Physics-guided machine learning for predicting complete tool influence functions in flexible ball-end polishing

The tool influence function (TIF) is fundamental to computer-controlled optical surfacing (CCOS) for deterministic material removal. Conventional TIF acquisition relies on either physics-based modeling with extensive parameter calibration or time-consuming spot experiments. Existing machine learning studies in polishing have mainly focused on scalar removal-rate prediction, while direct prediction of the complete radial TIF profile from pre-settable process parameters remains insufficiently explored. In this work, we propose a physics-guided machine-learning framework for end-to-end prediction of complete TIF radial profiles in flexible ball-end polishing from four controllable process parameters: normal load, spindle speed, pad hardness, and abrasive concentration. Physics-guided feature engineering, derived from the Preston equation and Hertz contact theory, expands the 4-dimensional raw parameter space into an 11-dimensional physics-informed feature space. A dual-model framework is then developed by combining two complementary physics-constrained gradient boosting regression (PC-GBR) models through equal-weight averaging. In PC-GBR, physical prior knowledge derived from the Preston equation and Hertz contact theory is incorporated through monotonic constraints on selected physics-guided features. Based on 53 valid replicate measurements aggregated into 15 operating-condition groups, the proposed framework is validated by leave-one-group-out cross-validation. It achieves a Peak MAPE of 7.5%, an MRR MAPE of 7.9%, and a mean Profile R2 of 0.948. Physics-guided feature engineering reduces MRR prediction error by 45% relative to raw inputs, and the predicted radial profile can be directly reconstructed into a full two-dimensional TIF for CCOS dwell-time computation.