Machine learning of kinetic energy densities with target and feature averaging: better results with fewer training data

Abstract

Machine learning of kinetic energy functionals (KEF), in particular kinetic energy density (KED) functionals, has recently attracted attention as a promising way to construct KEFs for orbital-free density functional theory (OF-DFT). Neural networks (NN) and kernel methods including Gaussian process regression (GPR) have been used to learn Kohn-Sham (KS) KED from density-based descriptors derived from KS DFT calculations. The descriptors are typically expressed as functions of different powers and derivatives of the electron density. This can generate large and extremely unevenly distributed datasets, which complicates effective application of machine learning techniques. Very uneven data distributions require many training data points, can cause overfitting, and ultimately lower the quality of a ML KED model. We show that one can produce more accurate ML models from fewer data by working with partially averaged density-dependent variables and KED. Averaging palliates the issue of very uneven data distributions and associated difficulties of sampling, while retaining enough spatial structure necessary for working within the paradigm of KEDF. We use GPR as a function of partially spatially averaged terms of the 4th order gradient expansion and the Kohn-Sham effective potential and obtain accurate and stable (with respect to different random choices of training points) kinetic energy models for Al, Mg, and Si simultaneously from as few as 2000 samples (about 0.3% of the total KS DFT data). In particular, accuracies on the order of 1% in a measure of the quality of energy-volume dependence B' = \frac{E(V_0-ΔV)-2E(V_0)+E(V_0 + ΔV)}{\big(\frac{ΔV}{V_0}\big)^2} are obtained simultaneously for all three materials.

References in corpus (19)

• The SIESTA method for ab initio order-N materials simulation
• Efficient index handling of multidimensional periodic boundary conditions
• By-passing the Kohn-Sham equations with machine learning
• Accurate and efficient linear scaling DFT calculations with universal applicability
• Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy
• 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
• Laplacian-level kinetic energy approximations based on the fourth-order gradient expansion: Global assessment and application to the subsystem formulation of density functional theory
• Kinetic energy densities based on the fourth order gradient expansion: performance in different classes of materials and improvement via 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
• Nonlocal Pseudopotential Energy Density Functional for Orbital-Free Density Functional Theory
• 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
• Highly Accurate Local Pseudopotentials of Li, Na, and Mg for Orbital Free Density Functional Theory
• An Efficient DFT Solver for Nanoscale Simulations and Beyond
• Orbital-free DFT study of the energetics of vacancy clustering and prismatic dislocation loop nucleation in aluminum
• Robust All-Electron Optimization in Orbital-Free Density Functional Theory Using the Trust Region Image Method

Cited by in corpus (2)

• A machine-learned kinetic energy model for light weight metals and compounds of group III-V elements
• Machine learning-guided construction of an analytic kinetic energy functional for orbital free density functional theory