High pressure hydrogen by machine learning and quantum Monte Carlo

TL;DR

A technique combining the accuracy of quantum Monte Carlo in describing the electron correlation with the efficiency of a Machine Learning Potential (MLP) is developed, and kernel regression in combination with SOAP features are used.

Abstract

We have developed a technique combining the accuracy of quantum Monte Carlo in describing the electron correlation with the efficiency of a Machine Learning Potential (MLP). We use kernel regression in combination with SOAP (Smooth Overlap of Atomic Position) features, implemented here in a very efficient way. The key ingredients are: i) a sparsification technique, based on farthest point sampling, ensuring generality and transferability of our MLPs and ii) the so called $Δ$-learning, allowing a small training data set, a fundamental property for highly accurate but computationally demanding calculations, such as the ones based on quantum Monte Carlo. As the first application we present a benchmark study of the liquid-liquid transition of high-pressure hydrogen and show the quality of our MLP, by emphasizing the importance of high accuracy for this very debated subject, where experiments are difficult in the lab, and theory is still far from being conclusive.

Figures (3)

• Figure 1: (a) Comparison between molecular dynamics simulations via MLPs (cyan and green lines for our GKR, yellow line for the NN-MLP of Chen et al. 2020CHE and the AIMD PBE and LDA references (blue and red lines, respectively) for 128 H at 1400 K. The values of the hyper-parameters used for all the MLPs are reported in the SI. (b) EOS of 128 H at 1000K using DFT with PBE and BLYP functionals and the appropriate ML corrections.
• Figure 2: (a) Isotherm curves at different values of temperature for a system of 256 hydrogen atoms. Dashed lines represent the transition pressure obtained when $p$ becomes constant (within the error bars) in some range of densities. (b) Isotherm for $T$ = 1200 K (black line). The molecular fraction (defined in the text) as a function of the Wigner Seitz radius $r_s$ (red line) and the radial distribution functions for $r_s$ = 1.415 and $r_s$ = 1.435 (boxes in the bottom) are also shown.
• Figure 3: Proposed transition lines of the LLT in hydrogen. Our results (red circles) . Previous (classical) QMC calculations taken from Refs. 2018MAZ and 2016PIE (light green and dark green squares). DFT results for several functionals taken from Ref. 2015KNU (black lines). DAC experimental data taken from Refs. 2015OHT and 2016ZAG (pink and orange triangles). Dynamical compression experiments taken from Refs. 2015KNU and 2018CEL (blue triangles and violet stars, respectively). The literature data were digitalized using WebPlotDigitizer 2020ROH.