Alberto Solera-Rico

Alberto Solera-Rico, Carlos Sanmiguel Vila, M. A. Gómez et al.

Variational autoencoder (VAE) architectures have the potential to develop reduced-order models (ROMs) for chaotic fluid flows. We propose a method for learning compact and near-orthogonal ROMs using a combination of a $β$-VAE and a transformer, tested on numerical data from a two-dimensional viscous flow in both periodic and chaotic regimes. The $β$-VAE is trained to learn a compact latent representation of the flow velocity, and the transformer is trained to predict the temporal dynamics in latent space. Using the $β$-VAE to learn disentangled representations in latent-space, we obtain a more interpretable flow model with features that resemble those observed in the proper orthogonal decomposition, but with a more efficient representation. Using Poincaré maps, the results show that our method can capture the underlying dynamics of the flow outperforming other prediction models. The proposed method has potential applications in other fields such as weather forecasting, structural dynamics or biomedical engineering.

Víctor Francés-Belda, Alberto Solera-Rico, Javier Nieto-Centenero et al.

Surrogate models that combine dimensionality reduction and regression techniques are essential to reduce the need for costly high-fidelity computational fluid dynamics data. New approaches using $β$-Variational Autoencoder ($β$-VAE) architectures have shown promise in obtaining high-quality low-dimensional representations of high-dimensional flow data while enabling physical interpretation of their latent spaces. We propose a surrogate model based on latent space regression to predict pressure distributions on a transonic wing given the flight conditions: Mach number and angle of attack. The $β$-VAE model, enhanced with Principal Component Analysis (PCA), maps high-dimensional data to a low-dimensional latent space, showing a direct correlation with flight conditions. Regularization through $β$ requires careful tuning to improve overall performance, while PCA preprocessing helps to construct an effective latent space, improving autoencoder training and performance. Gaussian Process Regression is used to predict latent space variables from flight conditions, showing robust behavior independent of $β$, and the decoder reconstructs the high-dimensional pressure field data. This pipeline provides insight into unexplored flight conditions. Furthermore, a fine-tuning process of the decoder further refines the model, reducing the dependence on $β$ and enhancing accuracy. Structured latent space, robust regression performance, and significant improvements in fine-tuning collectively create a highly accurate and efficient surrogate model. Our methodology demonstrates the effectiveness of $β$-VAEs for aerodynamic surrogate modeling, offering a rapid, cost-effective, and reliable alternative for aerodynamic data prediction.