Michelangelo Domina^1*, Filippo Bigi^1*, Paolo Pegolo^1*, Michele Ceriotti^1*

1 COSMO—Laboratory of Computational Science and Modelling, IMX, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

* Corresponding authors emails: michelangelo.domina@epfl.ch, filippo.bigi@epfl.ch, paolo.pegolo@epfl.ch, michele.ceriotti@epfl.ch

DOI10.24435/materialscloud:zq-a6 [version v1]

Publication date: May 09, 2025

How to cite this record

Michelangelo Domina, Filippo Bigi, Paolo Pegolo, Michele Ceriotti, Representing spherical tensors with scalar-based machine-learning models, Materials Cloud Archive 2025.74 (2025), https://doi.org/10.24435/materialscloud:zq-a6

Description

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.

Materials Cloud sections using this data

Files

File name	Size	Description
README.md MD5md5:c8eced2c1b23f543f6408d716a026996	2.5 KiB	Explanation of the content of the repository
environment.yml MD5md5:f1eb6625dbb20ab8279392bdd94f1fdb	356 Bytes	YAML file to create a conda environment with all the required software to reproduce the results of the associated manuscript
train_multiple_equivariants_qm7.zip MD5md5:5413ebda8490d55237338e8f33757d85	96.8 MiB	Data and scripts to train an equivariant model for dipole moments, polarizabilities, and hyperpolarizabilities of a subset of the QM7 dataset
comparison_with_lambda_soap.zip MD5md5:0667af7651789f90f22aa9c9dc423717	343.3 MiB	Data and scripts to obtain learning curves comparing the performances of the proposed machine learning model and an equivariant linear model
water_ir_spectrum.zip MD5md5:d38dbb9d76599c9d779021309bba81c9	2.2 GiB	Data and scripts to compute the infrared spectrum of liquid water and compare the machine learning predictions with those of a classical force field.
per_atom_equivariants_co2.zip MD5md5:06e64a0600bb208209655d75e857ceb7	25.4 MiB	Data and scripts to compute the dataset and train ML models for Born effective charges and Raman tensors of CO2 to test the predictions of the model for per-atom properties

License

Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.

External references

No external references available for this Materials Cloud Archive record.

Keywords

ERC machine learning EPFL metatrain equivariance MARVEL/P2