基于量子蒙特卡洛与$Δ$-学习的主氘雨贡纽曲线
Principal deuterium Hugoniot via Quantum Monte Carlo and $Δ$-learning
AI总结：
本文利用量子蒙特卡洛数据结合高斯核回归与$Δ$-学习训练机器学习势，在保持QMC精度的同时以平均场代价研究了高达$150$ GPa的主氘雨贡纽曲线，结果与实验吻合良好。
摘要：
我们提出了一项关于压力高达$150$ GPa的主氘雨贡纽曲线的研究，使用了以量子蒙特卡洛（QMC）能量、力和压力训练的机器学习势（MLPs）。具体而言，我们采用了一种最近提出的、基于高斯核回归与$Δ$-学习相结合的工作流程。通过充分利用该方法，我们在动力学中显式考虑了有限温度电子，其效应在温度高于$10$ kK时高度相关。我们的MLPs所得到的雨贡纽曲线与最新实验表现出良好的一致性，尤其是在低于60 GPa的区域。在更高压力下，我们的雨贡纽曲线比实验所得曲线略微更易压缩，但实验的不确定性通常随压力增大而增加。我们的工作表明，QMC可以成功地与$Δ$-学习相结合，以平均场计算的计算代价保持QMC精度，从而为不同热力学条件下的复杂扩展体系部署可靠的MLPs。
英文摘要：
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.
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