Hybrid Physical-Data Modeling Approach for Surface Scattering Characteristics of Low-Gloss Black Paint

This study presents a hybrid BRDF modeling framework combining a five-parameter physical model with a (20,20,20) Multilayer Perceptron (MLP) model network to address the critical challenge of accurate grazing-angle prediction for low-gloss black coatings (SB-3A, Z306, PNC). While the baseline parametric model achieves <5% RMSE at θi ≤ 60°, its inability to capture shadowing effects leads to >1.2 RMSE at 80° incidence. The proposed MLP model-enhanced solution reduces these high-angle errors to <0.012 RMSE while maintaining <5-min computational efficiency. Comprehensive validation shows the framework’s universality across materials with apparent anisotropy indices (ASI) of 0.465–30.26. The work demonstrates that neural networks can optimally compensate for missing physics in traditional models without sacrificing interpretability, offering immediate industrial value for aerospace coating analysis.