Knowledge-Guided Generative Surrogate Modeling for High-Dimensional Design Optimization Under Scarce Data

Abstract

Abstract. 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.