Machine learning-guided construction of an analytic kinetic energy functional for orbital free density functional theory

Abstract

Machine learning (ML) of kinetic energy functionals (KEF) for orbital-free density functional theory (OF-DFT) holds the promise of addressing an important bottleneck in large-scale ab initio materials modeling where sufficiently accurate analytic KEFs are lacking. However, ML models are not as easily handled as analytic expressions; they need to be provided in the form of algorithms and associated data. Here, we bridge the two approaches and construct an analytic expression for a KEF guided by interpretative machine learning of crystal cell-averaged kinetic energy densities (τ) of several hundred materials. A previously published dataset including multiple phases of 433 unary, binary, and ternary compounds containing Li, Al, Mg, Si, As, Ga, Sb, Na, Sn, P, and In was used for training, including data at the equilibrium geometry as well as strained structures. A hybrid Gaussian process regression - neural network (GPR-NN) method was used to understand the type of functional dependence of τ on the features which contained cell-averaged terms of the 4th order gradient expansion and the product of the electron density and Kohn-Sham effective potential. Based on this analysis, an analytic model is constructed that can reproduce Kohn-Sham DFT energy-volume curves with sufficient accuracy (pronounced minima that are sufficiently close to the minima of the Kohn-Sham DFT-based curves and with sufficiently close curvatures) to enable structure optimizations and elastic response calculations.

17 pages, 7 figures

References in corpus (42)

• The SIESTA method for ab initio order-N materials simulation
• Efficient index handling of multidimensional periodic boundary conditions
• SchNet - a deep learning architecture for molecules and materials
• PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments and Partial Charges
• By-passing the Kohn-Sham equations with machine learning
• Interpretable Scientific Discovery with Symbolic Regression: A Review
• Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network
• GPAW: An open Python package for electronic-structure calculations
• Accurate and efficient linear scaling DFT calculations with universal applicability
• Calculations on millions of atoms with DFT: Linear scaling shows its potential
• Orbital-free Bond Breaking via Machine Learning
• Large scale and linear scaling DFT with the CONQUEST code
• A Simple Generalized Gradient Approximation for the Non-interacting Kinetic Energy Density Functional
• A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledge
• Learning the exchange-correlation functional from nature with fully differentiable density functional theory
• Semilocal Pauli-Gaussian Kinetic Functionals for Orbital-Free Density Functional Theory Calculations of Solids
• Nonlocal Kinetic Energy Functionals By Functional Integration
• Kinetic energy densities based on the fourth order gradient expansion: performance in different classes of materials and improvement via machine learning
• ATLAS: A Real-Space Finite-Difference Implementation of Orbital-Free Density Functional Theory
• DFTpy: An efficient and object-oriented platform for orbital-free DFT simulations
• Nuclear energy density functionals from machine learning
• Orbital-Free Density Functional Theory: Kinetic Potentials and Ab-Initio Local Pseudopotentials
• Data-driven kinetic energy density fitting for orbital-free DFT: linear vs Gaussian process regression
• Overcoming the Barrier of Orbital-Free Density Functional Theory for Molecular Systems Using Deep Learning
• Nonlocal Pseudopotential Energy Density Functional for Orbital-Free Density Functional Theory
• Time-dependent Orbital-free Density Functional Theory: Background and Pauli kernel approximations
• Comparative Density Functional Theory and Density Functional Tight Binding Study of Arginine and Arginine-Rich Cell-Penetrating Peptide TAT Adsorption on Anatase TiO2
• Order-$N$ orbital-free density-functional calculations with machine learning of functional derivatives for semiconductors and metals
• Orbital-Free Density Functional Theory: Linear Scaling Methods for Kinetic Potentials, and Applications to Solid Al and S
• Neural network with optimal neuron activation functions based on additive Gaussian process regression
• Highly Accurate Local Pseudopotentials of Li, Na, and Mg for Orbital Free Density Functional Theory
• Non-parametric Local Pseudopotentials with Machine Learning: a Tin Pseudopotential Built Using Gaussian Process Regression
• Easy representation of multivariate functions with low-dimensional terms via Gaussian process regression kernel design: applications to machine learning of potential energy surfaces and kinetic energy densities from sparse data
• Degeneration of kernel regression with Matern kernels into low-order polynomial regression in high dimension
• Toward Physically Plausible Data-Driven Models: A Novel Neural Network Approach to Symbolic Regression
• KineticNet: Deep learning a transferable kinetic energy functional for orbital-free density functional theory
• Machine learning of kinetic energy densities with target and feature averaging: better results with fewer training data
• The loss of the property of locality of the kernel in high-dimensional Gaussian process regression on the example of the fitting of molecular potential energy surfaces
• Orders-of-coupling representation with a single neural network with optimal neuron activation functions and without nonlinear parameter optimization
• A machine-learned kinetic energy model for light weight metals and compounds of group III-V elements
• Machine learning the screening factor in the soft bond valence approach for rapid crystal structure estimation
• Grown-in beryllium diffusion in indium gallium arsenide: An ab initio, continuum theory and kinetic Monte Carlo study