Simulations Using Machine Learning Models Predict New Phase for Solid Hydrogen

Hydrogen, the most abundant element in the universe, is found everywhere, from the dust that occupies most of space, to the cores of stars, to much of the matter on Earth. This is reason enough to study hydrogen, but its individual atoms are also the simplest element with only one proton and one electron. For David Ceperley, professor of physics at the University of Illinois at Urbana and his School of Champaign, this makes hydrogen a natural starting point for formulating and testing the theory of matter.

Ceperley, who is also a member of the Illinois Center for Quantum Information Science and Technology, uses computer simulations to show how hydrogen atoms interact and bond to form different phases of matter, including solids, liquids, and gases. is researching However, a true understanding of these phenomena requires quantum mechanics, and quantum mechanical simulations are costly. To simplify the task, Ceperley and his collaborators developed a machine learning technique that can perform quantum mechanical simulations on unprecedented numbers of atoms.they reported physical review letter Their method discovered a new kind of high-pressure solid-state hydrogen that past theories and experiments had missed.

“Machine learning has taught us a lot,” said Ceperley. “Previous simulations showed signs of new behavior, but they were unreliable because they were only able to accommodate a small number of atoms. We used machine learning models to maximize the most accurate methods and I was able to see if it was happening, it really was.”

Hydrogen atoms form a quantum mechanical system, but it is very difficult even for computers to fully capture their quantum behavior. State-of-the-art techniques such as Quantum Monte Carlo (QMC) can adequately simulate hundreds of atoms, but understanding large-scale phase behavior requires simulating thousands of atoms over long periods of time. there is.

To make QMC more versatile, two former graduate students, Hongwei Niu and Yubo Yang, developed machine learning models trained on QMC simulations that can accommodate more atoms than QMC itself. He then used this model with postdoctoral fellow Scott Jensen to study how a solid phase of hydrogen that forms at very high pressures melts.

When the three people changed the temperature and pressure and grasped the whole picture, they noticed that there was something wrong with the solid phase. Molecules in solid hydrogen are usually nearly spherical, forming a configuration called hexagonal close-packing (Ceperley compared it to stacked oranges), but the researchers observed stages in which the molecules became elliptical. Did. Ceperley described them as egg-like.

“We started with the unambitious goal of improving the theory of what we know,” Jensen recalls. It was interesting: this new behavior appeared, and in fact it was the dominant behavior at high temperature and pressure, and the old theory had no hint.”

To validate the results, the researchers used data from density functional theory to train a machine learning model. Density Functional Theory is a widely used technique that is not as accurate as QMC but can accommodate a larger number of atoms. They found that a simplified machine learning model perfectly reproduced the results of the Standard Model. The researchers concluded that his large-scale QMC simulations powered by machine learning can explain effects and make predictions that standard methods cannot.

This work started a conversation between Ceperley’s collaborators and several experimentalists. Experimental results are limited because high-pressure measurements of hydrogen are difficult to perform. The new predictions have prompted several groups to revisit the issue and investigate more carefully the behavior of hydrogen under extreme conditions.

Ceperley said understanding hydrogen at high temperatures and pressures will help us better understand the gas planets Jupiter and Saturn, which are mostly made of hydrogen. Jensen added that the “simplicity” of hydrogen makes the material important to study. “We want to understand everything, so we should start with systems that we can attack,” he said. “Hydrogen is simple, so it’s worth knowing that you can deal with it.”