An invertible, invariant crystal representation for inverse design of solid-state materials using generative deep learning

The past decade has witnessed rapid progress in deep learning for molecular design, owing to the availability of invertible and invariant representations for molecules such as simplified molecular-input line-entry system (SMILES), which has powered cheminformatics since the late 1980s. However, the design of elemental components and their structural arrangement in solid-state materials to achieve certain desired properties is still a long-standing challenge in physics, chemistry and biology. This is primarily due to, unlike molecular inverse design, the lack of an invertible crystal representation that satisfies translational, rotational, and permutational invariances. To address this issue, we have developed a simplified line-input crystal-encoding system (SLICES), which is a string-based crystal representation that satisfies both invertibility and invariances. The reconstruction routine of SLICES successfully reconstructed 94.95% of over 40,000 structurally and chemically diverse crystal structures, showcasing an unprecedented invertibility. Furthermore, by only encoding compositional and topological data, SLICES guarantees invariances. We demonstrate the application of SLICES in the inverse design of direct narrow-gap semiconductors for optoelectronic applications. As a string-based, invertible, and invariant crystal representation, SLICES shows promise as a useful tool for in silico materials discovery.