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

TL;DR

This work presents PRDNet, a crystal property predictor that integrates a learned pseudo-particle diffraction module with graph-based representations to capture long-range atomic correlations. By constructing a complete, invariant reciprocal-space description through learnable form factors and Miller-index–driven structure factors, PRDNet enforces $E(3)$-invariance and fuses modalities at the representation level. Empirical results across MP, JARVIS-DFT, and MatBench demonstrate state-of-the-art performance on formation energy, band gaps, and elastic properties, highlighting the practical value of combining diffraction physics with graph learning. The approach offers a new paradigm for CPP by leveraging reciprocal-space information to encode global structure while maintaining symmetry invariances, with broader implications for materials discovery and design.

Abstract

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.

Figures (5)

• Figure 1: Relationship between crystal and reciprocal space.
• Figure 2: Representation limitations of projecting different atomic periodicity into the same graph representation using (a) multi-edge graphs, (b) atomic angular embedding, and (c) a periodic vector-based reference system. The gray region represents a lattice cell of the 2D crystal.
• Figure 3: Analogy to light diffraction demonstrating how reciprocal space encodes long‐range interactions.
• Figure 4: The configuration of PRDNet, which integrates crystal attention and pseudo-particle diffraction to capture both short- and long-range atomic interactions.
• Figure 5: Performance of PRDNet on formation energy and band gap prediction across different numbers of Miller indices.