PDDFormer: Pairwise Distance Distribution Graph Transformer for Crystal Material Property Prediction

Xiangxiang Shen, Zheng Wan, Lingfeng Wen, Licheng Sun, Ou Yang Ming Jie, Jijun Cheng, Xuan Tang, Xian Wei

Keywords: Pairwise Distance Distribution, Graph Transformer, Periodic crystal

TL;DR: We introduced the Pairwise Distance Distribution (PDD) and intra-unit cell PDD for characterizing crystal materials, resolving the ambiguity in crystal structure representation.

Abstract: The crystal structure can be simplified as a periodic point set repeating across the entire three-dimensional space along an underlying lattice. Traditionally, methods for representing crystals rely on descriptors like lattice parameters, symmetry, and space groups to characterize the structure. However, in reality, atoms in material always vibrate above absolute zero, causing continuous fluctuations in their positions. This dynamic behavior disrupts the underlying periodicity of the lattice, making crystal graphs based on static lattice parameters and conventional descriptors discontinuous under even slight perturbations. To this end, chemists proposed the Pairwise Distance Distribution (PDD) method, which has been used to distinguish all periodic structures in the world's largest real materials collection, the Cambridge Structural Database. However, achieving the completeness of PDD requires defining a large number of neighboring atoms, resulting in high computational costs. Moreover, it does not account for atomic information, making it challenging to directly apply PDD to crystal material property prediction tasks. To address these challenges, we propose the atom-Weighted Pairwise Distance Distribution (WPDD) and Unit cell Pairwise Distance Distribution (UPDD) for the first time, incorporating them into the construction of multi-edge crystal graphs. Based on this, we further developed WPDDFormer and UPDDFormer, graph transformer architecture constructed using WPDD and UPDD crystal graphs. We demonstrate that this method maintains the continuity and completeness of crystal graphs even under slight perturbations in atomic positions. Moreover, by modeling PDD as global information and integrating it into matrix-based message passing, we significantly reduced computational costs. Comprehensive evaluation results show that WPDDFormer achieves state-of-the-art predictive accuracy across tasks on benchmark datasets such as the Materials Project and JARVIS-DFT.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 2647