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research article

Wigner kernels: Body-ordered equivariant machine learning without a basis

Bigi, Filippo  
•
Pozdnyakov, Sergey N.  
•
Ceriotti, Michele  
July 28, 2024
The Journal of Chemical Physics

Machine-learning models based on a point-cloud representation of a physical object are ubiquitous in scientific applications and particularly well-suited to the atomic-scale description of molecules and materials. Among the many different approaches that have been pursued, the description of local atomic environments in terms of their discretized neighbor densities has been used widely and very successfully. We propose a novel density-based method, which involves computing "Wigner kernels." These are fully equivariant and body-ordered kernels that can be computed iteratively at a cost that is independent of the basis used to discretize the density and grows only linearly with the maximum body-order considered. Wigner kernels represent the infinite-width limit of feature-space models, whose dimensionality and computational cost instead scale exponentially with the increasing order of correlations. We present several examples of the accuracy of models based on Wigner kernels in chemical applications, for both scalar and tensorial targets, reaching an accuracy that is competitive with state-of-the-art deep-learning architectures. We discuss the broader relevance of these findings to equivariant geometric machine-learning. (c) 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercial 4.0International (CC BY-NC) license (https://creativecommons.org/licenses/by-nc/4.0/).

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Type
research article
DOI
10.1063/5.0208746
Web of Science ID

WOS:001281709000010

PubMed ID

39056390

Author(s)
Bigi, Filippo  

École Polytechnique Fédérale de Lausanne

Pozdnyakov, Sergey N.  

École Polytechnique Fédérale de Lausanne

Ceriotti, Michele  

École Polytechnique Fédérale de Lausanne

Date Issued

2024-07-28

Publisher

AIP Publishing

Published in
The Journal of Chemical Physics
Volume

161

Issue

4

Article Number

044116

Subjects

Science & Technology

•

Physical Sciences

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
COSMO  
FunderFunding(s)Grant NumberGrant URL

National Center of Competence in Research Materials' Revolution: Computational Design and Discovery of Novel Materialshttps://doi.org/10.13039/501100009150

182892

Swiss National Science Foundation (SNSF)

Swiss Platform for Advanced Scientific Computing (PASC)

Available on Infoscience
January 30, 2025
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/245913
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