Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China (Dated: September 26, 2023) We developed a deep generative model-based variational free energy approach to the equations of state of dense hydrogen. We employ a normalizing flow network to model the proton Boltzmann distribution and a fermionic neural network to model the electron wave function at given proton positions. By jointly optimizing the two neural networks we reached a comparable variational free energy to the previous coupled electron-ion Monte Carlo calculation. The predicted equation of state of dense hydrogen under planetary conditions is denser than the findings of ab initio molecular dynamics calculation and empirical chemical model. Moreover, direct access to the entropy and free energy of dense hydrogen opens new opportunities in planetary modeling and high-pressure physics research. Hydrogen is the most abundant element in the visible universe.

Researchers have used a combination of AI and quantum mechanics to reveal how hydrogen gradually turns into a metal in giant planets. Dense metallic hydrogen – a phase of hydrogen which behaves like an electrical conductor – makes up the interior of giant planets, but it is difficult to study and poorly understood. By combining artificial intelligence and quantum mechanics, researchers have found how hydrogen becomes a metal under the extreme pressure conditions of these planets. The researchers, from the University of Cambridge, IBM Research and EPFL, used machine learning to mimic the interactions between hydrogen atoms in order to overcome the size and timescale limitations of even the most powerful supercomputers. They found that instead of happening as a sudden, or first-order, transition, the hydrogen changes in a smooth and gradual way. The results are reported in the journal Nature.

Dense metallic hydrogen--a phase of hydrogen which behaves like an electrical conductor--makes up the interior of giant planets, but it is difficult to study and poorly understood. By combining artificial intelligence and quantum mechanics, researchers have found how hydrogen becomes a metal under the extreme pressure conditions of these planets. The researchers, from the University of Cambridge, IBM Research and EPFL, used machine learning to mimic the interactions between hydrogen atoms in order to overcome the size and timescale limitations of even the most powerful supercomputers. They found that instead of happening as a sudden, or first-order, transition, the hydrogen changes in a smooth and gradual way. The results are reported in the journal Nature.