Machine learning based nonlocal kinetic energy density functional for simple metals and alloys

Abstract

Developing an accurate kinetic energy density functional (KEDF) remains a major hurdle in orbital-free density functional theory. We propose a machine learning based physical-constrained nonlocal (MPN) KEDF and implement it with the usage of the bulk-derived local pseudopotentials and plane wave basis sets in the ABACUS package. The MPN KEDF is designed to satisfy three exact physical constraints: the scaling law of electron kinetic energy, the free electron gas limit, and the non-negativity of Pauli energy density. The MPN KEDF is systematically tested for simple metals, including Li, Mg, Al, and 59 alloys. We conclude that incorporating nonlocal information for designing new KEDFs and obeying exact physical constraints are essential to improve the accuracy, transferability, and stability of ML-based KEDF. These results shed new light on the construction of ML-based functionals.

arXiv comment10 pages, 5 figures

References in corpus (16)

• Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics
• DP-GEN: A concurrent learning platform for the generation of reliable deep learning based potential energy models
• Finding Density Functionals with Machine Learning
• Towards self-driving laboratories: The central role of density functional theory in the AI age
• Deep-Learning Density Functional Theory Hamiltonian for Efficient ab initio Electronic-Structure Calculation
• Issues and Challenges in Orbital-free Density Functional Calculations
• A Simple Generalized Gradient Approximation for the Non-interacting Kinetic Energy Density Functional
• 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
• DeePKS: a comprehensive data-driven approach towards chemically accurate density functional theory
• Nonlocal Kinetic Energy Functionals By Functional Integration
• ATLAS: A Real-Space Finite-Difference Implementation of Orbital-Free Density Functional Theory
• Toward Orbital-Free Density Functional Theory with Small Data Sets and Deep Learning
• Order-$N$ orbital-free density-functional calculations with machine learning of functional derivatives for semiconductors and metals
• Variational principle to regularize machine-learned density functionals: the non-interacting kinetic-energy functional
• Truncated Non-Local Kinetic Energy Density Functionals for Simple Metals and Silicon

Cited by in corpus (1)

• Multi-channel machine learning based nonlocal kinetic energy density functional for semiconductors