Application of expert-augmented machine learning modeling in high-strength and high-conductivity copper alloy development

Investigation into material data is frequently limited by small sample sizes, high noise levels, complex associations, high dimensionality, and the need for expert knowledge. To improve the effectiveness of machine learning modeling, incorporating expert knowledge is necessary. In this study, we assembled a dataset including 410 data points containing composition, condition, and property data, in which the state symbols of the copper alloy were recoded using the one-hot encoding method. Because of the substantial capacity of neural network algorithms for powerful nonlinear fitting, we employed these algorithms for modeling. The network structures of the strength and conductivity models were optimized to 21–55–70–1 and 21–50–65–1, respectively. After optimizing the network structure, expert knowledge was integrated into the neural network loss function. This approach quantitatively describes the strength of the monotonic relations between the status factors of components and performance by calculating the rank correlation coefficient between the independent and dependent variables. During model training, the rank correlation coefficient was incorporated into the neural network loss function to assess the similarity between the model output and expert knowledge in real-time. For instance, the relation in which strength increases with the hardening level was quantitatively expressed with a Spearman score, and these Spearman scores were added to the loss function. A machine learning model augmented by expert knowledge was trained using genetic algorithm-based optimization of network weights. After updating each network weight, orthogonal data were generated to evaluate the consistency between output data and expert knowledge. The Spearman correlation coefficients between the model input–output data and expert knowledge exceeded 0.98, and the R² scores of the strength and conductivity models achieved on the test set were >0.90. Multiobjective optimization based on composition, condition, strength, and conductivity models was conducted using a genetic algorithm, and Pareto-optimal solutions were obtained and experimentally validated after 100 generations of iteration. Three sets of components were selected from the Pareto-optimal solutions and were empirically tested for validation. The results showed that the tensile strength had reached 637 MPa, while conductivity was maintained at 77.5% IACS (International annealing copper standard), and when the conductivity was 80.2% IACS, the tensile strength was 600 MPa. The relative errors between the experimental and predicted values were <5%. Microstructure images of three experimental sample sets demonstrated that coarse second phases were present in the as-cast structure; however, these structures were dissolved and redistributed after the solid solution, cold deformation, and aging processes. The precipitated particles distributed along the grain boundary had low strength and conductivity. Our analysis revealed that the Mg and Ti elements were detrimental to the increase in strength, while Fe and Sn effectively increased strength. Additionally, Fe had a lower impact on conductivity than Sn. The results of this study demonstrate that the three optimized components identified can satisfy the performance requirements of interconnected frameworks in ultralarge-scale integrated circuits.