Deep Variational Free Energy Approach to Dense Hydrogen

TL;DR

This paper introduces a deep generative variational approach using neural networks to model dense hydrogen's equation of state, providing accurate predictions and new insights for planetary and high-pressure physics.

Contribution

It presents a novel deep variational free energy method employing neural networks for modeling dense hydrogen, achieving comparable accuracy to established Monte Carlo methods.

Findings

Predicted dense hydrogen is denser than previous models.

Method provides direct access to entropy and free energy.

Results are relevant for planetary and high-pressure physics.

Abstract

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.