Deep Variational Free Energy Approach to Dense Hydrogen
This work addresses the challenge of modeling dense hydrogen for planetary science and high-pressure physics, representing an incremental improvement with a novel hybrid method.
The researchers tackled the problem of predicting the equation of state for dense hydrogen under planetary conditions using a deep generative model-based variational free energy approach, achieving a comparable variational free energy to previous Monte Carlo calculations and predicting a denser state than other methods.
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.