Disentangled Latent Spaces for Reduced Order Models using Deterministic Autoencoders
This work addresses interpretability issues in reduced-order modeling for computational fluid dynamics and simulation sciences, offering a more robust alternative to probabilistic methods, though it is incremental as it builds on existing autoencoder approaches.
The paper tackled the lack of interpretability in data-driven reduced-order models by proposing non-probabilistic autoencoders that promote orthogonality or penalize correlation in latent variables, achieving competitive results on a periodic flow benchmark and demonstrating robustness in hyperparameter choice and ability to identify active latent variables.
Data-driven reduced-order models based on autoencoders generally lack interpretability compared to classical methods such as the proper orthogonal decomposition. More interpretability can be gained by disentangling the latent variables and analyzing the resulting modes. For this purpose, probabilistic $β$-variational autoencoders ($β$-VAEs) are frequently used in computational fluid dynamics and other simulation sciences. Using a benchmark periodic flow dataset, we show that competitive results can be achieved using non-probabilistic autoencoder approaches that either promote orthogonality or penalize correlation between latent variables. Compared to probabilistic autoencoders, these approaches offer more robustness with respect to the choice of hyperparameters entering the loss function. We further demonstrate the ability of a non-probabilistic approach to identify a reduced number of active latent variables by introducing a correlation penalty, a function also known from the use of $β$-VAE. The investigated probabilistic and non-probabilistic autoencoder models are finally used for the dimensionality reduction of aircraft ditching loads, which serves as an industrial application in this work.