High-pressure hydrogen by machine learning and quantum Monte Carlo

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 the smooth overlap of atomic position (SOAP) features, implemented here in a very efficient way. The key ingredients are as follows: (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 an 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 laboratory, and theory is still far from being conclusive.