Principal deuterium Hugoniot via Quantum Monte Carlo and $\Delta$-learning

TL;DR

This study uses Quantum Monte Carlo-based machine learning potentials with $ Delta$-learning to accurately model the principal deuterium Hugoniot up to 150 GPa, achieving good agreement with experiments and demonstrating a cost-effective approach for complex systems.

Contribution

The paper introduces a novel workflow combining QMC energies with $ Delta$-learning to develop reliable machine learning potentials for high-pressure deuterium.

Findings

Hugoniot curve matches recent experimental data below 60 GPa.

At higher pressures, the model predicts slightly more compressibility.

The approach maintains QMC accuracy at reduced computational cost.

Abstract

We present a study of the principal deuterium Hugoniot for pressures up to $150$ GPa, using Machine Learning potentials (MLPs) trained with Quantum Monte Carlo (QMC) energies, forces and pressures. In particular, we adopted a recently proposed workflow based on the combination of Gaussian kernel regression and $\Delta$-learning. By fully taking advantage of this method, we explicitly considered finite-temperature electrons in the dynamics, whose effects are highly relevant for temperatures above $10$ kK. The Hugoniot curve obtained by our MLPs shows a good agreement with the most recent experiments, particularly in the region below 60 GPa. At larger pressures, our Hugoniot curve is slightly more compressible than the one yielded by experiments, whose uncertainties generally increase, however, with pressure. Our work demonstrates that QMC can be successfully combined with $\Delta$-learning to deploy reliable MLPs for complex extended systems across different thermodynamic conditions, by keeping the QMC precision at the computational cost of a mean-field calculation.