Equivariant Graph Network Approximations of High-Degree Polynomials for Force Field Prediction

TL;DR

This paper introduces PACE, a novel equivariant graph network that leverages edge boosting and Atomic Cluster Expansion to accurately approximate high-degree equivariant polynomials, significantly improving force field predictions in molecular dynamics.

Contribution

The paper presents PACE, an innovative equivariant network that enhances polynomial approximation capabilities for better force field prediction in molecular simulations.

Findings

PACE achieves state-of-the-art accuracy in atomic energy and force prediction.

It demonstrates strong generalization across diverse molecular geometries and temperatures.

The method is validated on standard benchmarks with publicly available code.

Abstract

Recent advancements in equivariant deep models have shown promise in accurately predicting atomic potentials and force fields in molecular dynamics simulations. Using spherical harmonics (SH) and tensor products (TP), these equivariant networks gain enhanced physical understanding, like symmetries and many-body interactions. Beyond encoding physical insights, SH and TP are also crucial to represent equivariant polynomial functions. In this work, we analyze the equivariant polynomial functions for the equivariant architecture, and introduce a novel equivariant network, named PACE. The proposed PACE utilizes edge booster and the Atomic Cluster Expansion (ACE) technique to approximate a greater number of $SE(3) \times S_n$ equivariant polynomial functions with enhanced degrees. As experimented in commonly used benchmarks, PACE demonstrates state-of-the-art performance in predicting atomic energy and force fields, with robust generalization capability across various geometric distributions under molecular dynamics (MD) across different temperature conditions. Our code is publicly available as part of the AIRS library https://github.com/divelab/AIRS/.