Atomic Structure Generation from Structural Fingerprints

Data-driven machine learning methods have the potential to dramatically accelerate the rate materials design over conventional human-guided approaches. These methods would help identify or, in the case of generative models, even create novel crystal structures of materials with a set of specified functional properties to then be synthesized or isolated in the laboratory. For crystal structure generation, a key bottleneck lies in developing suitable atomic structure fingerprints or representations for the machine learning model, analogous to the graph-based or SMILES representations used in molecular generation. However, finding data-efficient representations invariant to translations, rotations, and permutations, while remaining invertible to the Cartesian atomic coordinates remains an ongoing challenge. Here, we propose an alternative approach to this problem by taking existing non-invertible representations with the desired invariances and developing a method to reconstruct the atomic coordinates through a global optimization scheme. This can then be coupled to a generative machine learning model which generates new materials within the representation space, rather than in the data-inefficient Cartesian space. In this work, we demonstrate this approach by using conditional variational autoencoders to generate representations from atom-centered symmetry functions, which are then reconstructed to their corresponding atomic positions using the developed optimization method. We are able to successfully generate novel and valid atomic structures of sub-nanometer Pt nanoparticles as a proof of concept. Furthermore, this method can be extended to any suitable structural representation, thereby providing a powerful, generalizable approach towards structure-based generation.