Physics Priors Improve Interpolation but Not Unseen-Composition Transfer in Wetting Surrogates

Whether a physically credible prior improves a machine-learning surrogate’s predictions, or only its plausibility, is not settled by agreement with a closed-form physical relation alone. We evaluate a Gaussian process (GP) whose prior mean is a physics-derived reference relation — the Wenzel/Cassie–Baxter formulation for a photocatalytic coating dataset, and an Owens–Wendt surface-energy decomposition for a static-polymer dataset — against a zero-mean GP and standard machine-learning baselines (RandomForest, XGBoost, MLP, SVR-RBF), on two contact-angle datasets: TiO2/PMC photocatalytic coatings under accumulating UV exposure (Dataset A, N=85) and 26 static polymer surfaces compiled from Sena et al. (Dataset B, N=26). Four validation protocols are kept explicitly separate: an external comparison of the closed-form relation against the independent Cassie and Baxter (1944) wire-grating measurements; point-wise K-fold cross-validation on Dataset A, which estimates interpolation within a partially observed composition trajectory; leave-one-composition-out (LOGO) validation on Dataset A, which estimates transfer to an unseen composition; and leave-one-polymer-out cross-validation (LOOCV) on Dataset B. The general two-fraction Cassie–Baxter form agreed with the independent 1944 measurements to approximately 1◦ mean absolute error (MAE) over four held-out geometries, supporting the physical reference itself. On Dataset A, GP-Physics was the strongest model under known-composition interpolation (8.55◦ MAE with a dose feature, versus 9.13◦ for GP-Zero and 15.11◦ for the next-best baseline), but dose-augmented tree models (XGBoost, RandomForest) were strongest under unseencomposition transfer (20.85◦ and 21.53◦ ), where both GP variants were the two weakest models (34.40◦ and 34.27◦ ). On Dataset B, GP-Zero was more accurate than GP-Physics across all three surface-energy parameterizations tested (analogy-derived, literature-informed, and expanded literature-informed), with the gap narrowing from 2.33◦ to 1.51◦ under increasingly literature-informed inputs but never reversing. Held-out coverage at the nominal 90% level was comparable between the two GP variants on Dataset A (0.882 vs. 0.882) but markedly worse for GP-Physics than GP-Zero on Dataset B (0.692 vs. 0.846); non-GP baseline intervals are naive Gaussian plug-ins from training-residual spread, not conformal or distribution-free intervals, and are reported as such. Taken together, these results show that the predictive benefit of a physics prior is conditional on the dataset, the provenance of its physical inputs, and the generalization boundary being evaluated — not a universal property of physics-informed modeling.