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Equivariant N-centered representations for atomistic machine learning

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The application of machine learning (ML) to the modeling of materials and molecules has proven to be extremely successful in accelerating the understanding, design, and characterization of materials. A major factor in this success has been the development of representations of atomic structures that reflect physics-based constraints of the targets. A class of these structural descriptions is built by symmetrizing correlations of an atom-density function that describes the associated atomic environment. These local objects are then subsequently used to model corresponding atomic properties, or atomic contributions to a global observable. However, many quantum mechanical quantities, such as the effective single-particle Hamiltonian projected on an atomic-orbital basis, are associated with multiple atom-centers, rendering the atom-centered approach inadequate to describe the additional degrees of freedom.

We recently proposed an N-center representation1 that extends the atom-centered framework to the case of targets that are simultaneously indexed by N atoms. Devising this family of multicenter representations opens avenues for new classes of machine learning models that are fully equivariant and thus incorporate molecular symmetries. Additionally, they can be used to construct integrated machine learning models, such as by calculating N-center integrals that can further serve to assist electronic structure calculations. As these N-center representations provide information on multiple centers and their connectivities, they also serve as a framework to capture the ideas of “message-passing”2, which are widely employed in deep ML models

[1] J. Nigam, M. Willatt, M. Ceriotti, JCP 156 , 014115, 2022

[2] J. Nigam, S. Pozdnyakov, G. Fraux, M. Ceriotti, arXiv:2202.01566

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