Hydrogen is a ubiquitous element found throughout the universe, from the outer space dust to the cores of stars and even many substances on Earth. Its simplicity, with just one proton and one electron, makes it an ideal starting point for formulating and testing theories of matter. David Ceperley, a physics professor at the University of Illinois Urbana-Champaign, uses computer simulations to study how hydrogen atoms interact and combine to form different phases of matter. However, quantum mechanical simulations are expensive, and a true understanding of these phenomena requires quantum mechanics.
To simplify the task, Ceperley and his team developed a machine learning technique that allows quantum mechanical simulations to be performed with an unprecedented number of atoms. They discovered a new kind of high-pressure solid hydrogen that past theory and experiments had missed. With their machine learning model, they could take full advantage of the most accurate methods and observe new behavior that had been missed in previous simulations.
Hydrogen atoms form a quantum mechanical system, but capturing their full quantum behavior is very difficult even on computers. The researchers developed a machine learning model trained with quantum Monte Carlo (QMC) simulations capable of accommodating many more atoms than QMC by itself. They then used the model to study how the solid phase of hydrogen that forms at very high pressures melts. They observed a phase where the molecules become oblong figures, which was the dominant behavior at high temperatures and pressures, something there was no hint of in older theory.
To verify their results, the researchers trained their machine learning model with data from density functional theory, a widely used technique that is less accurate than QMC but can accommodate many more atoms. They found that the simplified machine learning model perfectly reproduced the results of standard theory.
This work has inspired experimentalists to revisit the problem and more carefully explore hydrogen’s behavior under extreme conditions. Understanding hydrogen under high temperatures and pressures will enhance our understanding of gaseous planets primarily made of hydrogen, such as Jupiter and Saturn.