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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:443

Article

Zepeda-Nunez, Leonardo^1,3  Chen, Yixiao²  Zhang, Jiefu³  Jia, Weile³  Zhang, Linfeng²  Lin, Lin^3,4 

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[2] Princeton Univ, Program Appl & Computat Math, Princeton, NJ 08544 USA

[3] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[4] Lawrence Berkeley Natl Lab, Computat Res Div, Berkeley, CA USA

关键词: Deep neural networks;    Kohn-Sham density functional theory;    Symmetry;    Self-consistent field iteration;   

DOI  :  10.1016/j.jcp.2021.110523

来源: Elsevier

【 摘 要 】

The recently developed Deep Potential [Phys. Rev. Lett. 120 (2018) 143001 [27]] 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 self-consistent 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, with each snapshot containing a modest amount of data-points, 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). (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free