Physics-enhanced neural networks for equation-of-state calculations

Abstract

Rapid access to accurate equation-of-state (EOS) data is crucial in the warm-dense matter regime, as it is employed in various applications, such as providing input for hydrodynamic codes to model inertial confinement fusion processes. In this study, we develop neural network models for predicting the EOS based on first-principles data. The first model utilizes basic physical properties, while the second model incorporates more sophisticated physical information, using output from average-atom calculations as features. Average-atom models are often noted for providing a reasonable balance of accuracy and speed; however, our comparison of average-atom models and higher-fidelity calculations shows that more accurate models are required in the warm-dense matter regime. Both the neural network models we propose, particularly the physics-enhanced one, demonstrate significant potential as accurate and efficient methods for computing EOS data in warm-dense matter.

arXiv comment57 pages, 16 figures. Accepted for publication in Machine Learning: Science and Technology

References in corpus (40)

• Adam: A Method for Stochastic Optimization
• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Array Programming with NumPy
• Crystal Graph Convolutional Neural Networks for an Accurate and Interpretable Prediction of Material Properties
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Recent Advances and Applications of Deep Learning Methods in Materials Science
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• The Uniform Electron Gas at Warm Dense Matter Conditions
• FPEOS: A First-Principles Equation of State Table of Deuterium for Inertial Confinement Fusion Applications
• Ab initio simulation of warm dense matter
• The importance of finite-temperature exchange-correlation for warm dense matter calculations
• Issues and Challenges in Orbital-free Density Functional Calculations
• Non-empirical Generalized Gradient Approximation Free Energy Functional for Orbital-free Simulations
• Machine learning and density functional theory
• A Deep Dive into Machine Learning Density Functional Theory for Materials Science and Chemistry
• The data-driven future of high energy density physics
• First-Principles Equation of State Database for Warm Dense Matter Computation
• Effective Static Approximation: A Fast and Reliable Tool for Warm Dense Matter Theory
• Accurate Temperature Diagnostics for Matter under Extreme Conditions
• Electron-ion scattering in dense multi-component plasmas: application to the outer crust of an accreting neutron star
• Influence of finite temperature Exchange-Correlation effects in Hydrogen
• Frontiers of the physics of dense plasmas and planetary interiors: experiments, theory, applications
• Accelerating Finite-temperature Kohn-Sham Density Functional Theory with Deep Neural Networks
• Liquid metallic hydrogen and the structure of brown dwarfs and giant planets
• Pseudoatom molecular dynamics
• Electronic Density Response of Warm Dense Hydrogen: Ab initio Path Integral Monte Carlo Simulations
• Exact thermal density functional theory for a model system: Correlation components and accuracy of the zero-temperature exchange-correlation approximation
• The Relevance of Electronic Perturbations in the Warm Dense Electron Gas
• Benchmarking Exchange-Correlation Functionals in the Spin-Polarized Inhomogeneous Electron Gas under Warm Dense Conditions
• Non-empirical mixing coefficient for hybrid XC functionals from analysis of the XC kernel
• Assessing the accuracy of hybrid exchange-correlation functionals for the density response of warm dense electrons
• Mapping the Electronic Structure of Warm Dense Nickel via Resonant Inelastic X-ray Scattering
• D'yakov-Kontorovitch instability of shock waves in hot plasmas
• Reconciling ionization energies and band gaps of warm dense matter derived with ab initio simulations and average atom models
• Thermal Signals from Collective Electronic Excitations in Inhomogeneous Warm Dense Matter
• First-principles derivation and properties of density-functional average-atom models
• Improved calculations of mean ionization states with an average-atom model
• Training-free hyperparameter optimization of neural networks for electronic structures in matter
• Constraining Model Uncertainty in Plasma Equation-of-State Models with a Physics-Constrained Gaussian Process