To address the challenges of small-sample modeling and the diffculty of achieving a balance between hardness and thermal conductivity in aluminum-copper alloys through traditional design, this study proposes a machine learning framework based on physical features and multi-stage screening for performance prediction and composition optimization. The proposed framework consists of 5 sequential stages: data preparation, physical feature construction, multi-stage feature screening, predictive modeling and evaluation, and multi-objective composition optimization. A total of 24 aluminum-copper alloy samples prepared under the same die-casting process were collected, with hardness and thermal conductivity as the target properties, from which a 99-dimensional physically derived feature space was constructed using composition-weighted mean and variance descriptors of 44 physicochemical properties of 11 constituent elements. To reduce feature collinearity and redundancy and improve modeling reliability under small-sample conditions, a three-stage feature screening strategy combining hierarchical clustering, Lasso regularization, and exhaustive best subset search was employed to identify the core feature subsets for predicting hardness and thermal conductivity. Based on the screened optimal features, Lasso linear regression models with L₁ regularization were established for hardness and thermal conductivity, respectively. Model hyperparameters were optimized using leave-one-out cross-validation (LOOCV), while predictive performance was evaluated on an independent test set. Model performance was quantitatively assessed using the coeffcient of determination (R²) and root-mean-square error (RMSE), thereby characterizing prediction accuracy and generalization capability.
The results show that the hardness model achieves a test R² of 0.885 with an RMSE of 4.79, and the thermal conductivity model yields a test R² of 0.847 with an RMSE of 4.67, indicating good predictive performance on the independent test set. Furthermore, a composition optimization strategy coupling global Latin hypercube sampling (LHS) and local Gaussian refinement was proposed to achieve a balanced improvement in hardness and thermal conductivity. Within the feasible composition domain constrained by experimental boundaries, 10⁴ candidate compositions were uniformly generated via LHS for global exploration. Based on the equal-weight comprehensive scoring function, the top 20 high-performance seed compositions were selected from these candidates. Using these seed compositions as local sampling centers, another 10⁴ new samples were generated by Gaussian resampling, and composition normalization constraints were imposed to ensure the validity of the generated compositions. Finally, 4 groups of optimized alloy compositions were screened out, all achieving a comprehensive score of 0.77. The optimized alloys exhibit a hardness of 72~74 MPa and a thermal conductivity of 118~121 W/(m·K), indicating a balanced enhancement of the 2 target properties. Overall, the proposed method combines physically derived descriptors, multi-stage feature selection, predictive modeling, and two-stage composition optimization within a unified data-driven procedure. This combination helps retain physical interpretability while improving prediction performance under small-sample conditions and provides a data-driven approach for the collaborative optimization of hardness and thermal conductivity in Al-Cu alloys.