eprintid: 10191677
rev_number: 6
eprint_status: archive
userid: 699
dir: disk0/10/19/16/77
datestamp: 2024-05-07 13:42:08
lastmod: 2024-05-07 13:42:08
status_changed: 2024-05-07 13:42:08
type: proceedings_section
metadata_visibility: show
sword_depositor: 699
creators_name: Li, Xihan
title: Online PCA in Converging Self-consistent Field Equations
ispublished: pub
divisions: UCL
divisions: B04
divisions: C05
divisions: F48
note: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
abstract: Self-consistent Field (SCF) equation is a type of nonlinear eigenvalue problem in which the matrix to be eigen-decomposed is a function of its own eigenvectors. It is of great significance in computational science for its connection to the Schrödinger equation. Traditional fixed-point iteration methods for solving such equations suffer from non-convergence issues. In this work, we present a novel perspective on such SCF equations as a principal component analysis (PCA) for non-stationary time series, in which a distribution and its own top principal components are mutually updated over time, and the equilibrium state of the model corresponds to the solution of the SCF equations. By the new perspective, online PCA techniques are able to engage in so as to enhance the convergence of the model towards the equilibrium state, acting as a new set of tools for converging the SCF equations. With several numerical adaptations, we then develop a new algorithm for converging the SCF equation, and demonstrated its high convergence capacity with experiments on both synthesized and real electronic structure scenarios.
date: 2023-12-15
date_type: published
publisher: Curran Associates, Inc.
official_url: https://proceedings.neurips.cc/paper_files/paper/2023/hash/969c14957c0df5ce2db642b3a5fa985c-Abstract-Conference.html
oa_status: green
full_text_type: pub
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 2272615
lyricists_name: Li, Xihan
lyricists_id: XLILX45
actors_name: Li, Xihan
actors_id: XLILX45
actors_role: owner
full_text_status: public
pres_type: paper
publication: Advances in Neural Information Processing Systems
pagerange: 1-12
event_title: The 37th Annual Conference on Neural Information Processing Systems
event_location: New Orleans
book_title: Advances in Neural Information Processing Systems 36
citation:        Li, Xihan;      (2023)    Online PCA in Converging Self-consistent Field Equations.                     In:  Advances in Neural Information Processing Systems 36.  (pp. pp. 1-12).  Curran Associates, Inc.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10191677/1/Li%20I%20-%202023%20-%20Online%20PCA%20in%20Converging%20Self-consistent%20Field%20Equ.pdf