Deep Variational Free Energy Approach to Dense Hydrogen

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.

7+5 pages, 3+4 figures, code: https://github.com/fermiflow/hydrogen

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Cited by in corpus (13)

• First principles simulations of dense hydrogen
• Neural Wave Functions for Superfluids
• Neural canonical transformations for vibrational spectra of molecules
• Training models using forces computed by stochastic electronic structure methods
• Electric Polarization from Many-Body Neural Network Ansatz
• Bounding free energy difference with flow matching
• Deep learning quantum Monte Carlo for solids
• Deep variational free energy prediction of dense hydrogen solid at 1200K
• Accurate and thermodynamically consistent hydrogen equation of state for planetary modeling with flow matching
• Expressivity of determinantal ansatzes for neural network wave functions
• Neural Wave Functions for High-Pressure Atomic Hydrogen
• Deep generative modelling of canonical ensemble with differentiable thermal properties
• A Denser Hydrogen Inferred from First-Principles Simulations Challenges Jupiter's Interior Models