This study uses higher-order dynamic mode decomposition to analyze a high-fidelity database of the turbulent flow in an urban environment consisting of two buildings separated by a certain distance. We recognize the characteristics of the well-known arch vortex forming on the leeward side of the first building and document this vortex's generation and destruction mechanisms based on the resulting temporal modes. We show that the arch vortex plays a prominent role in the dispersion of pollutants in urban environments, where its generation leads to an increase in their concentration; therefore, the reported mechanisms are of extreme importance for urban sustainability.

This article introduces an innovative methodology that merges modal decomposition, extracting physical patterns, with deep learning networks (DLNs) for forecasting reacting flows. The model is generalizable and capable of predicting complex simulations with just one training of the model, showing transfer learning capabilities. The primary objective is to optimize computational resources while maintaining accuracy on the predictions. With the combination of proper orthogonal decomposition (POD) and DLNs, our approach offers an efficient and effective solution for flow dynamics prediction. The new hybrid (POD/DLN) predictive model is designed for solving reacting flow problems. The POD block segregates temporal and spatial information, while the DLN block operates solely on the temporal domain with significantly reduced dimensionality. The POD modes contain the main flow characteristics, turning the model into a physics‐based model. This architecture leads to substantial enhancements in computational cost and memory requirements, while maintaining the precision in the predictions. Such advancements are particularly crucial for addressing the challenges posed by high‐dimensional multivariate and complex time‐series forecasting tasks. Two different deep learning architectures have been tested to predict the temporal coefficients, based on recursive (RNN) and convolutional (CNN) neural networks, introducing a novel physics‐aware loss function. From each architecture, different models have been created to understand the behavior of each parameter of the neural network. The results show that these architectures are able to predict the temporal evolution of the reactive flow. To the authors' knowledge, this is the first time this type of hybrid models is used to temporal prediction in reactive flows. The generalization capabilities and robustness of this physics‐aware ROM shed light on new development of predictive models for this research field.

In this paper, higher-order dynamic mode decomposition (HODMD) was applied to find the main patterns and frequencies of a transient aerodynamic flow field when an aircraft wing experiences stall. This method was applied to a computational flow simulation with a turbulence model based on a hybrid Reynolds-averaged Navier-Stokes large-eddy simulation (RANS/LES) [commonly known as detached-eddy simulation (DES)], where a combination of two-dimensional (2D) and three-dimensional (3D) flow visualization techniques are used to understand the vortex shedding from the main wing and its interaction with the tailplane. Simulation results were compared to the experimental ones and the results with proper orthogonal decomposition (POD) were compared with the HODMD analysis. The main advantage of HODMD resides in its identification of the main physical phenomena and the most relevant instabilities that lead the fluid dynamics. New flow control strategies can be defined when the underlying physics and the flow dynamics are known. Moreover, HODMD is robust in noisy and turbulent databases using less data than fast Fourier transform (FFT), which gives potential for future flow control applications, focused on improving the aircraft’s efficiency.

This study investigates the generalization capabilities and robustness of purely deep learning (DL) models and hybrid models based on physical principles in fluid dynamics applications, specifically focusing on iteratively forecasting the temporal evolution of flow dynamics. Three autoregressive models were compared: a hybrid model (POD-DL) that combines proper orthogonal decomposition (POD) with a long short-term memory (LSTM) layer, a convolutional autoencoder combined with a convolutional LSTM (ConvLSTM) layer and a variational autoencoder (VAE) combined with a ConvLSTM layer. These models were tested on two high-dimensional, nonlinear datasets representing the velocity field of flow past a circular cylinder in both laminar and turbulent regimes. The study used latent dimension methods, enabling a bijective reduction of high-dimensional dynamics into a lower-order space to facilitate future predictions. While the VAE and ConvLSTM models accurately predicted laminar flow, the hybrid POD-DL model outperformed the others across both laminar and turbulent flow regimes. This success is attributed to the model's ability to incorporate modal decomposition, reducing the dimensionality of the data, by a non-parametric method, and simplifying the forecasting component. By leveraging POD, the model not only gained insight into the underlying physics, improving prediction accuracy with less training data, but also reduce the number of trainable parameters as POD is non-parametric. The findings emphasize the potential of hybrid models, particularly those integrating modal decomposition and deep learning, in predicting complex flow dynamics.