Deep Density: circumventing the Kohn-Sham equations via symmetry preserving neural networks

Abstract

The recently developed Deep Potential [Phys. Rev. Lett. 120, 143001, 2018] is a powerful method to represent general inter-atomic potentials using deep neural networks. The success of Deep Potential rests on the proper treatment of locality and symmetry properties of each component of the network. In this paper, we leverage its network structure to effectively represent the mapping from the atomic configuration to the electron density in Kohn-Sham density function theory (KS-DFT). By directly targeting at the self-consistent electron density, we demonstrate that the adapted network architecture, called the Deep Density, can effectively represent the electron density as the linear combination of contributions from many local clusters. The network is constructed to satisfy the translation, rotation, and permutation symmetries, and is designed to be transferable to different system sizes. We demonstrate that using a relatively small number of training snapshots, Deep Density achieves excellent performance for one-dimensional insulating and metallic systems, as well as systems with mixed insulating and metallic characters. We also demonstrate its performance for real three-dimensional systems, including small organic molecules, as well as extended systems such as water (up to $512$ molecules) and aluminum (up to $256$ atoms).

References in corpus (14)

• 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
• DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics
• ANI-1: An extensible neural network potential with DFT accuracy at force field computational cost
• Optimization Algorithm for the Generation of ONCV Pseudopotentials
• Machine Learning of Accurate Energy-Conserving Molecular Force Fields
• Nearsightedness of Electronic Matter
• O(N) methods in electronic structure calculations
• A Transferable Machine-Learning Model of the Electron Density
• Deep Learning and Density Functional Theory
• DGDFT: A Massively Parallel Method for Large Scale Density Functional Theory Calculations
• Efficient prediction of 3D electron densities using machine learning

Cited by in corpus (6)

• 86 PFLOPS Deep Potential Molecular Dynamics simulation of 100 million atoms with ab initio accuracy
• Deep neural network for the dielectric response of insulators
• DeePKS: a comprehensive data-driven approach towards chemically accurate density functional theory
• Deep-learning electronic-structure calculation of magnetic superstructures
• Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression
• Deep Learning in Protein Structural Modeling and Design