Fourier neural autoencoder with hyperbolic feature mapping for nonlinear decomposition of fluid flows

With the growing use of machine learning in fluid dynamics, autoencoder-based models have become a popular tool for learning low-dimensional representations of high-dimensional flow fields, where improving reconstruction accuracy remains a central focus. To that end, we propose the Fourier neural autoencoder: an autoencoder architecture enhanced with Fourier-based layers inspired by the Fourier neural operator, aimed at improving reconstruction accuracy. To further boost its capability, we develop a hyperbolic feature mapping technique that improves feature extraction. To explore our models in greater depth, we apply them to both non-variational and variational autoencoder variants. Since the Fourier neural autoencoder and hyperbolic feature mapping are independent of each other, we obtain four variants of our proposed approach: the Fourier neural autoencoder with and without hyperbolic feature mapping, each in both non-variational and variational forms. As a benchmark case, we apply our Fourier neural autoencoder to the flow past a single cylinder at a Reynolds number of 70. The results show that the model achieves higher reconstruction accuracy while having fewer parameters compared to a standard convolutional autoencoder. We further evaluate the model on more complex flow scenarios, including the unsteady Reynolds-averaged Navier–Stokes simulation of a NACA0012 airfoil at a Reynolds number of 1000 and the flow over two side-by-side circular cylinders at a Reynolds number of 100 with varying spacing. Our results suggest that both the Fourier neural autoencoder and hyperbolic feature mapping improve accuracy while reducing parameter counts compared to the standard autoencoder.