Insights into the Indexing of Powder X-ray Diffraction from a Robust Transformer Deep Learning

The indexing of powder X-ray diffraction (PXRD) for ab initio determination of unknown crystal structures remains challenging for systems with low-symmetry (e.g., triclinic and monoclinic), large unit cell ( V > 1000 ų), and nonideal data due to reliance on heuristic methods with limited robustness. Here, we propose AIdex-R2, a transformer-based end-to-end framework that performs joint inference of the extinction groups (EGs) and unit cell parameters from sequences of low-angle diffraction reflections. The model achieves ∼98.5% top-5 accuracy for EG identification and ∼1.44% mean absolute percentage error (MAPE) for cell parameter prediction (indexing), with an indexing success rate exceeding ∼90% under extremely realistic perturbations (e.g., zero-shift errors ±0.30°, uncertainty noise ±0.15°, reflection absence n = 4, and impurity reflections n = 2). Large-scale benchmarking shows superior performance over classical algorithms (TREOR, ITO, DICVOL) in both speed/efficiency and accuracy. Through interpretability studies of the internal decision-making mechanism, we confirm that the model adopts a discriminant logic dominated by the first diffraction peak (low 2 θ ) with dynamic weight allocation, providing a novel perspective and evidence for understanding the “black box” of PXRD indexing.