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Xie H, Li ZH, Wang H, Zhang L, Wang L. Deep Variational Free Energy Approach to Dense Hydrogen. PHYSICAL REVIEW LETTERS 2023; 131:126501. [PMID: 37802941 DOI: 10.1103/physrevlett.131.126501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2022] [Revised: 08/01/2023] [Accepted: 08/14/2023] [Indexed: 10/08/2023]
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.
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Affiliation(s)
- Hao Xie
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Zi-Hang Li
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Han Wang
- Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Fenghao East Road 2, Beijing 100094, China
| | - Linfeng Zhang
- DP Technology, Beijing 100080, China
- AI for Science Institute, Beijing 100080, China
| | - Lei Wang
- Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
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Lyne AM, Girolami M, Atchadé Y, Strathmann H, Simpson D. On Russian Roulette Estimates for Bayesian Inference with Doubly-Intractable Likelihoods. Stat Sci 2015. [DOI: 10.1214/15-sts523] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Beutier J, Vuilleumier R, Bonella S, Ciccotti G. Gas phase infrared spectra from quasi-classical Kubo time correlation functions. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1064550] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- J. Beutier
- Département de Chimie, École Normale Supérieure-PSL Research University , Paris, France
- Département de Chimie, Sorbonne Universités , UPMC Univ Paris 06, Paris, France
- Département de Chimie, CNRS , UMR 8640 PASTEUR, Paris, France
- Dipartimento di Fisica, Università di Roma ‘La Sapienza’ , Roma, Italy
| | - R. Vuilleumier
- Département de Chimie, École Normale Supérieure-PSL Research University , Paris, France
- Département de Chimie, Sorbonne Universités , UPMC Univ Paris 06, Paris, France
- Département de Chimie, CNRS , UMR 8640 PASTEUR, Paris, France
| | - S. Bonella
- Department of Chemistry, CECAM Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne , Batochime, Lausanne, Switzerland
| | - G. Ciccotti
- Dipartimento di Fisica, Università di Roma ‘La Sapienza’ , Roma, Italy
- School of Physics, University College of Dublin UCD , Dublin 4, Ireland
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Beutier J, Borgis D, Vuilleumier R, Bonella S. Computing thermal Wigner densities with the phase integration method. J Chem Phys 2014; 141:084102. [DOI: 10.1063/1.4892597] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
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Beutier J, Monteferrante M, Bonella S, Vuilleumier R, Ciccotti G. Gas phase infrared spectra via the phase integration quasi-classical method. MOLECULAR SIMULATION 2013. [DOI: 10.1080/08927022.2013.843776] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- J. Beutier
- Département de Chimie, UMR 8640 CNRS-ENS-UPMC, École Normale Supérieure, 24 rue Lhomond, 75005, Paris, France
| | - M. Monteferrante
- Dipartimento di Fisica and CNISM Unità 1, Università di Roma ‘La Sapienza’, Ple A. Moro 2, 00185, Rome, Italy
| | - S. Bonella
- Dipartimento di Fisica and CNISM Unità 1, Università di Roma ‘La Sapienza’, Ple A. Moro 2, 00185, Rome, Italy
| | - R. Vuilleumier
- Département de Chimie, UMR 8640 CNRS-ENS-UPMC, École Normale Supérieure, 24 rue Lhomond, 75005, Paris, France
| | - G. Ciccotti
- Dipartimento di Fisica and CNISM Unità 1, Università di Roma ‘La Sapienza’, Ple A. Moro 2, 00185, Rome, Italy
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Monteferrante M, Bonella S, Ciccotti G. Quantum dynamical structure factor of liquid neon via a quasiclassical symmetrized method. J Chem Phys 2013; 138:054118. [DOI: 10.1063/1.4789760] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Monteferrante M, Bonella S, Ciccotti G. Linearized symmetrized quantum time correlation functions calculation via phase pre-averaging. Mol Phys 2011. [DOI: 10.1080/00268976.2011.619506] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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Ball RC, Fink TMA, Bowler NE. Stochastic annealing. PHYSICAL REVIEW LETTERS 2003; 91:030201. [PMID: 12906405 DOI: 10.1103/physrevlett.91.030201] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2003] [Indexed: 05/24/2023]
Abstract
We show how to simulate a system in thermal equilibrium when the energy cannot be evaluated exactly: the error distribution needs to be symmetric, but it does not need to be known. We also solve the Ceperley-Dewing version of this problem, where the error distribution is taken to be fully known. These underlying ideas give an effective optimization strategy for problems where the evaluation of each design can be sampled only statistically, including an application to protein folding.
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Affiliation(s)
- Robin C Ball
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom.
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Ceperley DM, Dewing M. The penalty method for random walks with uncertain energies. J Chem Phys 1999. [DOI: 10.1063/1.478034] [Citation(s) in RCA: 57] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Horváth I, Kennedy A, Sint S. A new exact method for dynamical fermion computations with non-local actions. ACTA ACUST UNITED AC 1999. [DOI: 10.1016/s0920-5632(99)85217-7] [Citation(s) in RCA: 56] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Doll J, Freeman D. Decisions, decisions: Noise and its effects on integral Monte Carlo algorithms. Chem Phys Lett 1994. [DOI: 10.1016/0009-2614(94)00847-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Doll JD, Beck TL, Freeman DL. Quantum Monte Carlo dynamics: The stationary phase Monte Carlo path integral calculation of finite temperature time correlation functions. J Chem Phys 1988. [DOI: 10.1063/1.455551] [Citation(s) in RCA: 74] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Kennedy AD, Kuti J, Meyer S, Pendleton BJ. Quarks, noise, and the lattice. PHYSICAL REVIEW. D, PARTICLES AND FIELDS 1988; 38:627-635. [PMID: 9959185 DOI: 10.1103/physrevd.38.627] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Doll JD, Coalson RD, Freeman DL. Toward a Monte Carlo theory of quantum dynamics. J Chem Phys 1987. [DOI: 10.1063/1.453226] [Citation(s) in RCA: 75] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Haraguchi M, Hege HC, Linke V, Nakamura A, Stamatescu IO. Monte Carlo calculation of lattice QCD with exact treatment of dynamical quark loops. PHYSICAL REVIEW LETTERS 1987; 58:2011-2014. [PMID: 10034627 DOI: 10.1103/physrevlett.58.2011] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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