Divide and conquer: Machine learning accelerated design of lead-free solder alloys with high strength and high ductility

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The attainment of both high strength and high ductility is always the goal for structure materials, because the two properties generally are mutually competing, called strength-ductility trade-off. Nowadays, the data-driven paradigm combined with domain knowledge provides the state-of-the-art methodology to the design and discovery of novel structure materials with high strength and high ductility. To enhance both strength and ductility, a joint feature is proposed here as the product of strength multiplying ductility. The strategy of “divide and conquer” is developed to solve the challenging problem that material experimental data of mechanical behaviors are typically small and scatter greatly, while the design space is vast. The strategy of “divide and conquer” is realized by a newly developed data preprocessing algorithm, named the Tree-Classifier for Gaussian Process Regression (TCGPR, available as an open-source package: PyTcgpr). TCGPR effectively partitions a large design space into three distinct subdomains, allowing three Machine Learning (ML) models to conquer each subdomain. This approach significantly improves prediction accuracy and generalization. Subsequently, the Bayesian global optimization is applied to design next experiments, by balancing exploitation and exploration. The experimental results completely validate the ML predictions, unveiling novel lead-free solder alloys with both high strength and high ductility. Various material characterizations are also conducted to explore the mechanism of high strength and high ductility of the alloys. Figure 1 shows the framework of the present work for the alloy design. Figure 2 shows all experimental data, where Y denotes the product of strength and elongation, the three Y contours are predicted by the three ML models, and the sample S1-POI, sample S2-POI and sample S3-POI are on the three Y contours. Obviously, the three samples exhibit the better mechanical properties, in terms of both strength and ductility, than all samples in the original dataset, implying the effectiveness of the “divide and conquer” strategy.

Figure 1. Designing framework for lead-free solder alloy with high strength and high ductility.

Figure 2. Experimental validation results. The three pentagons and three rhombuses are the alloy samples designed by machine learning, and three curves are the Y contours, and five black icons denote the commercially available lead-free solder alloys for comparison.

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