A Physics-Guided Surrogate Neural Network for Aerodynamic Prediction and Geometry-Aware Inverse Design of CST Airfoils

Accurate aerodynamic surrogate modelling requires a framework that is not only predictive but also physically consistent, geometrically interpretable, and suitable for optimisation-driven design. This study presents a Physics-Guided Surrogate Neural Network (PGSNN) for CST-parameterised airfoils that integrates aerodynamic prediction, geometry reconstruction, and physics-constrained learning within a unified differentiable framework. The proposed architecture employs a shared latent representation with dual prediction heads, enabling the simultaneous learning of aerodynamic responses and the underlying CST geometry. To improve physical consistency and generalisation, aerodynamic knowledge is embedded directly into the training process through soft regularisation terms derived from lift theory, viscous drag scaling, compressibility effects, pitching-moment constraints, geometric admissibility, and shape smoothness. A comprehensive dataset spanning a wide range of operating conditions and airfoil geometries is generated using a hybrid sampling strategy, while geometry-level data partitioning is adopted to ensure rigorous evaluation on previously unseen airfoil shapes. The resulting surrogate preserves physically meaningful geometric information while maintaining compatibility with gradient-based optimisation. Furthermore, the differentiable nature of the framework enables constrained inverse design within the learned CST design space without requiring a separate optimisation network. By combining geometry-aware representation learning, embedded aerodynamic priors, and differentiable optimisation, the proposed PGSNN establishes a unified framework for surrogate-assisted aerodynamic analysis and airfoil design, providing a physically grounded alternative to purely data-driven approaches.