First-principles equation of state of CHON resin for inertial confinement fusion applications

Zhang, Shuai; Karasiev, Valentin V.; Shaffer, Nathaniel R.; Mihaylov, Deyan; Nichols, Kimberley; Paul, R.; Goshadze, R. M. N.; Ghosh, Maitrayee; Hinz, Joshua; Epstein, R.; Goedecker, Stefan; Hu, S. X.

doi:10.1103/physreve.106.045207

Cited by 8 publications

(3 citation statements)

References 73 publications

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“…, where 1228 are observations from experiments that reflect samples from the true underlying function f such that (E, P) = f(ρ, T), 63 are interpolated on the isochores 0.0196-0.0841 g cm −3 for temperature points 0.086-10.77 eV, and all remaining ones are extrapolations [54] from the observed data points. We consider extrapolations at density 1 × 10 −5 g cm −3 and temperature 8.62 × 10 −6 eV as boundary data points.…”

Section: Dataset Descriptionmentioning

confidence: 99%

Deep energy-pressure regression for a thermodynamically consistent EOS model

Yu,

Shankar Pandey,

Hinz

et al. 2024

Mach. Learn.: Sci. Technol.

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In this paper, we aim to explore novel machine learning (ML) techniques to facilitate and accelerate the construction of universal Equation-Of-State (EOS) models with a high accuracy while ensuring important thermodynamic consistency. When applying ML to fit a universal EOS model, there are two key requirements: (1) a high prediction accuracy to ensure precise estimation of relevant physics properties and (2) physical interpretability to support important physics-related downstream applications. We first identify a set of fundamental challenges from the accuracy perspective, including an extremely wide range of input/output space and highly sparse training data. We demonstrate that while a neural network (NN) model may fit the EOS data well, the black-box nature makes it difficult to provide physically interpretable results, leading to weak accountability of prediction results outside the training range and lack of guarantee to meet important thermodynamic consistency constraints. To this end, we propose a principled deep regression model that can be trained following a meta-learning style to predict the desired quantities with a high accuracy using scarce training data. We further introduce a uniquely designed kernel-based regularizer for accurate uncertainty quantification. An ensemble technique is leveraged to battle model overfitting with improved prediction stability. Auto-differentiation is conducted to verify that necessary thermodynamic consistency conditions are maintained. Our evaluation results show an excellent fit of the EOS table and the predicted values are ready to use for important physics-related tasks.

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Section: Dataset Descriptionmentioning

confidence: 99%

Deep energy-pressure regression for a thermodynamically consistent EOS model

Yu,

Shankar Pandey,

Hinz

et al. 2024

Mach. Learn.: Sci. Technol.

Self Cite

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“…All orbital-free and some part of orbital-based AIMD simulations were performed with the PROFESS@QUANTUM-ESPRESSO package. 18,32−34 using an Andersen or Berendsen thermostat 35,36 and all-electron local pseudopotentials 22,37 (LPPs).…”

Section: T H Imentioning

confidence: 99%

“…Two successful realizations of GGA-level functionals 19,20 improve the accuracy of theoretical predictions at intermediate temperatures compared to the TF approximation. A one-parameter tunable OF GGA functional 17 recently was used to construct a wide-range equation-of-state table for pure deuterium 21 and for a CHON quaternary compound, 22 demonstrating the practical utility and importance of orbital-free density functional development for inertial confinement fusion, plasma physics, and planetary science applications. However, the orbital-free GGA-level functionals usually become reasonably reliable starting at temperatures of a few tens of eV and increase the accuracy as T increases.…”

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confidence: 99%

Framework for Laplacian-Level Noninteracting Free-Energy Density Functionals

Karasiev,

Hinz,

Goshadze

2024

J. Phys. Chem. Lett.

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A framework for orbital-free Laplacian-level meta-generalized-gradient approximation (meta-GGA) for the noninteracting free-energy-density functionals based upon analysis of the fourth-order gradient expansion is developed. The framework presented here provides a new tool for developing advanced orbital-free thermal functionals at the meta-GGA level of theory. A nonempirical meta-GGA functional, which in the slowly varying density limit correctly reduces to the finite-temperature fourth-order gradient expansion for the noninteracting free energy, is constructed. Application to warm dense helium demonstrates that the developed meta-GGA functional drastically increases the accuracy of orbital-free-density functional theory simulations at temperatures below 40 eV as compared to the lower Thomas−Fermi and GGA rungs.

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Tunable noninteracting free-energy density functionals for high-energy-density physics applications

Karasiev,

Mihaylov,

Zhang

et al. 2024

Physics of Plasmas

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In this work, we introduce the concept of a tunable noninteracting free-energy density functional and present two examples realized: (i) via a simple one-parameter convex combination of two existing functionals and (ii) via the construction of a generalized gradient approximation (GGA) enhancement factor that contains one free parameter and is designed to satisfy a set of incorporated constraints. Functional (i), constructed as a combination of the local Thomas–Fermi and a pseudopotential-adapted GGA for the noninteracting free-energy, has already demonstrated its practical usability for establishing the high temperature end of the equation of state of deuterium [Phys. Rev. B 104, 144104 (2021)] and CHON resin [Phys. Rev. E 106, 045207 (2022)] for inertial confinement fusion applications. Hugoniot calculations for liquid deuterium are given as another example of how the application of computationally efficient orbital-free density functional theory (OF-DFT) can be utilized with the employment of the developed functionals. Once the functionals have been tuned such that the OF-DFT Hugoniot calculation matches the Kohn–Sham solution at some low-temperature point, agreement with the reference Kohn–Sham results for the rest of the high temperature Hugoniot path is very good with relative errors for compression and pressure on the order of 2% or less.

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First-principles equation of state of CHON resin for inertial confinement fusion applications

Cited by 8 publications

References 73 publications

Deep energy-pressure regression for a thermodynamically consistent EOS model

Deep energy-pressure regression for a thermodynamically consistent EOS model

Framework for Laplacian-Level Noninteracting Free-Energy Density Functionals

Tunable noninteracting free-energy density functionals for high-energy-density physics applications

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