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 $$\varvec{Ra}$$ 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 $$\varvec{V}_{\varvec{c}} \varvec{=} \varvec{104}$$ – $$\varvec{256}$$ m/min, feed rate $$\varvec{f = 0.035}$$ – $$\varvec{0.385}$$ mm/rev, and depth of cut $$\varvec{a}_{\varvec{p}} \varvec{=} \varvec{0.03}$$ – $$\varvec{0.37}$$ mm. Leave-One-Out cross-validation showed that PISRE achieved RMSE = 0.443 µm and $$\varvec{R}^{\varvec{2}} \varvec{=} \varvec{0.915}$$ , outperforming XGBoost (RMSE = 0.657, $$\varvec{R}^{\varvec{2}} \varvec{=} \varvec{0.814}$$ ) and Random Forest (RMSE = 0.716, $$\varvec{R}^{\varvec{2}} \varvec{=} \varvec{0.778}$$ ) by 32.6% and 38.1% in RMSE respectively. The optimised feed rate exponent ( $$\varvec{b} \varvec{\approx } \varvec{1.18}$$ ) is physically consistent with Ti-6Al-4V turning literature, and Spearman correlation analysis confirmed feed rate as the sole significant predictor of $$\varvec{Ra}$$ within the tested window ( $$\varvec{r}_{\varvec{s}} \varvec{=} \varvec{+0.937}$$ , $$\varvec{p} \varvec{<} \varvec{0.001}$$ ). Results show that physics-informed constraints enhance generalization and interpretability in small datasets compared to standard data-driven models.