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