Physics-Informed Symbolic Regression Ensemble (PISRE) for surface roughness prediction in Ti-6Al-4V dry turning

Predicting surface roughness in titanium alloy machining remains challenging due to the nonlinear interactions among process parameters and the small datasets inherent to experimental campaigns. Physics-Informed Symbolic Regression Ensemble (PISRE) is a novel physics-informed ensemble model for Ti-6Al-4V roughness Ra that integrates a physics layer with four log-optimized symbolic branches and an uncertainty-weighted mechanism for dynamic branch confidence. Experiments were conducted following a Central Composite Design yielding 19 runs spanning cutting velocity V_c = 104 – 256 m/min, feed rate f = 0.035 – 0.385 mm/rev, and depth of cut a_p = 0.03 – 0.37 mm. Leave-One-Out cross-validation showed that PISRE achieved RMSE = 0.443 µm and R^2 = 0.915 , outperforming XGBoost (RMSE = 0.657, R^2 = 0.814 ) and Random Forest (RMSE = 0.716, R^2 = 0.778 ) by 32.6% and 38.1% in RMSE respectively. The optimised feed rate exponent ( b ≈ 1.18 ) is physically consistent with Ti-6Al-4V turning literature, and Spearman correlation analysis confirmed feed rate as the sole significant predictor of Ra within the tested window ( r_s = +0.937 , p < 0.001 ). Results show that physics-informed constraints enhance generalization and interpretability in small datasets compared to standard data-driven models.