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 2D 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. CAEs achieve higher compression efficiency and sharper short-term reconstructions, but they produce latent dynamics that are 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. 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.
Multiscale systems are expensive to simulate because fast dynamics require small time-steps, while slow dynamics require long prediction horizons. We propose latent hierarchical time-stepping (L-HiTS), which combines nonlinear coordinate discovery with multiscale flow-map learning. A deep autoencoder first compresses the high-dimensional PDE state into a validated low-dimensional latent space. Residual neural network time-steppers are then trained and coupled directly in this reduced space using validation-based hierarchy selection and vectorized prediction. Unlike multiscale HiTS, L-HiTS performs recursive forecasting in latent coordinates and reconstructs the full state only after prediction. The method is validated on the FitzHugh–Nagumo model, the chaotic Kuramoto–Sivashinsky equation, and a two-dimensional Burgers’ system. L-HiTS achieves comparable prediction accuracy to multiscale HiTS while substantially reducing training and prediction costs, with near order-of-magnitude prediction-time savings in the reported cases.
Asif Hamid, Danish Rafiq, Shahkar Ahmad Nahvi et al.· International Journal of Dyn...· 0 citations
A Fourier-enhanced operator autoencoder for decoder-free reconstruction and latent learning of dynamical systems and achieves accuracy comparable to or better than classical AE-based reduced-order models while providing a more efficient latent-to-field reconstruction path.
Xuandong Lu, Yongming Liu· Machine Learning for Computa...· 0 citations
We use a large database of direct numerical simulations to investigate the transition of the Rayleigh--Taylor instability to turbulence and its evolution toward a late-time self-similar regime. In addition to tracking the growth of the mixing layer through the mean heavy-fluid concentration profile, we analyze one-dimensional profiles of turbulent kinetic energy and dissipation, two key quantities in classical turbulent-mixing models. We consider two reduced-order modeling strategies that differ in where nonlinearity is introduced: either in the construction of the latent space or in the description of its temporal evolution. The first method uses a linear encoder--decoder obtained using Proper Orthogonal Decomposition (POD), with nonlinear reduced dynamics learned by a physics-informed neural network (PINN). The second uses a nonlinear encoder--decoder learned by an autoencoder, while constraining the latent dynamics to remain linear and satisfy physical constraints. Both approaches achieve satisfactory performance in reconstructing, interpolating, and extrapolating the dynamics of the Rayleigh--Taylor instability.
Téo Granger, B. Nadiga, B. Gréa et al.· 0 citations
Deep learning surrogates for forecasting chaotic dynamical systems suffer from catastrophic error accumulation over long-term autoregressive rollouts. This behavior is partly tied to the underlying systems: chaotic spatiotemporal systems, such as the Kuramoto-Sivashinsky (KS) equation, visit phase space unevenly - dominated by recurrent, low-dimensional quiescent states (e.g., near-laminar flows) and punctuated by rare, dynamically complex topological transitions (e.g., wave-merging events). Under a sample-wise uniform objective, standard neural surrogates allocate their finite capacity to the statistically numerous quiescent states, under-representing the transient regimes that trigger disproportionate, localized errors. Existing imbalanced-regression methods reweight samples by target-space density. However, statistical target-space rarity need not coincide with the intrinsic dynamical rarity - the recurrence geometry of the attractor that is the source of the imbalance. To address this, we introduce Dynamics-Aware Weighting (DAW), a data-centric objective reweighting framework. Using the local dimension $d$ from dynamical systems theory as an a priori measure of a state's active degrees of freedom, DAW reshapes the loss landscape to allocate representational capacity toward the sparse, high-$d$ regimes where forecast errors are systematically large. On the chaotic KS equation, DAW consistently outperforms uniform training, purely statistical density weighting, and its randomly permuted ablation, reducing long-term autoregressive error relative to all baselines. Event-level analysis shows that DAW achieves this by suppressing the localized error amplifications incurred during sharp jumps in $d$, which accompany complex physical processes such as wave-merging in the KS system.
Stable prediction of unsteady flows requires accurate multiscale spatial representation and robust temporal propagation. We introduce the Compensated Koopman U-shaped Neural Operator (CoKo-UNO), which combines a U-shaped spectral backbone with Koopman-dominated latent propagation. Finite-dimensional Koopman truncation produces a state-dependent residual that is repeatedly reinjected during autoregressive rollout. CoKo-UNO models this residual with a selective state-space model (SSM), a principled input-dependent compensation mechanism, together with resolution-adaptive compensatory skip connections and an overlapping-warmup rollout strategy. \NEW{Across four benchmark problems, CoKo-UNO achieves the lowest mean rollout error among all compared methods. Its largest gain is a $76.76\%$ reduction relative to the strongest baseline, while requiring about $41.40\%$ of RNO's training time.} These results show that explicit residual compensation improves stable autoregressive prediction of unsteady flows.
It is argued that the outstanding obstacle to deploying world models in systems that cannot fail -- power, thermal, process control -- is not predictive fidelity but verifiability, and a research agenda for physics-grounded, verifiable world models is outlined that unifies the two lineages.