Marcel F. Langer^1*, Sergey N. Pozdnyakov^1*, Michele Ceriotti^1*

1 Laboratory of Computational Science and Modeling and National Centre for Computational Design and Discovery of Novel Materials MARVEL, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland

* Corresponding authors emails: marcel.langer@epfl.ch, sergey.pozdnyakov@epfl.ch, michele.ceriotti@epfl.ch

DOI10.24435/materialscloud:kz-3b [version v1]

Publication date: Oct 30, 2024

How to cite this record

Marcel F. Langer, Sergey N. Pozdnyakov, Michele Ceriotti, Probing the effects of broken symmetries in machine learning, Materials Cloud Archive 2024.175 (2024), https://doi.org/10.24435/materialscloud:kz-3b

Description

Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models targeting the properties of matter at the atomic scale. Both established and state-of-the-art approaches, with almost no exceptions, are built to be exactly equivariant to translations, permutations, and rotations of the atoms. Incorporating symmetries—rotations in particular—constrains the model design space and implies more complicated architectures that are often also computationally demanding. There are indications that unconstrained models can easily learn symmetries from data, and that doing so can even be beneficial for the accuracy of the model. We demonstrate that an unconstrained architecture can be trained to achieve a high degree of rotational invariance, testing the impacts of the small symmetry breaking in realistic scenarios involving simulations of gas-phase, liquid, and solid water. We focus specifically on physical observables that are likely to be affected—directly or indirectly—by non-invariant behavior under rotations, finding negligible consequences when the model is used in an interpolative, bulk, regime. Even for extrapolative gas-phase predictions, the model remains very stable, even though symmetry artifacts are noticeable. We also discuss strategies that can be used to systematically reduce the magnitude of symmetry breaking when it occurs, and assess their impact on the convergence of observables. This archive collect the input files, scripts, and data for the paper referenced below. In particular, it contains the trained MLIP for this work, the input files for simulations, the post-processing scripts and their outputs, as well as the plotting scripts and resulting figures. A detailed readme can be found below, and a more detailed one in each subfolder. The data in this archive is mirrored at https://github.com/sirmarcel/eqt-archive, where issues can be raised and discussed.

Materials Cloud sections using this data

Files

File name	Size	Description
eqt-archive.zip MD5md5:23d0abd85d65cfba698f54edfa427b1e	127.3 MiB	Archive containing the data
README.md MD5md5:5f7d89558068adc23efc3e28f415442e	2.1 KiB	Readme detailing contents of eqt-archive.zip

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

Keywords

machine learning water equivariance MARVEL/P2