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.

arXiv comment7+5 pages, 3+4 figures, code: https://github.com/fermiflow/hydrogen

References in corpus (39)

• Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• Twist-averaged Boundary Conditions in Continuum Quantum Monte Carlo
• Solving Statistical Mechanics Using Variational Autoregressive Networks
• Flow-based generative models for Markov chain Monte Carlo in lattice field theory
• Equivariant flow-based sampling for lattice gauge theory
• Evidence for supercritical behavior of high-pressure liquid hydrogen
• Neural Network Renormalization Group
• Path Integral Monte Carlo Simulation of the Low-Density Hydrogen Plasma
• Stable liquid Hydrogen at high pressure by a novel ab-initio molecular dynamics
• Estimation of Thermodynamic Observables in Lattice Field Theories with Deep Generative Models
• Backflow Correlations for the Electron Gas and Metallic Hydrogen
• Asymptotically unbiased estimation of physical observables with neural samplers
• Algorithmic differentiation and the calculation of forces by quantum Monte Carlo
• The Penalty Method for Random Walks with Uncertain Energies
• Phase diagram of hydrogen and a hydrogen-helium mixture at planetary conditions by Quantum Monte Carlo simulations
• Jupiter internal structure: the effect of different equations of state
• Variational Density Matrix Method for Warm Condensed Matter and Application to Dense Hydrogen
• Coupled Electron Ion Monte Carlo Calculations of Dense Metallic Hydrogen
• Equation of state of metallic hydrogen from Coupled Electron-Ion Monte Carlo simulations
• Discovering Quantum Phase Transitions with Fermionic Neural Networks
• Fate of density functional theory in high-pressure solid hydrogen
• Unexpectedly high pressure for molecular dissociation in liquid hydrogen by a reliable electronic simulation
• Targeted free energy estimation via learned mappings
• Ab initio calculation of real solids via neural network ansatz
• Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas
• Electronic Density Response of Warm Dense Hydrogen: Ab initio Path Integral Monte Carlo Simulations
• Stable solid molecular hydrogen above 900K from a machine-learned potential trained with diffusion Quantum Monte Carlo
• Normalizing flows for atomic solids
• Linear scaling electronic structure calculations and accurate sampling with noisy forces
• High pressure hydrogen by machine learning and quantum Monte Carlo
• Trial wave functions for High-Pressure Metallic Hydrogen
• Ab-initio study of interacting fermions at finite temperature with neural canonical transformation
• Accelerated ab-initio Molecular Dynamics: probing the weak dispersive forces in dense liquid hydrogen
• Understanding high pressure hydrogen with a hierarchical machine-learned potential
• Interatomic force from neural network based variational quantum Monte Carlo
• Free energy calculation of crystalline solids using normalizing flow
• $m^{\ast }$ of two-dimensional electron gas: a neural canonical transformation study
• Neural-Network Quantum States for Periodic Systems in Continuous Space

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• 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