Noise augmented machine learning for predicting ageing hardening behavior of Mg–Gd alloys: From data scarcity to physically interpretable modelling

Age-hardening in Mg-Gd alloys is governed by coupled effects of composition and heat treatment history. However, predictive modelling remains challenging because available datasets are small and structurally biased toward discrete composition/temperature conditions and continuous ageing-time sampling. In this work, a physically constrained machine-learning framework was developed to predict the hardness evolution of binary Mg-Gd alloys and to improve prediction robustness under data-scarce conditions. A literature-derived dataset containing 298 data points was used to train and compare XGBoost, Random Forest, Support Vector Regression, and AdaBoost models. To mitigate sampling bias, uniform noise bounded by experimental uncertainty was introduced into Gd content and ageing-temperature features during training. Under repeated random point-level validation, XGBoost showed the best baseline performance, and the proposed noise-augmentation strategy further improved the prediction accuracy from R 2 = 0.88 to 0.92 while reducing the MAE from 6.81 to 5.32 HV. Independent experimental-source validation using an Mg-13Gd alloy aged at 200 °C was further performed to evaluate prediction consistency, with R 2 increasing from 0.74 to 0.90. SHAP and partial-dependence analyses revealed model-learned relationships among Gd content, ageing temperature, and ageing time, with trends consistent with established precipitation-hardening knowledge and over-ageing behavior. The proposed framework offers an effective route for robust, interpretable modelling of composition-processing-property relationships in precipitation-hardenable magnesium alloys.