mlsanityData to 7 Oct 2026

Deep Variational Free Energy Approach to Dense Hydrogen

arXiv 2209.06095 ↗First posted 13 Sep 2022cond-mat.str-el cs.LG physics.comp-phcited by 6

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Abstract (arXiv)

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.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 23 of its 77 references that are in the map. First posted on arXiv 13 Sep 2022.

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23 of 77 references.

References · 23

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11 more
  1. 2018Neural Network Renormalization Groupcited by 48
  2. 2021Normalizing flows for atomic solidscited by 39
  3. 2021Ab-Initio Potential Energy Surfaces by Pairing GNNs with Neural Wave Functionscited by 36
  4. 2018Monge-Amp`ere Flow for Generative Modelingcited by 33
  5. 2022Discovering Quantum Phase Transitions with Fermionic Neural Networkscited by 25
  6. 2020Scalable Normalizing Flows for Permutation Invariant Densitiescited by 22
  7. 2021Solving the electronic Schr"odinger equation for multiple nuclear geometries with weight-sharing deep neural networkscited by 22
  8. 2020Exchangeable Neural ODE for Set Modelingcited by 19
  9. 2021Ab-initio study of interacting fermions at finite temperature with neural canonical transformationcited by 16
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  11. 2021High pressure hydrogen by machine learning and quantum Monte Carlocited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 1; 2025: 2; 2026: 2.

6 papers.

  1. 2023Pairing-based graph neural network for simulating quantum materialscited by 9
  2. 2024Deep generative modelling of canonical ensemble with differentiable thermal propertiescited by 2
  3. 2026Differentiable free energy surface: a variational approach to directly observing rare events using generative deep-learning modelscited by 1
  4. 2026Generative Path-Finding Method for Wasserstein Gradient Flowcited by 1
  5. 2025Accurate and thermodynamically consistent hydrogen equation of state for planetary modeling with flow matchingcited by 0
  6. 2025Revisiting the Broken Symmetry Phase of Solid Hydrogen: A Neural Network Variational Monte Carlo Studycited by 0