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To date, the International Zeolite Association Structure Commission (IZA-SC) has cataloged merely 255 distinct zeolite structures, with millions of theoretically possible structures yet to be discovered. The synthesis of a specific zeolite typically necessitates the use of an organic structure-directing agent (OSDA), since the selectivity for a particular zeolite is largely determined by the affinity between the OSDA and the zeolite. Therefore, finding the best affinity OSDA-zeolite pair is the key to the synthesis of targeted zeolite. However, OSDA-zeolite pairs frequently exhibit complex geometric structures, i.e., a complex crystal structure formed by a large number of atoms. Although some existing machine learning methods can represent the periodicity of crystals, they cannot accurately represent crystal structures with local variability. To address this issue, we propose a novel approach called Zeoformer, which can effectively represent coarse-grained crystal periodicity and fine-grained local variability. Zeoformer reconstructs the unit cell centered around each atom and encodes the pairwise distances between this central atom and other atoms within the reconstructed unit cell. The introduction of pairwise distances within the reconstructed unit cell more effectively represents the overall structure of the unit cell and the differences between different unit cells, enabling the model to more accurately and efficiently predict the properties of OSDA-zeolite pairs and general crystal structures. Through comprehensive evaluation, our Zeoformer model demonstrates the best performance on OSDA-zeolite pair datasets and two types of crystal material datasets., Comment: 7 pages, 5 figures

Diffusion generative models (DMs) have achieved promising results in image and graph generation. However, real-world graphs, such as social networks, molecular graphs, and traffic graphs, generally share non-Euclidean topologies and hidden hierarchies. For example, the degree distributions of graphs are mostly power-law distributions. The current latent diffusion model embeds the hierarchical data in a Euclidean space, which leads to distortions and interferes with modeling the distribution. Instead, hyperbolic space has been found to be more suitable for capturing complex hierarchical structures due to its exponential growth property. In order to simultaneously utilize the data generation capabilities of diffusion models and the ability of hyperbolic embeddings to extract latent hierarchical distributions, we propose a novel graph generation method called, Hyperbolic Graph Diffusion Model (HGDM), which consists of an auto-encoder to encode nodes into successive hyperbolic embeddings, and a DM that operates in the hyperbolic latent space. HGDM captures the crucial graph structure distributions by constructing a hyperbolic potential node space that incorporates edge information. Extensive experiments show that HGDM achieves better performance in generic graph and molecule generation benchmarks, with a $48\%$ improvement in the quality of graph generation with highly hierarchical structures., Comment: accepted by AAAI 2024