Graph Atomic Cluster Expansion for semilocal interactions beyond equivariant message passing

TL;DR

This paper introduces a graph-based extension of the Atomic Cluster Expansion that efficiently models semilocal interactions in molecules and materials, improving accuracy and scalability over existing message-passing approaches.

Contribution

The authors develop a graph Atomic Cluster Expansion that incorporates graph basis functions, enabling transparent and efficient modeling of semilocal interactions beyond traditional message passing.

Findings

Achieves high accuracy on small molecules and carbon models.

Scales linearly with neighbors and graph layers.

Outperforms traditional message-passing ML potentials.

Abstract

The Atomic Cluster Expansion provides local, complete basis functions that enable efficient parametrization of many-atom interactions. We extend the Atomic Cluster Expansion to incorporate graph basis functions. This naturally leads to representations that enable the efficient description of semilocal interactions in physically and chemically transparent form. Simplification of the graph expansion by tensor decomposition results in an iterative procedure that comprises current message-passing machine learning interatomic potentials. We demonstrate the accuracy and efficiency of the graph Atomic Cluster Expansion for a number of small molecules, clusters and a general-purpose model for carbon. We further show that the graph Atomic Cluster Expansion scales linearly with number of neighbors and layer depth of the graph basis functions.