Phase Transitions of Zirconia: Machine-Learned Force Fields Beyond Density Functional Theory

TL;DR

This paper introduces a machine learning approach that combines active learning and $\Delta$-learning to create force fields for zirconia that surpass DFT accuracy by efficiently incorporating RPA calculations.

Contribution

The authors develop a novel MLFF generation method that integrates on-the-fly learning with RPA corrections, enabling high-accuracy simulations beyond DFT at reduced computational cost.

Findings

Successfully reproduces high-level quantum calculations for zirconia

Efficiently models phase transitions of zirconia

Reduces computational cost of RPA-based force fields

Abstract

We present an approach to generate machine-learned force fields (MLFF) with beyond density functional theory (DFT) accuracy. Our approach combines on-the-fly active learning and $\Delta$-machine learning in order to generate an MLFF for zirconia based on the random phase approximation (RPA). Specifically, an MLFF trained on-the-fly during DFT based molecular dynamics simulations is corrected by another MLFF that is trained on the differences between RPA and DFT calculated energies, forces and stress tensors. Thanks to the relatively smooth nature of the differences, the expensive RPA calculations are performed only on a small number of representative structures of small unit cells. These structures are determined by a singular value decomposition rank compression of the kernel matrix with low spatial resolution. This dramatically reduces the computational cost and allows us to generate an MLFF fully capable of reproducing high-level quantum-mechanical calculations beyond DFT. We carefully validate our approach and demonstrate its success in studying the phase transitions of zirconia.