A Physics-Guided Gradient Boosting Approach for Few-Shot Prediction of Plastic Work Density in BGA Solder Joints

Abstract

With the increasing power density in advanced packaging, the thermo-mechanical reliability of Ball Grid Array (BGA) solder joints has become a critical concern. While data-driven machine learning models are applied for fatigue prediction, they typically suffer from severe overfitting and violate physical laws under data-scarce (few-shot) scenarios. Here, we propose a physics-guided gradient boosting approach for the precise prediction of solder joint plastic work density. Dimensionless physical descriptors, including stiffness ratio and coefficient of thermal expansion mismatch, were constructed to enhance cross-condition robustness. Furthermore, analytical viscoplastic energy bounds were derived as physics proxies, and monotonicity constraints were integrated into the tree-building process. Experimental results demonstrate that, compared to conventional data-driven approaches, the proposed model achieves significantly faster convergence and maintains high predictive accuracy even when trained on merely 5% of the dataset. Additionally, SHAP analysis reveals that the introduced theoretical energy bounds dominate the predictions, verifying that the model successfully captures the underlying thermo-mechanical mechanisms rather than overfitting numerical noise.