Diagnosing and narrowing the simulation-to-real gap in powder X-ray diffraction with a wet-dry agentic loop

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.

Powder X-ray diffraction (XRD) is central to materials characterization, yet reliable end-to-end automation remains challenging. An XRD agent must interpret diffraction evidence, operate refinement software, manage coupled parameters in a defensible order, and distinguish numerical improvement from physical validity. In this paper, we propose AutoXRD, an autonomous large language model (LLM) agent framework that organizes powder-XRD analysis as stepwise refinement, grounds actions in observed evidence, and applies deterministic crystallographic and physical checks before accepting results. We further introduce XRDBench with two complementary tracks. XRDBench-QA contains 100 bounded diagnostic tasks that isolate scientific reasoning and decision-making, whereas XRDBench-E2E contains 34 executable workflows that test whether agents can compose these capabilities into complete analyses requiring file inspection, crystallographic-software execution, iterative refinement, evidence preservation, and reporting. We evaluate ten recent LLMs across 1,340 model--task runs. Models average only 57.8 out of 100, falling from 61.9 on XRDBench-QA to 53.7 on XRDBench-E2E. They perform best on refinement-history assessment and result acceptance, but remain substantially weaker on refinement-action selection, phase quantification, indexing, and Rietveld refinement. GPT-5.6 Sol achieves the highest overall score of 81.1, GPT-5.6 Terra the highest XRDBench-E2E point estimate of 81.0, and GPT-5.6 Luna the best score--cost trade-off. Ablations show that all six AutoXRD components consistently improve performance, supporting the framework design. Finally, execution-trace analysis reveals recurring failures in coupled-parameter control, quantitative reasoning, evidence preservation, and workflow termination, motivating stronger scientific constraints, uncertainty-aware decisions, and more efficient planning.

Artificial intelligence can rapidly propose candidate phases and structures from X-ray diffraction (XRD), but these hypotheses often fail in downstream refinement because peak intensities cannot be stably assigned under severe overlap and diffraction consistency is enforced only weakly. Here we introduce the whole-pattern expectation--maximization (WPEM) algorithm, a physics-constrained whole-pattern decomposition and refinement workflow that turns Bragg's law into an explicit constraint within a batch expectation--maximization framework. WPEM models the full profile as a probabilistic mixture density and iteratively infers component-resolved intensities while keeping peak centres Bragg-consistent, producing a continuous, physically admissible intensity representation that remains stable in heavily overlapped regions and in the presence of mixed radiation or multiple phases. We benchmark WPEM on standard reference patterns (PbSO$_4$ and Tb$_2$BaCoO$_5$), where it yields lower $R_p/R_{wp}$ than widely used packages (FullProf and TOPAS) under matched refinement conditions. We further demonstrate generality across realistic experimental scenarios, including phase-resolved decomposition in multiphase materials, quantitative recovery of mixture compositions, separation of crystalline peaks from amorphous backgrounds in semicrystalline systems, high-throughput operando lattice tracking, automated refinement of compositionally disordered solid solutions, and quantitative phase-resolved analysis of complex archaeological samples from synchrotron powder XRD. By providing Bragg-consistent, uncertainty-aware intensity partitioning as a refinement-ready interface, WPEM closes the gap between AI-generated hypotheses and diffraction-admissible structure refinement on challenging XRD data.