Synchrotron X-ray-informed machine learning for local hardness mapping in a Cu–Ni–Ti–Hf–Zr high-entropy shape-memory alloy

Abstract

A supervised machine-learning framework was used to relate colocated synchrotron X-ray fluorescence (XRF), X-ray nanodiffraction (XND), thermodynamic descriptors, and nanoindentation measurements to local hardness in an as-cast Cu 15 Ni 35 Ti 25 Hf 12. 5Zr 12.5 high-entropy shape-memory alloy (HESMA). The analysis used 516 measurement points and evaluated multilayer perceptron, k-nearest-neighbor, random-forest, and CatBoost regressors under fold-aware leave-one-out cross-validation (LOOCV). Three feature families were compared: pointwise-normalized local XRF composition values alone, XRF/XND/thermodynamic features without elastic modulus E, and a multimodal family including nanoindentation-derived E and fold-aware interaction terms. For CatBoost, the composition-only, E-free, and multimodal models yielded LOOCV R 2 values of 0.065, 0.214, and 0.342, respectively, with corresponding mean absolute errors of 63.4, 57.5, and 53.8 HV. The out-of-fold maps reproduced broad regional hardness trends but retained substantial pointwise residuals. Leave-one-grain-out validation produced non-positive R 2 values, showing that reliable transfer to an unseen grain was not established. These results define the method as a mapping-domain framework for quantifying local composition–structure–property associations rather than a general predictor across grains, composition ranges, or alloy systems.