Surrogate models are widely used in mechanical design and manufacturing process optimization, where high-fidelity computational models may be unavailable or prohibitively expensive. Their effectiveness, however, is often limited by data scarcity, as purely data-driven surrogates struggle to achieve high predictive accuracy in such situations. Subject matter experts (SMEs) frequently possess valuable domain knowledge about functional relationships, yet few surrogate modeling techniques can systematically integrate this information with limited data. We address this challenge with RBF-Gen, a knowledge-guided surrogate modeling framework that combines scarce data with domain knowledge. This method constructs a radial basis function (RBF) space with more centers than training samples and leverages the null space via a generator network, inspired by the principle of maximum information preservation. The introduced latent variables provide a principled mechanism to encode structural relationships and distributional priors during training, thereby guiding the surrogate toward physically meaningful solutions. Numerical studies demonstrate that RBF-Gen significantly outperforms standard RBF surrogates on 1D and 2D structural optimization problems in data-scarce settings, and achieves superior predictive accuracy on a real-world semiconductor manufacturing dataset. These results highlight the potential of combining limited experimental data with domain expertise to enable accurate and practical surrogate modeling in mechanical and process design problems.