Statistical regression methods are widely used in remote sensing applications but tend to lack physical interpretability. In this paper, we introduce a methodological framework to improve modelemulation and its understanding with machine learning feature selection. Our wrapper-forward feature selection method seamlessly integrates physics knowledge into model emulation, improving the tradeoff between accuracy and interpretability. We illustrate our methodology by applying it to atmospheric radiative transfer models in the context of global sensitivity analysis (GSA) and emulation. Our approach consistently aligns with variance-based GSA, pinpointing the critical features of aerosol properties, solar zenith angle, and water vapor. While our physically-based emulators yield only a modest accuracy improvement of 0.2% over conventional Gaussian Processes emulators, its introduction signifies a step forward to physics-aware machine learning-based emulation. The emulator performance remains steadfast, unaffected by substantial changes, further underscoring the reliability of our approach.