Flow field predictions using hybrid autoregressive reduced-order models: A critical assessment

Accurate modeling of the complex dynamics of fluid flows is a fundamental challenge in computational physics and engineering. This study integrates High-Order Singular Value Decomposition (HOSVD) with Long Short-Term Memory (LSTM) architectures to address the complexities of hybrid reduced-order modeling in fluid dynamics. The methodology is tested across numerical and experimental datasets, including two- and three-dimensional (2D and 3D) cylinder wake flows, spanning both laminar and turbulent regimes. The emphasis is also on exploring how the depth and complexity of LSTM architectures contribute to improving predictive performance. For simple laminar flows, architectures with a single dense layer effectively capture the periodic dynamics, demonstrating the network's ability to model non-linearities and complex dynamics. For the other cases, the addition of extra layers provides higher accuracy at minimal computational cost. Other results demonstrate that HOSVD shows improved accuracy, particularly in more complex cases, such as the 3D cylinder and experimental datasets, while differences remain modest for simpler flows. Efficient mode truncation by HOSVD-based models enables the capture of complex temporal patterns, leading to reliable predictions even in noisy datasets.