HerEOS: A framework for consistent treatment of the Equation of State in ALE hydrodynamics

Zeman, Michal; Holec, Milan; Váchal, Pavel

doi:10.1016/j.camwa.2018.10.014

Cited by 4 publications

References 17 publications

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Neural network representations of multiphase Equations of State

Kevrekidis,

Serino,

Kaltenborn

et al. 2024

Sci Rep

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Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general Equation of State model are adherence to the Laws of Thermodynamics, incorporation of phase transitions, and multiscale accuracy. Analytic models that adhere to all three are hard to develop and cumbersome to work with, often resulting in sacrificing one of these elements for the sake of efficiency. In this work, two deep-learning methods are proposed that provably satisfy the first and second conditions on a large-enough region of thermodynamic variable space. The first is based on learning the generating function (thermodynamic potential) while the second is based on structure-preserving, symplectic neural networks, respectively allowing modifications near or on phase transition regions. They can be used either “from scratch” to learn a full Equation of State, or in conjunction with a pre-existing consistent model, functioning as a modification that better adheres to experimental data. We formulate the theory and provide several computational examples to justify both approaches, highlighting their advantages and shortcomings.

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Neural network representations of multiphase Equations of State

Kevrekidis,

Serino,

Kaltenborn

et al. 2024

Sci Rep

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Second-order magnetic field generation model for Lagrangian and ALE plasma simulations

Kucharik,

Nikl,

Limpouch

2023

AIP Conference Proceedings

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The development of thermodynamically consistent and physics-informed equation-of-state model through machine learning

Hinz,

Yu,

Pandey

et al. 2024

APL Machine Learning

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Ab initio molecular dynamics (AIMD) simulations have become an important tool used in the construction of equations of state (EOS) tables for warm dense matter. Due to computational costs, only a limited number of system state conditions can be simulated, and the remaining EOS surface must be interpolated for use in radiation-hydrodynamic simulations of experiments. In this work, we develop a thermodynamically consistent EOS model that utilizes a physics-informed machine learning approach to implicitly learn the underlying Helmholtz free-energy from AIMD generated energies and pressures. The model, referred to as PIML-EOS, was trained and tested on warm dense polystyrene producing a fit within a 1% relative error for both energy and pressure and is shown to satisfy both the Maxwell and Gibbs–Duhem relations. In addition, we provide a path toward obtaining thermodynamic quantities, such as the total entropy and chemical potential (containing both ionic and electronic contributions), which are not available from current AIMD simulations.

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HerEOS: A framework for consistent treatment of the Equation of State in ALE hydrodynamics

Cited by 4 publications

References 17 publications

Neural network representations of multiphase Equations of State

Neural network representations of multiphase Equations of State

Second-order magnetic field generation model for Lagrangian and ALE plasma simulations

The development of thermodynamically consistent and physics-informed equation-of-state model through machine learning

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