Schrödinger principal-component analysis: On the duality between principal-component analysis and the Schrödinger equation

Ziming Liu, Sitian Qian, Yixuan Wang, Yuxuan Yan, and Tianyi Yang
Phys. Rev. E 104, 025307 – Published 20 August 2021

Abstract

Principal component analysis (PCA) has been applied to analyze random fields in various scientific disciplines. However, the explainability of PCA remains elusive unless strong domain-specific knowledge is available. This paper provides a theoretical framework that builds a duality between the PCA eigenmodes of a random field and eigenstates of a Schrödinger equation. Based on the duality we propose the Schrödinger PCA algorithm to replace the expensive PCA solver with a more sample-efficient Schrödinger equation solver. We verify the validity of the theory and the effectiveness of the algorithm with numerical experiments.

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  • Received 13 February 2021
  • Revised 30 July 2021
  • Accepted 4 August 2021

DOI:https://doi.org/10.1103/PhysRevE.104.025307

©2021 American Physical Society

Physics Subject Headings (PhySH)

Interdisciplinary PhysicsParticles & FieldsGeneral Physics

Authors & Affiliations

Ziming Liu1,*, Sitian Qian2, Yixuan Wang3,†, Yuxuan Yan2, and Tianyi Yang2

  • 1Department of Physics, Massachusetts Institute of Technology, Cambridge Massachusetts 02139, USA
  • 2School of Physics, Peking University, Beijing 100871, China
  • 3Applied and Computational Mathematics, California Institute of Technology, Pasadena, California 91125, USA

  • *zmliu@mit.edu
  • roywang@caltech.edu

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Vol. 104, Iss. 2 — August 2021

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