The balance between compactness and forecast accuracy of data-driven latent-space reduced-order models in controlled wake flows

Model-based active flow control requires predictive models that are accurate, stable and fast enough for real-time optimisation. In controlled wake flows, this is often achieved through reduced-order models (ROMs) that first compress high-dimensional velocity snapshots into a latent space and then learn a time-stepping predictor for the dynamics in the latent space. Here, we study how the choice of the spatial encoder affects the predictability of the resulting latent coordinates for wake flows under control inputs. Using two actuated two-dimensional wake configurations, a simplified truck wake and the fluidic pinball, we compare proper orthogonal decomposition (POD) against nonlinear convolutional autoencoders (CAEs) and two types of variational autoencoders for compression, and evaluate several temporal predictors based on long short-term memory networks. The CAEs achieve higher compression efficiency and sharper short-term reconstructions, but they produce a latent dynamics that is more irregular and with broadband spectral content. As a consequence, long-horizon forecasts degrade faster and show a higher probability of catastrophic divergence than POD-based models. The POD yields smoother latent trajectories that are easier to learn and extrapolate, leading to more reliable predictions beyond the short-term regime. These results reveal a clear trade-off between compactness and forecast accuracy, and suggest that the stability of the latent dynamics prediction can outweigh maximal compression. This is particularly relevant for control strategies rooted in forecasts of the dynamics, such as model predictive control and reinforcement learning. The findings provide practical guidance for designing actuation-aware, hardware-feasible predictive ROMs for real-time flow control.