ED-CSP: Crystal Structure Prediction from Electron Diffraction

2026-08-06

AI Summary

Reconstructing three-dimensional crystal structures from sparse, uncalibrated electron diffraction (ED) data poses a highly challenging generative inverse problem. This work proposes ED-CSP, the first framework capable of end-to-end crystal structure generation using only sparse multi-view ED spots, without requiring diffraction calibration, label prediction, or database retrieval. By incorporating chemical composition and atomic counts, ED-CSP jointly predicts lattice parameters and fractional atomic coordinates through a relational set encoder, a permutation-invariant multi-view aggregator, and a periodic flow generator. On the CHILI-100K benchmark, it achieves an MR@5 of 57.49%, improving to 66.27% with expanded training data; notably, it maintains strong performance on out-of-distribution compositions with an MR@5 of 53.52%, substantially outperforming PXRDGen and demonstrating both genuine generative capability and robust generalization.

Abstract

Recovering a periodic 3D crystal structure from sparse, unindexed electron diffraction (ED) observations is a challenging generative inverse problem. Existing ED-based learning methods mainly predict crystallographic labels, reconstruct structures from indexed reflections, or retrieve candidates from finite structure libraries. Here, we introduce ED-CSP, a machine learning framework that predicts crystal structures from chemical composition, atom count, and multiple detector-plane ED spot sets. ED-CSP combines a relational set encoder, permutation-invariant multi-view aggregation, and a periodic flow generator to jointly predict lattice parameters and fractional atomic coordinates. To train the model, we construct ED-CS, a dataset of 4.85 million simulated multi-view ED crystal structures, deduplicated across seven materials repositories and filtered to exclude CHILI-100K overlaps. On 2,075 held-out CHILI-100K materials, ED-CSP trained only on CHILI achieves a structural match rate of 57.49% MR@5, outperforming PXRDGen (52.92%), a state-of-the-art crystal structure prediction model conditioned on powder X-ray diffraction. Scaling training data further improves performance: initializing from a one-million-structure precursor raises MR@5 to 66.27%. On 1,024 compositions absent from the training retrieval library, the model still achieves 53.52% MR@5, demonstrating true generative capability beyond exact-formula retrieval. Replacing target ED observations with diffraction from non-isomorphic structures of identical composition decreases MR@5 by 22.09 percentage points, confirming that predictions depend on the input diffraction patterns rather than composition alone. ED-CSP and ED-CS establish a benchmark for generative crystal structure prediction from sparse ED observations and provide a foundation for future transfer to experimental data.

Problem

• crystal structure prediction
• electron diffraction
• generative inverse problem
• unindexed diffraction
• 3D crystal structure

Innovation

• electron diffraction
• crystal structure prediction
• generative inverse problem
• multi-view aggregation
• periodic flow generator