Organizations: Laboratoire de Mathématiques de Lens (LML), UR 2462, Université d’Artois, Lens, France · Laboratoire de Réactivité et de Chimie des Solides (LRCS), CNRS UMR 7314, UPJV, Amiens, France · Réseau sur le Stockage Electrochimique de l’Energie (RS2E), CNRS FR 3459, Amiens, France · ALISTORE-European Research Institute, CNRS FR 3104, Amiens, France
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.
Crystal structure prediction (CSP) is fundamental to computational materials discovery. Generative models including CDVAE, DiffCSP, FlowMM, and CrystalFlow learn stable-crystal distributions directly, but diffusion and flow-matching inference requires tens to thousands of sequential network evaluations per candidate. We introduce uFlowCSP, a MeanFlow-based CSP model that learns the average, rather than instantaneous, probability-flow velocity. It generates a complete structure in one to five evaluations, delivering 5x-58x faster inference with equal or better performance. A chemistry- and symmetry-aware Transformer uses canonical atom ordering, global composition, and per-token chemistry embeddings. A coarse crystal-system token is used only during training; it provides additive gains, particularly improving space-group agreement despite being absent at inference, which remains formula-only. On MP-20 with 20 candidates per target, one step matches CrystalFlow (78.38% vs. 78.34%) with 100x fewer evaluations and about 10x lower wall-clock time. Five steps reach 83.64%, exceeding CrystalFlow (78.34% at 2,000 evaluations) and DiffCSP (77.93% at about 20,000), while using 20x fewer evaluations. uFlowCSP generates 10,000 structures in 0.39-1.31 minutes, versus 6.5 for CrystalFlow and 76.1 for DiffCSP. Under CSPBench's energy-ranked top-five structure-and-space-group criterion, five-step uFlowCSP reaches 72%/72%/65% structure, space-group, and consensus match rates. CrystalFlow reaches 78%/73%/68% at 100 steps but falls to 49%/32%/31% at five. Thus, uFlowCSP improves accuracy per network evaluation, not merely peak accuracy.
Determining the crystal structure of a material from its powder X-ray diffraction (PXRD) pattern is a central challenge in materials science. PXRD is an accessible and widely used characterization technique, yet recovering the atomic structure from diffraction data requires solving an underdetermined inverse problem due to the loss of phase information. Generative modeling can provide a prior over atomic structure and learn the mapping from PXRD patterns to crystal structures via simulated structure-spectrum pairs. We present XRDiff, a diffusion model that recovers crystal structures from PXRD given either the stoichiometry or, in a more challenging setting, the elemental constituents and total number of atoms in the unit cell. We evaluate on datasets where each stoichiometry has multiple polymorphs and all polymorphs of a given composition are held out together, ensuring that high performance reflects genuine use of the diffraction signal. XRDiff achieves strong structure recovery rates on simulated benchmarks, indicating that the model learns a spectrum-to-structure mapping precise enough to differentiate between polymorphs. To address generalization to experimental data, we compare a full-spectrum encoding against an encoding based on peak descriptors. The peak-based encoding generalizes substantially better, outperforming even a model trained on full spectra with augmentations fitted to the experimental noise distribution. These results demonstrate that representations robust to the noise and artifacts present in real-world PXRD offer a practical and scalable path toward closing the simulation-to-experiment gap, enabling zero-shot crystal structure solution from experimental PXRD with full or partial chemical composition input.
Deep generative models are widely reported to enable de novo crystal structure prediction (CSP), but their capability has not been measured consistently against template-based methods. We evaluate 12 representative generative CSP models, spanning latent-variable, diffusion, flow-matching, autoregressive, and manifold random-walk architectures, against TCSP 2.0 on 180 test structures and a leakage-controlled subset of 46. All methods use identical structure-matching, symmetry, and consensus criteria. Template retrieval is the strongest single method, reaching 68.3% top-1 success; symmetry-aware EquiCSP (66.4%) and Uni-3DAR (62.9%) form the next tier. However, comparison with TCSP 2.0 shows that most structures correctly predicted by generative models are also correctly predicted by template substitution. Thus, the set of structures uniquely reachable by generation is small, limiting its practical advantage for discovering structures outside existing prototype libraries. To test the source of this performance, we removed entire stoichiometric prototype families from the training set and retrained the strongest generative model. Accuracy declined by 50-78% across four families, establishing that performance is substantially prototype-dependent. A small minority of structures survived removal of their prototype family, demonstrating a real but limited retrieval-independent predictive capacity. Present generative CSP models therefore function largely as implicit, softer-edged prototype libraries rather than genuinely de novo predictors. Enlarging this residual capacity, rather than aggregate match rate alone, is the central open problem.