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 V₂ = 104 – 256 m/min, feed rate f = 0. 035 – 0. 385 mm/rev, and depth of cut a₏ = 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 (rₒ = +0. 937, p < 0. 001). Results show that physics-informed constraints enhance generalization and interpretability in small datasets compared to standard data-driven models.