Principal deuterium Hugoniot via Quantum Monte Carlo and $Δ$-learning
This work addresses the problem of simulating complex extended systems under varying thermodynamic conditions for researchers in computational physics, demonstrating an incremental improvement by combining existing methods.
The study tackled predicting the principal deuterium Hugoniot up to 150 GPa using machine learning potentials trained with Quantum Monte Carlo data, achieving good agreement with experiments below 60 GPa but slightly more compressible results at higher pressures.
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 $Δ$-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 $Δ$-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.