On the integration of geometry agnostic variational-autoencoders into large-scale SVD based models

This manuscript introduces GAVI (Geometry Agnostic Variational-autoencoder Integration), a scalable technique for model order reduction of terabyte-level state spaces. Such methodology is agnostic to the spatial location of the data points, hence, it can handle any complex geometry regardless of the grid type in which it is represented. The dimensionality reduction of GAVI is performed on two separate steps. First, a parallel QR factorization is applied to the snapshot matrix to decompose, then a variational autoencoder learns a latent representation of the reduced R matrix. The final step can be done at laptop level regardless of the size of the original data. The methodology is used to compress the streamwise velocity component of the flow around a circular cylinder at $R{e}_D=U_{\infty }D/\nu =10^4$, the pressure coefficient of the flow around the Windsor body at $R{e}_L=U_{\infty }L/\nu =2.9\times 10^6$ and the streamwise velocity of the realistic urban flow in the Zona Universitària neighborhood located in Barcelona. The latter example is the most demanding one as the 1032 snapshots, which are represented on an unstructured grid of 335 million points, have a total size of 2.05 Tb. GAVI can compress the full dataset into 6 latent vectors that recover up to the 95.29% of the energy.