VQCrystal: Leveraging Vector Quantization for Discovery of Stable Crystal Structures

Discovering functional crystalline materials through computational methods remains a formidable challenge in materials science. Here, we introduce VQCrystal, an innovative deep learning framework that leverages discrete latent representations to overcome key limitations in current approaches to crystal generation and inverse design. VQCrystal employs a hierarchical VQ-VAE architecture to encode global and atom-level crystal features, coupled with a machine learning-based inter-atomic potential(IAP) model and a genetic algorithm to realize property-targeted inverse design. Benchmark evaluations on diverse datasets demonstrate VQCrystal's advanced capabilities in representation learning and novel crystal discovery. Notably, VQCrystal achieves state-of-the-art performance with 91.93\% force validity and a Fr\'echet Distance of 0.152 on MP-20, indicating both strong validity and high diversity in the sampling process. To demonstrate real-world applicability, we apply VQCrystal for both 3D and 2D material design. For 3D materials, the density-functional theory validation confirmed that 63.04\% of bandgaps and 99\% of formation energies of the 56 filtered materials matched the target range. Moreover, 437 generated materials were validated as existing entries in the full database outside the training set. For the discovery of 2D materials, 73.91\% of 23 filtered structures exhibited high stability with formation energies below -1 eV/atom. Our results highlight VQCrystal's potential to accelerate the discovery of novel materials with tailored properties.