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

arXiv: https://arxiv.org/abs/2408.12984 · HTML: https://mlsanity.com/paper/2408.12984/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 23 Aug 2024.

## Builds on (most cited first, 13 of 13)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Approximately Equivariant Networks for Imperfectly Symmetric Dynamics](https://mlsanity.com/paper/2201.11969/) (2022)
- [Periodic Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2209.11807/) (2022)
- [Efficient Approximations of Complete Interatomic Potentials for Crystal Property Prediction](https://mlsanity.com/paper/2306.10045/) (2023)
- [Complete and Efficient Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2403.11857/) (2024)
- [CrysMMNet: Multimodal Representation for Crystal Property Prediction](https://mlsanity.com/paper/2307.05390/) (2023)
- [Crystalformer: Infinitely Connected Attention for Periodic Structure Encoding](https://mlsanity.com/paper/2403.11686/) (2024)
- [CrysGNN : Distilling pre-trained knowledge to enhance property prediction for crystalline materials](https://mlsanity.com/paper/2301.05852/) (2023)
- [Machine Learning Enabled Computational Screening of Inorganic Solid Electrolytes for Dendrite Suppression with Li Metal Anode](https://mlsanity.com/paper/1804.04651/) (2018)
- [A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Prediction](https://mlsanity.com/paper/2406.12888/) (2024)
- [Material Property Prediction using Graphs based on Generically Complete Isometry Invariants](https://mlsanity.com/paper/2212.11246/) (2022)

## Abstract (arXiv)

Crystal structures can be simplified as a periodic point set that repeats across three-dimensional space along an underlying lattice. Traditionally, crystal representation methods characterize the structure using descriptors such as lattice parameters, symmetry, and space groups. However, in reality, atoms in materials always vibrate above absolute zero, causing their positions to fluctuate continuously. This dynamic behavior disrupts the fundamental periodicity of the lattice, making crystal graphs based on static lattice parameters and conventional descriptors discontinuous under slight perturbations. Chemists proposed the pairwise distance distribution (PDD) method to address this problem. However, the completeness of PDD requires defining a large number of neighboring atoms, leading to high computational costs. Additionally, PDD does not account for atomic information, making it challenging to apply it directly to crystal material property prediction tasks. To tackle these challenges, we introduce the atom-Weighted Pairwise Distance Distribution (WPDD) and Unit cell Pairwise Distance Distribution (UPDD) and apply them to the construction of multi-edge crystal graphs. We demonstrate the continuity and general completeness of crystal graphs under slight atomic position perturbations. Moreover, by modeling PDD as global information and integrating it into matrix-based message passing, we significantly reduce 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.