Physics-Guided Surrogate Modelling for Microhardness Prediction in LPBF 316L Using Thermal-Gradient and Energy-Density Features

Laser Powder Bed Fusion (LPBF) of 316L stainless steel is highly sensitive to laser power, scan speed, and beam size, which makes property prediction challenging especially when only small, scattered experimental datasets are available. Traditional machine-learning models trained directly on such limited data often struggle with overfitting and poor generalization. In this study, we present a lightweight, physics-Guided surrogate modelling framework designed specifically for small-data LPBF environments. Starting from 74 literature-reported microhardness measurements, we create an expanded training set using a cluster-aware Kernel Density Estimation (KDE) strategy that generates new samples only within physically meaningful regions of the P–v–spot space. A SAFE_DIST constraint ensures that surrogate points do not become near-duplicates of actual experiments, while a ±3 HV noise model preserves realistic hardness variability seen in LPBF studies. To incorporate first-order thermal behaviour without resorting to computationally expensive simulations, we construct three analytical descriptors: an energy-density proxy, a Rosenthal-inspired thermal-gradient indicator, and a thermo-mechanical efficiency (TME) metric. Together, these features improve interpretability and guide the model toward thermally consistent predictions. Ensemble regressors trained solely on the surrogate dataset demonstrate strong predictive capability on unseen real measurements, achieving an independent real-only test R² of 0.84. A strict real-only leave-one-out cross-validation (LOOCV) yields a conservative R² of 0.64, consistent with the inherent scatter of LPBF microhardness data. When trained on the full augmented dataset, the model achieves an overall R² of 0.91, reflecting the smooth, physically coherent nature of the surrogate space. The resulting process maps and learning-curve trends align closely with established LPBF thermal–microstructural behaviour, confirming that the framework learns underlying physics rather than memorizing datapoints. Overall, this work provides a simulation-free, data-efficient, and thermally grounded approach for predicting microhardness in LPBF 316L, offering a practical foundation for rapid parameter exploration, process optimization, and extension to other materials and LPBF responses.