Representing spherical tensors with scalar-based machine-learning models

DOI

Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects – from atoms to the macroscopic scale – transform under the action of rigid rotations. Equivariant models of 3D point clouds are able to approximate structure-property relations in a way that is fully consistent with the structure of the rotation group, by combining intermediate representations that are themselves spherical tensors. The symmetry constraints however make this approach computationally demanding and cumbersome to implement, which motivates increasingly popular unconstrained architectures that learn approximate symmetries as part of the training process. In this work, we explore a third route to tackle this learning problem, where equivariant functions are expressed as the product of a scalar function of the point cloud coordinates and a small basis of tensors with the appropriate symmetry. We also propose approximations of the general expressions that, while lacking universal approximation properties, are fast, simple to implement, and accurate in practical settings.

Identifier
DOI https://doi.org/10.24435/materialscloud:zq-a6
Related Identifier https://doi.org/10.1063/5.0284802
Related Identifier https://archive.materialscloud.org/communities/mcarchive
Related Identifier https://doi.org/10.24435/materialscloud:sb-2y
Metadata Access https://archive.materialscloud.org/oai2d?verb=GetRecord&metadataPrefix=oai_dc&identifier=oai:materialscloud.org:2677
Provenance
Creator Domina, Michelangelo; Bigi, Filippo; Pegolo, Paolo; Ceriotti, Michele
Publisher Materials Cloud
Contributor Domina, Michelangelo; Bigi, Filippo; Pegolo, Paolo; Ceriotti, Michele
Publication Year 2025
Rights info:eu-repo/semantics/openAccess; Creative Commons Attribution 4.0 International; https://creativecommons.org/licenses/by/4.0/legalcode
OpenAccess true
Contact archive(at)materialscloud.org
Representation
Language English
Resource Type info:eu-repo/semantics/other
Format application/octet-stream; application/zip; text/markdown
Discipline Materials Science and Engineering