Fast proper orthogonal descriptors for many-body interatomic potentials

TL;DR

This paper introduces a fast, scalable method for generating proper orthogonal descriptors that efficiently represent atomic environments, improving the construction of many-body interatomic potentials for materials science.

Contribution

A novel algorithm that computes proper orthogonal descriptors with linear complexity, enabling efficient and scalable many-body potential development.

Findings

Method reduces computational complexity from exponential to linear.

Demonstrated on Tantalum DFT data, outperforming existing potentials.

Provides a systematic framework for constructing new interatomic potentials.

Abstract

The development of differentiable invariant descriptors for accurate representations of atomic environments plays a central role in the success of interatomic potentials for chemistry and materials science. We introduce a method to generate fast proper orthogonal descriptors for the construction of many-body interatomic potentials and discuss its relation to exising empirical and machine learning interatomic potentials. A traditional way of implementing the proper orthogonal descriptors has a computational complexity that scales exponentially with the body order in terms of the number of neighbors. We present an algorithm to compute the proper orthogonal descriptors with a computational complexity that scales linearly with the number of neighbors irrespective of the body order. We show that our method can enable a more efficient implementation for a number of existing potentials and provide a scalable systematic framework to construct new many-body potentials. The new potentials are demonstrated on a data set of density functional theory calculations for Tantalum and compared with other interatomic potentials.