Edward (Eddie) G. Friedman

Determining crystal symmetry from powder X-ray diffraction is a central problem in materials characterization, yet multiple space groups can produce indistinguishable patterns, making automated classification difficult. We show that attention-based architectures, while superior to convolutional networks for this task, are insufficient on their own: reliable symmetry extraction requires encoding crystallographic knowledge into both the network architecture and the training curriculum. We introduce a physics-informed transformer that classifies powder patterns into 99 extinction groups, the most specific symmetry classification accessible from diffraction data alone, using an explicit sin^2(theta) coordinate channel, physics-aware positional encoding, and a structured multi-task decoder that separates geometric rule learning from holistic pattern recognition. A three-stage curriculum of balanced synthetic pretraining, realistic fine-tuning with explicit preferred-orientation modeling, and Bayesian prior injection proves essential for bridging the synthetic-to-real domain gap, while post-hoc temperature scaling rather than additional training is the key remaining ingredient for robust real-data transfer. By mapping predictions onto the directed acyclic graph of maximal translationengleiche subgroups, we show that the calibrated model’s errors are not random but physically structured: they remain local on the subgroup hierarchy and flow predominantly toward lower-symmetry descendants, consistent with the physical erasure of systematic-absence cues by real-world noise. These results establish that physics-informed target design, curriculum, and calibrated inference matter as much as model capacity for scientific machine learning on diffraction data.