High pressure hydrogen by machine learning and quantum Monte Carlo

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 linear regression in combination with SOAP (Smooth Overlap Atomic Position) approach, 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 ∆-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 a 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.

A structural optimization algorithm with stochastic forces and stresses

“…One of the frontiers in quantum science is to develop computational methods which can go beyond DFT-based methods in accuracy, with reasonable computational cost. Progress has been made from several fronts, for example, with the combination of DFT and the GW [8], approaches based on dynamical mean field theory (DMFT) [9], quantum Monte Carlo methods [10][11][12][13], quantum chemistry methods [14,15], etc. For instance, the computation of forces and stresses with plane-wave auxiliary field quantum Monte Carlo (PW-AFQMC) [11,16] has recently been demonstrated [17], paving the way for ab initio geometry optimization in this many-body framework.…”

Onset of metallic transition in molecular liquid hydrogen

“…Theoretically, LLPT of hydrogen is often described as a transition from the insulating molecular phase to the metallic atomic phase, supported by computational simulations [12][13][14][15][16][17][18][19][20], indicating or assuming that the molecular-atomic transition (MAT) and the insulatingmetallic transition (IMT) occur simultaneously. In recent years, new attention has been paid to the supercritical behavior and the location of liquid-liquid critical point in the computational community, involving studies using density functional theory (DFT), machine learning potentials and quantum Monte Carlo (QMC) [21][22][23][24][25][26]. Based on these studies, it is understood that below the critical point, if the temperature is above the melting line, LLPT is one phase transition where H 2 molecule dissociates and metallizes simultaneously; but above the critical point, the dissociation and metallization happen in a smooth and continuous manner.…”