Turbulent flows, a longstanding challenge in classical physics, are characterized by their nonlinear, multi-scale, and chaotic behavior. While the Navier-Stokes equations provide a comprehensive mathematical foundation, solving them numerically remains computationally expensive. This poses a challenge for iterative applications, such as closed-loop control or design optimization, which require surrogate models for faster simulations. In this paper, reduced-order models (ROMs) are explored as a promising solution. ROMs are techniques designed to capture the essential dynamics of turbulent flows at a significantly reduced computational cost by identifying and exploiting features inherent in the flow field. Two main classes of ROMs can be defined: projection-based methods and operator-based methods. Projection-based models, while effective, are inherently intrusive, as they require the application of basis expansions and projections onto the full-order model's operators. In contrast, operator-based ROMs offer non-intrusive alternatives but depend on prior knowledge of the ROM structure. To address the limitations of both approaches, this work explores the potential of neural compression algorithms, i.e. the application of neural networks for unsupervised feature extraction to compress data into lower-dimensional representations. As a proof of concept, this study examines the flow developing around a one degree-of-freedom elastically-mounted cylinder experiencing vortex-induced vibrations. The dataset consists of time-resolved, two-component velocity snapshots obtained experimentally by Particle Image Velocimetry for different Reynolds numbers, ranging from 6000 to 16000, based on the cylinder diameter and the free-stream velocity , in the wake of the oscillating cylinder. This work makes several contributions: (i) it assesses the performance of both AE and VAE compared to POD in reconstructing unseen flow regimes; (ii) it develops a single model capable of representing all Reynolds numbers in the dataset with just three variables; and (iii) it proposes novel techniques to analyze and exploit the mapping learned by the neural network.