ED-CSP Predicts Crystal Structures from Electron Diffraction

Recovering the precise 3D atomic arrangement of a crystal structure from limited and unindexed electron diffraction (ED) data is a notoriously difficult inverse problem in materials science. Traditional methods often rely on extensive libraries or indexed reflections, limiting their applicability to novel or complex materials. This research introduces ED-CSP, a machine learning framework designed to tackle this generative challenge directly. ED-CSP takes chemical composition, atom count, and multiple detector-plane ED spot sets as input. It employs a sophisticated architecture combining a relational set encoder, permutation-invariant multi-view aggregation, and a periodic flow generator. This allows the model to jointly predict both lattice parameters and fractional atomic coordinates, effectively reconstructing the full 3D crystal structure. To train ED-CSP, a massive dataset called ED-CS was constructed, comprising 4.85 million simulated multi-view ED crystal structures. When evaluated on held-out materials, ED-CSP achieved a structural match rate of 57.49% (MR@5), surpassing PXRDGen, a state-of-the-art model based on powder X-ray diffraction. Scaling the training data further improved performance to 66.27% MR@5. Crucially, the model demonstrated true generative capability by achieving 53.52% MR@5 on compositions entirely absent from its training retrieval library, confirming it predicts structures rather than merely retrieving them. The dependence on input diffraction patterns, rather than just composition, was also validated, establishing ED-CSP and ED-CS as a significant benchmark for generative crystal structure prediction from sparse ED observations.