Representations in machine learning for atomic scale simulations

Guillaume Fraux

Atomistic simulations are only as accurate as the description of the interactions between particles we are able to compute. The most accurate method involves solving the Schrödinger equation for the atoms and corresponding electrons. Unfortunately, this requires large computing resources and limits the scale of these simulations. Over the last decade, machine learning interatomic potentials (MLIP) have been introduced and improved, and they are now able to reach accuracy close to Density Functional Theory (DFT) at a fraction of the cost. A lot of existing MLIP are based on a representation of the local atomic structure which encodes all the symmetries of the structure: rotations,
translations, permutations, inversions, etc. Making the representation invariant or covariant with respect to these symmetries ensures the resulting model will be as well, and make training it more data efficient. I will present some of our efforts to improve these representations, from incorporation more physical information (long range potentials with multipole expansion [1], exploiting similarities between elements in the same period/group [2]), predicting target properties with more complex symmetries such as Hamiltonian matrix elements [3, 4], to making sure the representations are complete and can differentiate between all structures [5]. I will also present our software implementation efforts, and how we allow fast simulations with user-defined models, and provide an experimentation ground for new representations, models or combinations of

[1] A. Grisafi; M. Ceriotti, J. Chem. Phys. (2019) 151,20 p204105 DOI: 10.1063/1.5128375
[2] N. Lopanitsyna, G. Fraux, M. Springer, S. De, M. Ceriotti, arXiv: 2212.13254
[3] J. Nigam; M. Willatt; M. Ceriotti, J. Chem. Phys. (2022) 156,1, p014115
DOI: 10.1063/5.0072784
[4] J. Nigam; S. Pozdnyakov; G. Fraux; M. Ceriotti J. Chem. Phys. (2022) 156,20 p204115 DOI: 10.1063/5.0087042
[5] J. Nigam, S. Pozdnyakov, K. Huguenin-Dumittan, M. Ceriotti, arXiv:2302.14770

To the top of the page