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This article presents a new method to identify the main patterns describing the flow motion in complex flows. The algorithm is an extension of the higher-order dynamic mode decomposition (HODMD), which compresses the snapshots from the analysed database and progressively updates new compressed snapshots on-the-fly , so it is denoted as HODMD on-the-fly (HODMD-of). This algorithm can be applied in parallel to the numerical simulations (or experiments), and it exhibits two main advantages over offline algorithms: (i) it automatically selects on-the-fly the number of necessary snapshots from the database to identify the relevant dynamics; and (ii) it can be used from the beginning of a numerical simulation (or experiment), since it uses a sliding-window to automatically select, also on-the-fly, the suitable interval to perform the data analysis, i.e. it automatically identifies and discards the transient dynamics. The HODMD-of algorithm is suitable to build reduced order models, which have a much lower computational cost than the original simulation. The performance of the method has been tested in three different cases: the axi-symmetric synthetic jet, the three-dimensional wake of a circular cylinder and the turbulent wake behind a wall-mounted square cylinder. The obtained speed-up factors are around 7 with respect to HODMD; this value depends on the simulation and the configuration of the hyperparameters. HODMD-of also provides a significant reduction of the memory requirements, between 40 − 80 % amongst the two- and three-dimensional cases studied in this paper. • Novel algorithm based on HODMD that combines rank reduction strategies with the on-the-fly methodology. • The algorithm automatically selects the optimal time interval to extract the main flow patterns. • Significant reduction of the memory requirements and speed-up related with standard HODMD. • Suitable to build reduced order models. [ABSTRACT FROM AUTHOR]

• Machine learning framework for the reconstruction of unsteady fluid flows fields. • Variational approach for a robust reduction of the high dimensional field. • Investigations on three canonical cases. • Combination of linear or nonlinear reduction with regressive or direct reconstruction. This paper investigates the use of data-driven methods for the reconstruction of unsteady fluid flow fields. The proposed framework is based on the combination of machine learning tools: dimensionality reduction to extract dominant spatial directions from data, reconstruction algorithm to recover encoded data by limited measurements and cross-validation for hyperparameter optimization. For the encoding part, linear and nonlinear extraction of patterns are considered: proper orthogonal decomposition (POD), linear autoencoder (LAE) and variational autoencoder (VAE). For the reconstruction part, regressive reconstruction (neural network, linear, support vector, gradient boosting) and library-based reconstruction are compared, each method being cross-validated to ensure good generalization on testing data. The position of sensors is optimized using an enhanced clustering algorithm. The robustness of regressive reconstructions to noise measurements is also addressed, showing the benefits of variational approaches in the reduction phase. The strategy is tested for three increasing complexity flows: 2D vortex shedding (R e = 200), 2D spatial mixing layer and 3D vortex shedding (R e = 20000). The results suggest that proper machine learning approaches to fluid flow data can lead to effective reconstruction models that can be used for the rapid estimation of complex flows. [ABSTRACT FROM AUTHOR]

Originated from the complex network theory, the Lagrangian flow network (LFN) has motivated various tools to analyze fluid flows' transport and mixing behaviors. These tools include the so-called finite time escape rate (FTER), the transition matrix, and also the finite time entropy. This paper proposes novel Eulerian algorithms to compute these LFN quantities in two dimensions based on a partial differential equation (PDE) formulation for the underlying flow map. Compared to the typical Lagrangian computations based on ray tracing, our numerical approaches are computationally efficient. Moreover, for velocity fields obtained numerically by computational fluid dynamic (CFD) solvers, our approach does not require further interpolation of the velocity field but can use the discrete velocity data directly. Finally, we will apply our proposed algorithms to several test examples, including a real-life dataset, to demonstrate the performance of the method. [ABSTRACT FROM AUTHOR]