Autoencoders vs. Numerical Analysis--Informed Manifold Learning for Navier--Stokes Flows

This research paper presents a comparative study between autoencoders (AEs) and parsimonious diffusion maps (PDMs) for reduced-order modeling of Navier-Stokes flows. The authors revisit manifold-learning methods grounded in classical numerical analysis as an alternative to the dominant AE approach in data-driven reduced-order modeling. The paper benchmarks PDMs against proper orthogonal decomposition (POD)-based methods to evaluate their effectiveness in capturing flow dynamics.