Deep Variational Free Energy Calculation of Hydrogen Hugoniot
This work addresses discrepancies in theoretical and experimental data for hydrogen/deuterium in warm dense matter, which is important for high-energy-density physics and astrophysics applications, though it appears incremental as it builds on existing variational and neural network methods.
The researchers tackled the problem of computing the equation of state for hydrogen in warm dense matter by developing a deep variational free energy framework that uses three neural networks to model nuclei and electrons, achieving results that provide a benchmark for deuterium in this region.
We develop a deep variational free energy framework to compute the equation of state of hydrogen in the warm dense matter region. This method parameterizes the variational density matrix of hydrogen nuclei and electrons at finite temperature using three deep generative models: a normalizing flow model that represents the Boltzmann distribution of the classical nuclei, an autoregressive transformer that models the distribution of electrons in excited states, and a permutational equivariant flow model that constructs backflow coordinates for electrons in Hartree-Fock orbitals. By jointly optimizing the three neural networks to minimize the variational free energy, we obtain the equation of state and related thermodynamic properties of dense hydrogen. We compare our results with other theoretical and experimental results on the deuterium Hugoniot curve, aiming to resolve existing discrepancies. The calculated results provide a valuable benchmark for deuterium in the warm dense matter region.