Local inversion of the chemical environment representations
M Cobelli and P Cahalane and S Sanvito, PHYSICAL REVIEW B, 106, 035402 (2022).
Machine-learning generative methods for material design are constructed by representing a given chemical structure, either a solid or a molecule, over appropriate atomic features, generally called structural descriptors. These must be fully descriptive of the system, must facilitate the training process, and must be invertible, so that one can extract the atomic configurations corresponding to the output of the model. In general, this last requirement is not automatically satisfied by the most efficient structural descriptors, namely the representation is not directly invertible. Such a drawback severely limits our freedom of choice in selecting the most appropriate descriptors for the problem, and thus our flexibility to construct generative models. In this paper, we present an optimization method capable of inverting the local many- body descriptors of the chemical environment, back to a Cartesian representation. This is not a global inversion scheme, but it allows one to find the Cartesian representation of variations of known structures, such as those produced by molecular distortions. The algorithm, which is implemented together with the bispectrum representation, is demonstrated for a number of molecules with different bonding structures and atomic species. The scheme presented here thus represents a convenient approach to the local inversion of structural descriptors, enabling the construction of structural generative models.
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