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

In model-based active flow control, the effectiveness of the controller depends on the ability to predict future flow states in real-time. This paper investigates the trade-off between the compactness of latent-space representations (how much data is compressed) and the accuracy of the resulting dynamical forecasts. Specifically, the authors compare linear Proper Orthogonal Decomposition (POD) against nonlinear Convolutional Autoencoders (CAEs) to determine which approach yields more stable and predictable latent dynamics for control applications.

The researchers evaluated two 2D wake flow configurations: a simplified truck model with single-input synthetic jet actuation and the fluidic pinball with multi-input rotating cylinder actuation. They used POD and various CAE architectures (including variational variants) to compress high-dimensional velocity snapshots into a latent space. They then trained Long Short-Term Memory (LSTM) networks to predict the temporal evolution of these latent coordinates under active control. The models were assessed based on their reconstruction quality and, crucially, their ability to maintain forecast accuracy over long time horizons without diverging.

The study reveals a clear tension between compression and predictability. CAEs offer superior compression and sharper short-term reconstructions, making them attractive for data storage. However, they produce latent dynamics that are irregular and possess broadband spectral content, which makes them difficult for LSTM networks to learn and extrapolate. Consequently, CAE-based models are prone to catastrophic divergence during long-horizon forecasting. In contrast, POD generates smoother, more structured latent trajectories that align better with the underlying physical dynamics of the wake, leading to significantly more robust and reliable long-term predictions.