Reliable heavy-ion fusion cross sections in the sub-barrier region are essential for selecting beam-target combinations and incident energies in superheavy-nucleus synthesis, but their prediction remains diffcult because quantum tunneling is strongly modified by couplings to collective excitations, nucleon transfer, and static deformation. Conventional phenomenological formulas impose rigid analytic barrier shapes, whereas purely data-driven models may violate the Coulomb asymptotic behavior when extrapolated to sparsely sampled energies. To address both limitations, we develop a physics-informed Light Gradient Boosting Machine (PI-LightGBM) by combining the Swiatecki-Wilczynska (S-W) phenomenological formula with a residual-learning strategy. A database containing 3842 fusion cross-section-energy points from 235 reaction systems is assembled. Among them, 219 systems (3585 points) are used for training and validation, while 16 systems (257 points) constitute a reaction-wise isolated test set. The S-W prediction and the Coulomb baseline barrier provide the macroscopic reference, and LightGBM learns logarithmic residual corrections from projectile and target charges and masses, collision energy, mass asymmetry, Coulomb and size factors, isospin asymmetry, distance-to-magic-number indicators, and deformation-related proxies. Ten bootstrap submodels are aggregated to obtain the ensemble mean and a 90% confidence interval, thereby combining physical constraints, data-driven correction, and uncertainty quantification within a unified framework. On the independent test set, PI-LightGBM achieves a global root-mean-square logarithmic error of 0.26, compared with 0.94 for the purely data-driven LightGBM model, 3.03 for the S-W model, 2.86 for the Wong formula, and 0.86 for a physics-informed neural-network fit. For the extracted barrier heights, the coeffcient of determination is 0.984 and the root-mean-square error is 4.50 MeV. The normalized barrierheight deviations are approximately Gaussian, with a mean of -0.008 and a standard deviation of 0.075, and show no systematic increase with barrier height. Relative to the Coulomb baseline, the predicted effective barriers are lower by 7.23 MeV on average, corresponding to a mean relative difference of 0.092; this behavior indicates a stable but system-dependent correction beyond the macroscopic Coulomb scale. Fusion barrier distributions extracted by finite differences for ¹⁷O + ¹⁴⁴Sm, ¹⁶O + ¹⁴⁴Sm, and ¹⁶O + ¹⁴⁸Sm more closely follow the experimental peak positions and widths than the S-W baseline and the purely data-driven model, suggesting that isotope dependence and transfer-channel effects are partially accounted for. SHAP analysis further identifies normalized collision energy as the dominant individual feature, while kinematic, mass-and-charge, and microscopic shell/deformation features contribute 47.21%, 42.46%, and 10.33%, respectively. These results demonstrate that the proposed framework integrates physical asymptotics, residual learning, uncertainty quantification, and interpretable feature analysis, and provides a practical candidate for predicting fusion observables in unmeasured systems and for supporting the evaluation of reaction conditions in superheavy-nucleus synthesis and nucleus-nucleus interaction potentials.