Physically Organized Latent Spaces in Unsupervised Autoencoders: Evidence from Aerodynamic Databases

Abstract: Using aerodynamic databases of progressively increasing complexity - from linear analytical theory to nonlinear separated RANS flows - we demonstrate that an autoencoder, trained solely by reconstruction, can spontaneously organize the latent representation according to physically meaningful variables and aerodynamic laws. Although the latent coordinates themselves vary under random initialization, the underlying physical organization is reproducible, even quantitatively. In addition, we present a three-dimensional latent space representation of the airfoil flow obtained by an unsupervised autoencoder with sequential training in which the inviscid field is decoupled from the boundary layer effects with the third latent variable strongly correlated with the Reynolds number and aerodynamic drag. Cross-validated regression and affine-alignment measures show that physical parameters and responses are strongly and linearly encoded in the learned coordinates, consistently across independent trainings.