Using machine learning to solve a dense hydrogen conundrum

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Hydrogen is the simplest element in the universe, yet its behavior in extreme conditions such as very high pressure and temperature is still far from being well understood. Dense hydrogen constitutes the bulk of the content of giant gas planets and brown dwarf stars and it’s a material of interest for both fundamental physics and technological applications such as in jet fuel or as a possible room-temperature superconductor.

In a collaboration with scientists from École Polytechnique Fédérale de Lausanne (EPFL) and University of Cambridge, we report in the journal Nature on using machine learning techniques for unprecedented large-scale simulations of dense hydrogen, revealing for the first time the presence of a supercritical state and a continuous liquid-liquid transition at megabar pressures, with important implications for planetary science, fundamental physics and technological applications. (Watch this video for a 3-minute summary of the paper.)

Mutually contradicting experimental results

Modelling the dynamics of giant gas planets and stars requires a profound understanding of the way elements like hydrogen and helium behave at extremely high pressures and temperatures. These are conditions that can’t be easily reproduced in the controlled environment of a laboratory. However, in laboratory experiments conducted in the last few years, several research groups have managed to recreate those conditions and have come to conclude that hydrogen undergoes a sharp liquid-liquid transition between a metallic and an insulating state at the pressures occurring inside giant planets like Jupiter and Saturn. But those experiments have turned out to yield contradictory results as to how and at what exact pressures that transition occurs. That has triggered a lively controversy in the high pressure physics community.

Neural network architecture helps prevent limitations of previous simulations

Our new research could help solve the riddle by reconciling the discrepancies in the interpretation of previous experimental data. The simulations now show that dense hydrogen exhibits in fact a smooth crossover from insulating to metallic behavior rather than an abrupt first-order phase transition. We reach that conclusion after scanning a large portion of the phase diagram of hydrogen using a neural network architecture to generate a machine learning model of the hydrogen potential. The model increased the efficiency of the computations by several orders of magnitude, allowing for the accurate, fully quantum mechanical treatment of the system across an unprecedentedly large volume and time scale. That way, a simulation that would have required hundreds of millions of CPU-years was performed at the cost of only millions of CPU-hours.

A supercritical state rules out sharp liquid-liquid transition

Our results provide evidence for a supercritical state of hydrogen which in turn rules out a  first-order liquid-liquid transition between insulating molecular hydrogen and metallic atomic hydrogen. According to our equilibrium molecular dynamics simulations, computed after having determined the melting line of hydrogen with our machine learning potential, such a sharp transition is prevented by freezing.

A good start and next steps

This work highlights how machine learning can help accelerate scientific discovery, in particular in areas where laboratory experiments are very difficult to carry out and traditional computing techniques fall short of the performance requirements for large-scale simulations. But this is just thee beginning. In the future, we intend to build on these results and use the capabilities afforded by neural networks to continue exploring the physics of dense hydrogen in the interior of giant gas planets and brown dwarfs, as well as extending our study to mixtures of hydrogen and helium, which we expect to give us a more complete understanding of the dynamics in those systems.

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