Physics-informed feature-to-feature learning for design-space dimensionality reduction in shape optimisation

High-dimensional parametric design problems cause optimisers and physics simulations to suffer from the curse-of-dimensionality, resulting in high computational cost. In this work, to release this computational burden, we adopted a two-step feature-to-feature learning methodology to discover a lower-dimensional latent space, based on the combination of geometry-and physics-informed principal component analysis and the active subspace method. At the first step, statistical dependencies implicit in the design parameters encode important geometric features of the underline shape. During the second step, functional features of designs are extracted in term of previously learned geometric features. Afterwards, both geometric and functional features are augmented together to create a functionally-active subspace, whose basis not only captures the geometric variance of designs but also induces the variability in the designs' physics. As the new subspace accumulates both the functional and geometric variance, therefore, it can be exploited for efficient design exploration and the construction of improved surrogate models for designs' physics prediction. The validation and experimental studies presented in this work show the beneficial effects of the current approach in comparison to a conventional single-step feature learning.