Normalizing flows for atomic solids

TL;DR

This paper introduces a normalizing flow-based machine learning model for atomic solids that accurately estimates free energies and reproduces structural properties without requiring ground-truth samples or multi-staging.

Contribution

It presents a novel application of normalizing flows to model atomic solids, enabling direct free energy estimation and high-quality sampling without ground-truth data.

Findings

Accurately estimates Helmholtz free energies for ice and Lennard-Jones systems.

Generates samples nearly indistinguishable from molecular dynamics.

Achieves high-quality results without multi-staging.

Abstract

We present a machine-learning approach, based on normalizing flows, for modelling atomic solids. Our model transforms an analytically tractable base distribution into the target solid without requiring ground-truth samples for training. We report Helmholtz free energy estimates for cubic and hexagonal ice modelled as monatomic water as well as for a truncated and shifted Lennard-Jones system, and find them to be in excellent agreement with literature values and with estimates from established baseline methods. We further investigate structural properties and show that the model samples are nearly indistinguishable from the ones obtained with molecular dynamics. Our results thus demonstrate that normalizing flows can provide high-quality samples and free energy estimates without the need for multi-staging.