Physics-Informed Feature-Space Invariants for Sim-to-Real FCC/HCP Phase Classification in High-Entropy Alloys

High-entropy alloys (HEAs) can undergo FCC–HCP phase transformations and may contain coexisting phases, making reliable X-ray diffraction (XRD) phase identification challenging. We investigate whether classifiers trained entirely on computational XRD data can transfer to experimental XRD patterns of chemically distinct HEAs without experimentally labeled training data. Rather than using high-dimensional 2θ–intensity profiles, each pattern is represented by two physics-informed features, x = [(d1/d2)^2, I2/I1]^T, based on dominant peak spacings and intensities. We generate 120 synthetic XRD patterns from Materials Project structures, comprising 60 FCC and 60 HCP structures, and evaluate Linear SVM, RBF SVM, and a cosine-kernel SVM implemented through classical simulation as a quantum-kernel analogue. On a held-out set of 54 chemically diverse Materials Project structures containing 4–6 elements, the models achieve 57.4%, 63.0%, and 75.9% accuracy, respectively, while a one-feature threshold baseline achieves 63.0%. On 17 independent experimental HEA XRD patterns, all three models achieve 100% accuracy without retraining or fine-tuning. The experimental result is interpreted cautiously given the limited sample size (95% Clopper–Pearson CI: 80.5–100%). These results provide preliminary evidence of sim-to-real transfer using compact physics-informed XRD features.