Accelerating Finite-temperature Kohn-Sham Density Functional Theory with Deep Neural Networks

Abstract

We present a numerical modeling workflow based on machine learning (ML) which reproduces the the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible computational cost. Based on deep neural networks, our workflow yields the local density of states (LDOS) for a given atomic configuration. From the LDOS, spatially-resolved, energy-resolved, and integrated quantities can be calculated, including the DFT total free energy, which serves as the Born-Oppenheimer potential energy surface for the atoms. We demonstrate the efficacy of this approach for both solid and liquid metals and compare results between independent and unified machine-learning models for solid and liquid aluminum. Our machine-learning density functional theory framework opens up the path towards multiscale materials modeling for matter under ambient and extreme conditions at a computational scale and cost that is unattainable with current algorithms.

References in corpus (44)

• Scikit-learn: Machine Learning in Python
• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Restoring the density-gradient expansion for exchange in solids and surfaces
• Generalized gradient approximation for solids and their surfaces
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• Optimized norm-conserving Vanderbilt pseudopotentials
• Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons
• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics
• SchNet - a deep learning architecture for molecules and materials
• ANI-1: An extensible neural network potential with DFT accuracy at force field computational cost
• Quantum ESPRESSO toward the exascale
• Perspective on density functional theory
• Quantum-Chemical Insights from Deep Tensor Neural Networks
• A Spectral Analysis Method for Automated Generation of Quantum-Accurate Interatomic Potentials
• A Performance and Cost Assessment of Machine Learning Interatomic Potentials
• By-passing the Kohn-Sham equations with machine learning
• Finding Density Functionals with Machine Learning
• Horovod: fast and easy distributed deep learning in TensorFlow
• How to represent crystal structures for machine learning: towards fast prediction of electronic properties
• Exact factorization of the time-dependent electron-nuclear wavefunction
• Probing the ultimate limits of metal plasticity
• Ensemble density-functional theory for ab-initio molecular dynamics of metals and finite-temperature insulators
• Insightful classification of crystal structures using deep learning
• Hierarchical modeling of molecular energies using a deep neural network
• Correlated electron-nuclear dynamics: Exact factorization of the molecular wavefunction
• A Massive Core in Jupiter Predicted From First-Principles Simulations
• Local Spin-density Approximation Exchange-correlation Free-energy Functional
• New indication for a dichotomy in the interior structure of Uranus and Neptune from the application of modified shape and rotation data
• Ab initio Exchange-Correlation Free Energy of the Uniform Electron Gas at Warm Dense Matter Conditions
• Hydrogen-Helium Mixtures in the Interiors of Giant Planets
• Jupiter models with improved ab initio hydrogen EOS (H-REOS.2)
• The first principles calculation of transport coefficients
• Thermal evolution and structure models of the transiting super-Earth GJ 1214b
• DFT: A Theory Full of Holes?
• Learning the electronic density of states in condensed matter
• Orbital-free Bond Breaking via Machine Learning
• Exact conditions and scaling relations in finite temperature density functional theory
• A sparse representation for potential energy surface
• Data-driven Material Models for Atomistic Simulation
• Exchange-correlation energy for the 3D homogeneous electron gas at arbitrary temperature
• Thermal Density Functional Theory in Context
• Constraining the interior of extrasolar giant planets with the tidal Love number k_2 using the example of HAT-P-13b
• Ab Initio Molecular Dynamics on the Electronic Boltzmann Equilibrium Distribution

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• Accelerating Equilibration in First-Principles Molecular Dynamics with Orbital-Free Density Functional Theory
• Linear Jacobi-Legendre expansion of the charge density for machine learning-accelerated electronic structure calculations
• Towards a Quantum Fluid Theory of Correlated Many-Fermion Systems from First Principles
• Grad DFT: a software library for machine learning enhanced density functional theory
• First-principles derivation and properties of density-functional average-atom models
• Towards Large-Scale and Spatio-temporally Resolved Diagnosis of Electronic Density of States by Deep Learning
• Predicting The One-Particle Density Matrix With Machine Learning
• Predicting hot-electron free energies from ground-state data
• Training-free hyperparameter optimization of neural networks for electronic structures in matter
• Machine learning the electronic structure of matter across temperatures
• Equivariant Tensor Network Potentials
• Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data
• Piecewise Interaction Picture Density Matrix Quantum Monte Carlo
• Effect of molecular and electronic geometries on the electronic density in FLO-SIC
• A general formalism for machine-learning models based on multipolar-spherical harmonics
• Physics-enhanced neural networks for equation-of-state calculations
• atoMEC: An open-source average-atom Python code
• Machine learning based prediction of the electronic structure of quasi-one-dimensional materials under strain
• A charge-density machine-learning workflow for computing the infrared spectrum of molecules