Toward Orbital-Free Density Functional Theory with Small Data Sets and Deep Learning

Abstract

We use voxel deep neural networks to predict energy densities and functional derivatives of electron kinetic energies for the Thomas-Fermi model and Kohn-Sham density functional theory calculations. We show that the ground-state electron density can be found via direct minimization for a graphene lattice without any projection scheme using a voxel deep neural network trained with the Thomas-Fermi model. Additionally, we predict the kinetic energy of a graphene lattice within chemical accuracy after training from only 2 Kohn-Sham density functional theory (DFT) calculations. We identify an important sampling issue inherent in Kohn-Sham DFT calculations and propose future work to rectify this problem. Furthermore, we demonstrate an alternative, functional derivative-free, Monte Carlo based orbital free density functional theory algorithm to calculate an accurate 2-electron density in a double inverted Gaussian potential with a machine-learned kinetic energy functional.

Cited by in corpus (16)

• Towards self-driving laboratories: The central role of density functional theory in the AI age
• Linear Jacobi-Legendre expansion of the charge density for machine learning-accelerated electronic structure calculations
• Machine Learning Diffusion Monte Carlo Energies
• Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
• KineticNet: Deep learning a transferable kinetic energy functional for orbital-free density functional theory
• Machine learning based nonlocal kinetic energy density functional for simple metals and alloys
• Multi-channel machine learning based nonlocal kinetic energy density functional for semiconductors
• Deep learning density functionals for gradient descent optimization
• Orbital-Free Quasi-Density Functional Theory
• Lean CNNs for mapping electron charge density fields to material properties
• Deep learning nonlocal and scalable energy functionals for quantum Ising models
• Nuclear cusps and singularities in the non-additive kinetic potential bi-functional from analytical inversion
• On the Kinetic Energy Density Functional: The Limit of the Density Derivative Order
• Calculating potential energy surfaces with quantum computers by measuring only the density along adiabatic transitions
• Solving deep-learning density functional theory via variational autoencoders
• Nonlocal Orbital-Free Kinetic Energy Functional from the Jellium-with-Gap Model for Finite Systems