Data-driven Reduced-order Modeling for Transonic Flow Fields

Reduced-order modeling (ROM) is crucial for simplifying complex fluid dynamics problems, but traditional models can struggle with nonlinearities. This work addresses the need to compare different AI-based architectures for data-driven ROM, including principal component analysis (PCA), autoencoders (AE), and variational autoencoders (VAE). Our focus was on identifying an efficient model that not only reduces the computational burden but also provides interpretable physical insights into the aerodynamic problems being studied. 

In this work, I developed a physics-aware ROM using a β-variational autoencoder (β-VAE), which improves upon conventional ROMs by focusing on extracting interpretable and independent latent variables (LVs). The β-VAE effectively balances reconstruction accuracy with a regularized latent space, ensuring that each LV corresponds to a distinct physical feature. This disentanglement process allows the ROM to use only the most relevant LVs, which significantly reduces the number of regression models needed for high-dimensional data prediction. This method not only simplifies the modeling process but also retains key physical insights, making it highly suitable for real-time simulations.

One of the key findings of my research was that the LVs automatically extracted by the β-VAE corresponded to the actual physical parameters used to generate the dataset—specifically, the Mach number and angle of attack. This demonstrates that the β-VAE can capture the underlying physical structure of the problem without prior knowledge, highlighting its potential for physics-aware modeling in various engineering applications. By focusing only on these physics-aware LVs, the ROM framework I developed achieves both high accuracy and computational efficiency, offering a valuable tool for engineering design and analysis.

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