# Beyond Structure: Invariant Crystal Property Prediction with Pseudo-Particle Ray Diffraction

arXiv: https://arxiv.org/abs/2509.21778 · HTML: https://mlsanity.com/paper/2509.21778/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 51 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Builds on (most cited first, 15 of 15)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [Periodic Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2209.11807/) (2022)
- [Ewald-based Long-Range Message Passing for Molecular Graphs](https://mlsanity.com/paper/2303.04791/) (2023)
- [An Alternative Probabilistic Interpretation of the Huber Loss](https://mlsanity.com/paper/1911.02088/) (2019)
- [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)
- [SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases](https://mlsanity.com/paper/2308.13212/) (2023)
- [Crystalformer: Infinitely Connected Attention for Periodic Structure Encoding](https://mlsanity.com/paper/2403.11686/) (2024)
- [Capturing long-range interaction with reciprocal space neural network](https://mlsanity.com/paper/2211.16684/) (2022)
- [Ab Initio Structure Solutions from Nanocrystalline Powder Diffraction Data](https://mlsanity.com/paper/2406.10796/) (2024)
- [Learning a Fourier Transform for Linear Relative Positional Encodings in Transformers](https://mlsanity.com/paper/2302.01925/) (2023)
- [Materials Generation in the Era of Artificial Intelligence: A Comprehensive Survey](https://mlsanity.com/paper/2505.16379/) (2025)

## Built on by (most cited first, 4 of 4)

- [XDecomposer: Learning Prior-Free Set Decomposition for Multiphase X-ray Diffraction](https://mlsanity.com/paper/2605.05866/) (2026)
- [AI-Driven Structure Refinement of X-ray Diffraction](https://mlsanity.com/paper/2602.16372/) (2026)
- [SVGym (SciVerseGym): An Environment for Reinforcement Learning and Bayesian Optimization in Crystal Discovery](https://mlsanity.com/paper/2606.22425/) (2026)
- [Reducing Symmetry Increase in Equivariant Neural Networks](https://mlsanity.com/paper/2608.12010/) (2026)

## Abstract (arXiv)

Crystal property prediction, governed by quantum mechanical principles, is computationally prohibitive to solve exactly for large many-body systems using traditional density functional theory. While machine learning models have emerged as efficient approximations for large-scale applications, their performance is strongly influenced by the choice of atomic representation. Although modern graph-based approaches have progressively incorporated more structural information, they often fail to capture long-range atomic interactions due to finite receptive fields and local encoding schemes. This limitation leads to distinct crystals being mapped to identical representations, hindering accurate property prediction. To address this, we introduce PRDNet that leverages unique reciprocal-space diffraction besides graph representations. To enhance sensitivity to elemental and environmental variations, we employ a data-driven pseudo-particle to generate a synthetic diffraction pattern. PRDNet ensures full invariance to crystallographic symmetries. Extensive experiments are conducted on Materials Project, JARVIS-DFT, and MatBench, demonstrating that the proposed model achieves state-of-the-art performance. The code is openly available at https://github.com/Bin-Cao/PRDNet.