Physics-Informed Machine Learning for Predicting Carburizing Process Outcomes in 20Cr2Ni4 Steel: A Cascade Modeling Approach

Carburizing process optimization requires accurate prediction of multiple interrelated outcomes, yet existing models either oversimplify the physics or require prohibitively large datasets. Here, we present a physics-informed machine learning (PIML) cascade model for vacuum carburizing of 20Cr2Ni4 gear steel that predicts surface carbon content, maximum hardness, and effective case depth through a three-stage sequential architecture. The model integrates Fick’s diffusion law and empirical carbon–hardness relationships with ensemble learning using physics-derived features to reduce data requirements while maintaining interpretability. Validation against experimental data yields coefficient of determination values of 0.968 (surface carbon, RMSE = 0.0023 wt%), 0.963 (maximum hardness, RMSE = 1.27 HV), and 0.999 (case depth, RMSE = 0.0053 mm) on physics-augmented test data; leave-one-out cross-validation (LOOCV) on original experimental data yields R2 = 0.87–0.95, representing true generalization capability. Feature importance analysis reveals that physics-derived features collectively account for over 70% of the prediction power, with the characteristic diffusion length (Dt) contributing 42.2%, followed by temperature-related features (22.4%) and time-related features (14.8%). Compared to pure physics-based and data-driven approaches, the proposed framework achieves superior accuracy for case depth prediction while preserving physical consistency. The methodology demonstrates potential for adaptation to other vacuum-carburizing applications with similar Cr-Ni steel compositions, although extension to fundamentally different processes (e.g., gas carburizing and nitriding) would require process-specific recalibration.