Extending Parametric Model Embedding with Physical Information for Design-space Dimensionality Reduction in Shape Optimization

Design-space dimensionality reduction is essential to mitigate the cost of high-fidelity simulation-based optimization, especially when dealing with high-dimensional geometric parameterizations. Traditional linear techniques, such as principal component analysis, are widely used but often neglect the physical response of the system and lack invertibility to the design space, i.e., the ability to reconstruct the original design parameters from a reduced representation. This work introduces two physics-aware extensions of the parametric model embedding (PME) framework, aimed at generating reduced representations that incorporate physical information while maintaining analytical backmapping. The first, physics-informed PME (PI-PME), combines geometric and physical variability; the second, physics-driven PME (PD-PME), relies solely on physical responses. The proposed methods enable the construction of interpretable and physically relevant reduced spaces that can be used for design-space exploration, surrogate modeling, and optimization. The approach is demonstrated on multiple engineering configurations, including airfoils, propellers, gliders, and hulls, showing its ability to capture performance-relevant directions and preserve parametric consistency. The methodology is offline and non-intrusive, compatible with low-fidelity simulations, and requires only a modest number of samples to ensure variance convergence.