Leveraging generative models with periodicity-aware, invertible and invariant representations for crystalline materials design.

Designing periodicity-aware, invariant and invertible representations provides an opportunity for the inverse design of crystalline materials with desired properties by generative models. This objective requires optimizing representations and refining the architecture of generative models, yet its feasibility remains uncertain, given current progress in molecular inverse generation. In this Perspective, we highlight the progress of various methods for designing representations and generative schemes for crystalline materials, discuss the challenges in the field and propose a roadmap for future developments.