion allows small descriptor sets.

Validated on diverse elemental datasets including metals and semiconductors.

Abstract

We present the proper orthogonal descriptors for efficient and accuracy representation of the potential energy surface. The potential energy surface is represented as a many-body expansion of parametrized potentials in which the potentials are functions of atom positions and parameters. The Karhunen-Lo\`eve (KL) expansion is employed to decompose the parametrized potentials into a set of proper orthogonal descriptors (PODs). Because of the rapid convergence of the KL expansion, relevant snapshots can be sampled exhaustively to represent the atomic neighborhood environment accurately with a small number of descriptors. The proper orthogonal descriptors are used to develop interatomic potentials by using a linear expansion of the descriptors and determining the expansion coefficients from a weighted least-squares regression against a density functional theory (DFT) training set. We present a comprehensive evaluation of the POD potentials on previously published DFT data sets comprising Li, Mo, Cu, Ni, Si, Ge, and Ta elements. The data sets represent a diverse pool of metals, transition metals, and semiconductors. The accuracy of the POD potentials are comparable to that of state-of-the-art machine learning potentials such as the spectral neighbor analysis potential (SNAP) and the atomic cluster expansion (ACE).