A Hessian-Based Assessment of Atomic Forces for Training Machine Learning Interatomic Potentials

TL;DR

This paper introduces a Hessian-based method to identify reliable molecular fragments for atomic force calculations, improving training data quality for machine learning interatomic potentials especially in large or complex systems.

Contribution

It presents a novel Hessian analysis technique to determine structurally converged fragments for accurate atomic force estimation in ML potentials.

Findings

The method effectively identifies local regions suitable for force calculations.

It estimates the significance of long-range interactions in complex systems.

Application to MOF-5 demonstrates its utility in hybrid materials.

Abstract

In recent years, many types of machine learning potentials (MLPs) have been introduced, which are able to represent high-dimensional potential-energy surfaces (PES) with close to first-principles accuracy. Most current MLPs rely on atomic energy contributions given as a function of the local chemical environments. Frequently, in addition to total energies also atomic forces are used to construct the potentials, as they provide detailed local information about the PES. Since many systems are too large for electronic structure calculations, obtaining reliable reference forces from smaller subsystems like molecular fragments or clusters can substantially simplify the construction of the training sets. Here, we propose a method to determine structurally converged molecular fragments providing reliable atomic forces based on an analysis of the Hessian. The method, which serves as a locality test and allows to estimate the importance of long-range interactions, is illustrated for a series of molecular model systems and the metal-organic framework MOF-5 as an example for a complex organic-inorganic hybrid material.