Towards aerodynamic surrogate modeling based on $\beta$-variational autoencoders

TL;DR

This paper introduces a novel aerodynamic surrogate modeling approach using $eta$-VAE architectures combined with PCA and Gaussian Process Regression to efficiently predict pressure distributions with high accuracy.

Contribution

It presents a new surrogate modeling framework leveraging $eta$-VAE, PCA, and Gaussian Process Regression for improved aerodynamic data prediction and interpretability.

Findings

Latent space correlates with flight conditions.

Regularization and PCA improve autoencoder performance.

Fine-tuning enhances model accuracy and reduces $eta$ dependence.

Abstract

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 $\beta$-Variational Autoencoder ($\beta$-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 $\beta$-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 $\beta$ 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 $\beta$, 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 $\beta$ 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 $\beta$-VAEs for aerodynamic surrogate modeling, offering a rapid, cost-effective, and reliable alternative for aerodynamic data prediction.