Representing spherical tensors with scalar-based machine-learning models

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{
  "updated": "2025-05-09T12:42:30.529663+00:00", 
  "id": "2677", 
  "revision": 6, 
  "metadata": {
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    "_oai": {
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    }, 
    "status": "published", 
    "mcid": "2025.74", 
    "id": "2677", 
    "doi": "10.24435/materialscloud:zq-a6", 
    "title": "Representing spherical tensors with scalar-based machine-learning models", 
    "edited_by": 576, 
    "license": "Creative Commons Attribution 4.0 International", 
    "version": 1, 
    "publication_date": "May 09, 2025, 14:42:30", 
    "contributors": [
      {
        "familyname": "Domina", 
        "affiliations": [
          "COSMO\u2014Laboratory of Computational Science and Modelling, IMX, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015 Lausanne, Switzerland"
        ], 
        "givennames": "Michelangelo", 
        "email": "michelangelo.domina@epfl.ch"
      }, 
      {
        "familyname": "Bigi", 
        "affiliations": [
          "COSMO\u2014Laboratory of Computational Science and Modelling, IMX, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015 Lausanne, Switzerland"
        ], 
        "givennames": "Filippo", 
        "email": "filippo.bigi@epfl.ch"
      }, 
      {
        "familyname": "Pegolo", 
        "affiliations": [
          "COSMO\u2014Laboratory of Computational Science and Modelling, IMX, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015 Lausanne, Switzerland"
        ], 
        "givennames": "Paolo", 
        "email": "paolo.pegolo@epfl.ch"
      }, 
      {
        "familyname": "Ceriotti", 
        "affiliations": [
          "COSMO\u2014Laboratory of Computational Science and Modelling, IMX, \u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, 1015 Lausanne, Switzerland"
        ], 
        "givennames": "Michele", 
        "email": "michele.ceriotti@epfl.ch"
      }
    ], 
    "references": [], 
    "owner": 225, 
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    "keywords": [
      "ERC", 
      "machine learning", 
      "EPFL", 
      "metatrain", 
      "equivariance", 
      "MARVEL/P2"
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    "is_last": true, 
    "conceptrecid": "2676", 
    "description": "Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects \u2013 from atoms to the macroscopic scale \u2013 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. \nIn 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."
  }, 
  "created": "2025-05-08T09:34:12.461614+00:00"
}