# High pressure hydrogen by machine learning and quantum Monte Carlo

arXiv: https://arxiv.org/abs/2112.11099 · HTML: https://mlsanity.com/paper/2112.11099/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 28 references that are in the map.
- First posted on arXiv 21 Dec 2021.

## Built on by (most cited first, 3 of 3)

- [Deep Variational Free Energy Approach to Dense Hydrogen](https://mlsanity.com/paper/2209.06095/) (2022)
- [Hydrogen under Pressure as a Benchmark for Machine-Learning Interatomic Potentials](https://mlsanity.com/paper/2409.13390/) (2024)
- [Principal deuterium Hugoniot via Quantum Monte Carlo and Delta-learning](https://mlsanity.com/paper/2301.03570/) (2023)

## Abstract (arXiv)

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 Delta-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.