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This study presents a transformer-based approach for fault-tolerant control in fixed-wing Unmanned Aerial Vehicles (UAVs), designed to adapt in real time to dynamic changes caused by structural damage or actuator failures. Unlike traditional Flight Control Systems (FCSs) that rely on classical control theory and struggle under severe alterations in dynamics, our method directly maps outer-loop reference values -- altitude, heading, and airspeed -- into control commands using the in-context learning and attention mechanisms of transformers, thus bypassing inner-loop controllers and fault-detection layers. Employing a teacher-student knowledge distillation framework, the proposed approach trains a student agent with partial observations by transferring knowledge from a privileged expert agent with full observability, enabling robust performance across diverse failure scenarios. Experimental results demonstrate that our transformer-based controller outperforms industry-standard FCS and state-of-the-art reinforcement learning (RL) methods, maintaining high tracking accuracy and stability in nominal conditions and extreme failure cases, highlighting its potential for enhancing UAV operational safety and reliability.

For the last 140 years, the mechanisms of transport and dissipation of energy in a turbulent flow have not been completely understood due to the complexity of this phenomenon. The dissipation of energy due to turbulence is significative, and understanding turbulence physics is crucial for fighting the present climate emergency. Previous research has focused on analyzing the so-called coherent structures of the flow (Q events, streaks, and vortices), which are regions of high turbulence transport, high/low streamwise fluctuation, and rotation, respectively. However, the connection between these classically studied structures and the flow development is still uncertain. To fill this gap, here we show a data-driven methodology for objectively identifying high-importance regions in a turbulent flow. A deep-learning model is trained to predict a future state of a turbulent channel flow and the gradient-SHAP explainability algorithm is used to calculate the importance of each grid point for such a prediction. Finally, high-importance regions are computed using the SHAP data, analyzing and comparing their characteristics with those of the other coherent structures. The SHAP analysis provides an objective way to identify the regions of highest importance in the turbulent flow, which exhibit different levels of agreement with the classically studied structures.

The increasing number of unmanned aerial vehicles (UAVs) in urban environments requires a strategy to minimize their environmental impact, both in terms of energy efficiency and noise reduction. In order to reduce these concerns, novel strategies for developing prediction models and optimization of flight planning, for instance through deep reinforcement learning (DRL), are needed. Our goal is to develop DRL algorithms capable of enabling the autonomous navigation of UAVs in urban environments, taking into account the presence of buildings and other UAVs, optimizing the trajectories in order to reduce both energetic consumption and noise. This is achieved using fluid-flow simulations which represent the environment in which UAVs navigate and training the UAV as an agent interacting with an urban environment. In this work, we consider a domain domain represented by a two-dimensional flow field with obstacles, ideally representing buildings, extracted from a three-dimensional high-fidelity numerical simulation. The presented methodology, using PPO+LSTM cells, was validated by reproducing a simple but fundamental problem in navigation, namely the Zermelo's problem, which deals with a vessel navigating in a turbulent flow, travelling from a starting point to a target location, optimizing the trajectory. The current method shows a significant improvement with respect to both a simple PPO and a TD3 algorithm, with a success rate (SR) of the PPO+LSTM trained policy of 98.7%, and a crash rate (CR) of 0.1%, outperforming both PPO (SR = 75.6%, CR=18.6%) and TD3 (SR=77.4% and CR=14.5%). This is the first step towards DRL strategies which will guide UAVs in a three-dimensional flow field using real-time signals, making the navigation efficient in terms of flight time and avoiding damages to the vehicle.

The use of data-driven methods in fluid mechanics has surged dramatically in recent years due to their capacity to adapt to the complex and multi-scale nature of turbulent flows, as well as to detect patterns in large-scale simulations or experimental tests. In order to interpret the relationships generated in the models during the training process, numerical attributions need to be assigned to the input features. One important example are the additive-feature-attribution methods. These explainability methods link the input features with the model prediction, providing an interpretation based on a linear formulation of the models. The SHapley Additive exPlanations (SHAP values) are formulated as the only possible interpretation that offers a unique solution for understanding the model. In this manuscript, the additive-feature-attribution methods are presented, showing four common implementations in the literature: kernel SHAP, tree SHAP, gradient SHAP, and deep SHAP. Then, the main applications of the additive-feature-attribution methods are introduced, dividing them into three main groups: turbulence modeling, fluid-mechanics fundamentals, and applied problems in fluid dynamics and heat transfer. This review shows thatexplainability techniques, and in particular additive-feature-attribution methods, are crucial for implementing interpretable and physics-compliant deep-learning models in the fluid-mechanics field.

Different types of neural networks have been used to solve the flow sensing problem in turbulent flows, namely to estimate velocity in wall-parallel planes from wall measurements. Generative adversarial networks (GANs) are among the most promising methodologies, due to their more accurate estimations and better perceptual quality. This work tackles this flow sensing problem in the vicinity of the wall, addressing for the first time the reconstruction of the entire three-dimensional (3-D) field with a single network, i.e. a 3-D GAN. With this methodology, a single training and prediction process overcomes the limitation presented by the former approaches based on the independent estimation of wall-parallel planes. The network is capable of estimating the 3-D flow field with a level of error at each wall-normal distance comparable to that reported from wall-parallel plane estimations and at a lower training cost in terms of computational resources. The direct full 3-D reconstruction also unveils a direct interpretation in terms of coherent structures. It is shown that the accuracy of the network depends directly on the wall footprint of each individual turbulent structure. It is observed that wall-attached structures are predicted more accurately than wall-detached ones, especially at larger distances from the wall. Among wall-attached structures, smaller sweeps are reconstructed better than small ejections, while large ejections are reconstructed better than large sweeps as a consequence of their more intense footprint.

We conducted high-resolution large-eddy simulations (LESs) to explore the effects of opposition control (OC) on turbulent boundary layers (TBLs) over a wing at a chord-based Reynolds number (${Re}_c$) of 200,000. Two scenarios were studied: flow over the suction sides of the NACA0012 wing section at a $0^{\circ}$ angle of attack, and the NACA4412 wing section at a $5^{\circ}$ angle of attack, representing TBLs under mild and strong nonuniform adverse pressure gradients (APGs), respectively. Our results show that the effectiveness of OC in reducing friction drag decreases significantly with increasing APG intensity. This reduction is linked to intensified wall-normal convection caused by the stronger APG. OC, designed to reduce near-wall fluctuations, attenuates the outer peak of streamwise velocity fluctuations and the production term of the turbulent kinetic energy budget. We also confirmed the formation of a "virtual wall," where the balance between viscous diffusion and dissipation at the virtual wall plane mirrors that at the physical wall. Spectral analyses reveal that the wall-normal transport of small-scale structures to the outer region due to the APG negatively impacts OC performance. We also examined uniform blowing and body-force damping as control strategies. Uniform blowing mimics the effects of a stronger APG, while body-force damping shares similarities with OC in the streamwise development of the TBL, despite differences in turbulent statistics. This study is the first detailed analysis of OC applied to TBLs under nonuniform APGs with complex geometries.

The present study investigates streamwise ($\overline{u^2}$) energy-transfer mechanisms in the inner and outer regions of turbulent boundary layers (TBLs). Particular focus is placed on the $\overline{u^2}$-production, its inter-component and wall-normal transport as well as dissipation, all of which become statistically significant in the outer region with increasing friction Reynolds number ($Re_{\tau}$). These properties are analyzed using published data sets of zero, weak and moderately strong adverse-pressure-gradient (APG) TBLs across a decade of $Re_{\tau}$, revealing similarity in energy-transfer pathways for all these TBLs. It is found that both the inner and outer peaks of $\overline{u^2}$ are always associated with local maxima in the $\overline{u^2}$-production and its inter-component transport, and the regions below/above each of these peaks are always dominated by wall-ward/away-from-wall transport of $\overline{u^2}$, thereby classifying the $\overline{u^2}$-profiles into four distinct regimes. This classification reveals existence of phenomenologically similar energy-transfer mechanisms in the `inner' and `outer' regions of moderately strong APG TBLs, which meet at an intermediate location coinciding with the minimum in $\overline{u^2}$ profiles. Given that the wall-ward/away-from-wall transport of $\overline{u^2}$ is governed by the $\rm Q_4$(sweeps)/$\rm Q_2$(ejections) quadrants of the Reynolds shear stress, it is argued that the emergence of the $\overline{u^2}$ outer peak corresponds with the statistical dominance of $\rm Q_4$ events in the outer region. Besides unravelling the dynamical significance of $\rm Q_2$ and $\rm Q_4$ events in the outer region of turbulent boundary layers, the present analysis also proposes new phenomenological arguments for testing on canonical wall-turbulence data at very high $Re_{\tau}$., Comment: Manuscript accepted in the Journal of Fluid Mechanics, with 22 pages and 8 figures

The wall cycle in wall-bounded turbulent flows is a complex turbulence regeneration mechanism that remains not fully understood. This study explores the potential of deep reinforcement learning (DRL) for managing the wall regeneration cycle to achieve desired flow dynamics. We integrate the StableBaselines3 DRL libraries with the open-source DNS solver CaNS to create a robust platform for dynamic flow control. The DRL agent interacts with the DNS environment, learning policies that modify wall boundary conditions to optimize objectives such as the reduction of the skin-friction coefficient or the enhancement of certain coherent structures features. Initial experiments demonstrate the capability of DRL to achieve drag-reduction rates comparable with those achieved via traditional methods, though limited to short time periods. We also propose a strategy to enhance the coherence of velocity streaks, assuming that maintaining straight streaks can inhibit instability and further reduce skin friction. The implementation makes use of the message-passing-interface (MPI) wrappers for efficient communication between the Python-based DRL agent and the DNS solver, ensuring scalability on high-performance computing architectures. Our results highlight the promise of DRL in flow control applications and underscore the need for more advanced control laws and objective functions. Future work will focus on optimizing actuation periods and exploring new computational architectures to extend the applicability and the efficiency of DRL in turbulent flow management.

Deep reinforcement learning (DRL) has found application in numerous use-cases pertaining to flow control. Multi-agent RL (MARL), a variant of DRL, has shown to be more effective than single-agent RL in controlling flows exhibiting locality and translational invariance. We present, for the first time, an implementation of MARL-based control of three-dimensional Rayleigh-B\'enard convection (RBC). Control is executed by modifying the temperature distribution along the bottom wall divided into multiple control segments, each of which acts as an independent agent. Two regimes of RBC are considered at Rayleigh numbers $\mathrm{Ra}=500$ and $750$. Evaluation of the learned control policy reveals a reduction in convection intensity by $23.5\%$ and $8.7\%$ at $\mathrm{Ra}=500$ and $750$, respectively. The MARL controller converts irregularly shaped convective patterns to regular straight rolls with lower convection that resemble flow in a relatively more stable regime. We draw comparisons with proportional control at both $\mathrm{Ra}$ and show that MARL is able to outperform the proportional controller. The learned control strategy is complex, featuring different non-linear segment-wise actuator delays and actuation magnitudes. We also perform successful evaluations on a larger domain than used for training, demonstrating that the invariant property of MARL allows direct transfer of the learnt policy., Comment: Submitted to the special issue titled 'Machine Learning for Fluid Dynamics' in the journal Flow, Turbulence and Combusion. 39 pages and 20 figures

Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have been developed for solving inverse problems that only leverage a pre-trained unconditional diffusion model and do not require additional task-specific training. In such methods, however, the inherent intractability of determining the conditional score function during the reverse diffusion process poses a real challenge, leaving the methods to settle with an approximation instead, which affects their performance in practice. Here, we propose a MAP estimation framework to model the reverse conditional generation process of a continuous time diffusion model as an optimization process of the underlying MAP objective, whose gradient term is tractable. In theory, the proposed framework can be applied to solve general inverse problems using gradient-based optimization methods. However, given the highly non-convex nature of the loss objective, finding a perfect gradient-based optimization algorithm can be quite challenging, nevertheless, our framework offers several potential research directions. We use our proposed formulation to develop empirically effective algorithms for image restoration. We validate our proposed algorithms with extensive experiments over multiple datasets across several restoration tasks.

Flow control is key to maximize energy efficiency in a wide range of applications. However, traditional flow-control methods face significant challenges in addressing non-linear systems and high-dimensional data, limiting their application in realistic energy systems. This study advances deep-reinforcement-learning (DRL) methods for flow control, particularly focusing on integrating group-invariant networks and positional encoding into DRL architectures. Our methods leverage multi-agent reinforcement learning (MARL) to exploit policy invariance in space, in combination with group-invariant networks to ensure local symmetry invariance. Additionally, a positional encoding inspired by the transformer architecture is incorporated to provide location information to the agents, mitigating action constraints from strict invariance. The proposed methods are verified using a case study of Rayleigh-B\'enard convection, where the goal is to minimize the Nusselt number Nu. The group-invariant neural networks (GI-NNs) show faster convergence compared to the base MARL, achieving better average policy performance. The GI-NNs not only cut DRL training time in half but also notably enhance learning reproducibility. Positional encoding further enhances these results, effectively reducing the minimum Nu and stabilizing convergence. Interestingly, group invariant networks specialize in improving learning speed and positional encoding specializes in improving learning quality. These results demonstrate that choosing a suitable feature-representation method according to the purpose as well as the characteristics of each control problem is essential. We believe that the results of this study will not only inspire novel DRL methods with invariant and unique representations, but also provide useful insights for industrial applications.

Are score function estimators an underestimated approach to learning with $k$-subset sampling? Sampling $k$-subsets is a fundamental operation in many machine learning tasks that is not amenable to differentiable parametrization, impeding gradient-based optimization. Prior work has focused on relaxed sampling or pathwise gradient estimators. Inspired by the success of score function estimators in variational inference and reinforcement learning, we revisit them within the context of $k$-subset sampling. Specifically, we demonstrate how to efficiently compute the $k$-subset distribution's score function using a discrete Fourier transform, and reduce the estimator's variance with control variates. The resulting estimator provides both exact samples and unbiased gradient estimates while also applying to non-differentiable downstream models, unlike existing methods. Experiments in feature selection show results competitive with current methods, despite weaker assumptions., Comment: ICML 2024 Workshop on Differentiable Almost Everything: Differentiable Relaxations, Algorithms, Operators, and Simulators

A phenomenological description is presented to explain the intermediate and low-frequency/large-scale contributions to the wall-shear-stress (${\tau}_w$) and wall-pressure (${p}_w$) spectra of canonical turbulent boundary layers, which are well known to increase with Reynolds number. The explanation is based on the concept of active and inactive motions (Townsend, J. Fluid Mech., vol. 11, 1961) associated with the attached-eddy hypothesis. Unique data sets of simultaneously acquired ${\tau}_w$, ${p}_w$ and velocity fluctuation time series in the log region are considered, across friction-Reynolds-number ($Re_{\tau}$) range of $\mathcal{O}$($10^3$) $\lesssim$ $Re_{\tau}$ $\lesssim$ $\mathcal{O}$($10^6$). A recently proposed energy-decomposition methodology (Deshpande et al., J. Fluid Mech., vol. 914, 2021) is implemented to reveal the active and inactive contributions to the ${\tau}_w$- and $p_w$-spectra. Empirical evidence is provided in support of Bradshaw's (J. Fluid Mech., vol. 30, 1967) hypothesis that the inactive motions are responsible for the non-local wall-ward transport of the large-scale inertia-dominated energy, which is produced in the log region by active motions. This explains the large-scale signatures in the ${\tau}_w$-spectrum, which grow with $Re_{\tau}$ despite the statistically weak signature of large-scale turbulence production, in the near-wall region. For wall pressure, active and inactive motions respectively contribute to the intermediate and large scales of the $p_w$-spectrum. Both these contributions are found to increase with increasing $Re_{\tau}$ owing to the broadening and energization of the wall-scaled (attached) eddy hierarchy. This potentially explains the rapid $Re_{\tau}$-growth of the $p_w$-spectra relative to ${\tau}_w$, given the dependence of the latter only on the inactive contributions., Comment: Preprint submitted for review to the Journal of Fluid Mechanics, with 18 pages and 7 figures

Artificial Intelligence (AI) has the potential to revolutionize space exploration by delegating several spacecraft decisions to an onboard AI instead of relying on ground control and predefined procedures. It is likely that there will be an AI/ML Processing Unit onboard the spacecraft running an inference engine. The neural-network will have pre-installed parameters that can be updated onboard by uploading, by telecommands, parameters obtained by training on the ground. However, satellite uplinks have limited bandwidth and transmissions can be costly. Furthermore, a mission operating with a suboptimal neural network will miss out on valuable scientific data. Smaller networks can thereby decrease the uplink cost, while increasing the value of the scientific data that is downloaded. In this work, we evaluate and discuss the use of reduced-precision and bare-minimum neural networks to reduce the time for upload. As an example of an AI use case, we focus on the NASA's Magnetosperic MultiScale (MMS) mission. We show how an AI onboard could be used in the Earth's magnetosphere to classify data to selectively downlink higher value data or to recognize a region-of-interest to trigger a burst-mode, collecting data at a high-rate. Using a simple filtering scheme and algorithm, we show how the start and end of a region-of-interest can be detected in on a stream of classifications. To provide the classifications, we use an established Convolutional Neural Network (CNN) trained to an accuracy >94%. We also show how the network can be reduced to a single linear layer and trained to the same accuracy as the established CNN. Thereby, reducing the overall size of the model by up to 98.9%. We further show how each network can be reduced by up to 75% of its original size, by using lower-precision formats to represent the network parameters, with a change in accuracy of less than 0.6 percentage points.

This study aims to overcome the limitations of conventional deep-learning approaches based on convolutional neural networks in complex geometries and unstructured meshes by exploring the potential of Graph U-Nets for unsteady flow-field prediction. We present a comprehensive investigation of Graph U-Nets, originally developed for classification tasks, now tailored for mesh-agnostic spatio-temporal forecasting of fluid dynamics. Our focus is on enhancing their performance through systematic hyperparameter tuning and architectural modifications. We propose novel approaches to improve mesh-agnostic spatio-temporal prediction of transient flow fields using Graph U-Nets, enabling accurate prediction on diverse mesh configurations. Key enhancements to the Graph U-Net architecture, including the Gaussian-mixture-model convolutional operator and noise injection approaches, provide increased flexibility in modeling node dynamics: the former reduces prediction error by 95\% compared to conventional convolutional operators, while the latter improves long-term prediction robustness, resulting in an error reduction of 86\%. We demonstrate the effectiveness of these enhancements in both transductive and inductive learning settings, showcasing the adaptability of Graph U-Nets to various flow conditions and mesh structures. This work contributes to the field of reduced-order modeling for computational fluid dynamics by establishing Graph U-Nets as a viable and flexible alternative to convolutional neural networks, capable of accurately and efficiently predicting complex fluid flow phenomena across diverse scenarios.

Direct numerical simulations (DNS) stand out as formidable tools in studying turbulent flows. Despite the fact that the achievable Reynolds number remains lower than those available through experimental methods, DNS offers a distinct advantage: the complete knowledge of the velocity field, facilitating the evaluation of any desired quantity. This capability should extend to compute derivatives. Among the classic functions requiring derivatives is the indicator function, $\Xi(y^+) = y^+\frac{{\rm d}\overline{U}_x^+}{{\rm d}y^+}$. This function encapsulates the wall-normal derivative of the streamwise velocity, with its value possibly influenced by mesh size and its spatial distribution. The indicator function serves as a fundamental element in unraveling the interplay between inner and outer layers in wall-bounded flows, including the overlap region, and forms a critical underpinning in turbulence modeling. Our investigation reveals a sensitivity of the indicator function on the utilized mesh distributions, prompting inquiries into the conventional mesh-sizing paradigms for DNS applications., Comment: 6 pages conference preprint. arXiv admin note: substantial text overlap with arXiv:2311.05204

Indicator functions of the streamwise normal-stress profiles (NSP), based on careful differentiation of some of the best direct numerical simulations (DNS) data from channel and pipe flows, over the range $550

There is much debate on whether quantum computing on current NISQ devices, consisting of noisy hundred qubits and requiring a non-negligible usage of classical computing as part of the algorithms, has utility and will ever offer advantages for scientific and industrial applications with respect to traditional computing. In this position paper, we argue that while real-world NISQ quantum applications have yet to surpass their classical counterparts, strategic approaches can be used to facilitate advancements in both industrial and scientific applications. We have identified three key strategies to guide NISQ computing towards practical and useful implementations. Firstly, prioritizing the identification of a "killer app" is a key point. An application demonstrating the distinctive capabilities of NISQ devices can catalyze broader development. We suggest focusing on applications that are inherently quantum, e.g., pointing towards quantum chemistry and material science as promising domains. These fields hold the potential to exhibit benefits, setting benchmarks for other applications to follow. Secondly, integrating AI and deep-learning methods into NISQ computing is a promising approach. Examples such as quantum Physics-Informed Neural Networks and Differentiable Quantum Circuits (DQC) demonstrate the synergy between quantum computing and AI. Lastly, recognizing the interdisciplinary nature of NISQ computing, we advocate for a co-design approach. Achieving synergy between classical and quantum computing necessitates an effort in co-designing quantum applications, algorithms, and programming environments, and the integration of HPC with quantum hardware. The interoperability of these components is crucial for enabling the full potential of NISQ computing., Comment: 5 pages, 1 figure

Technological advancements have substantially increased computational power and data availability, enabling the application of powerful machine-learning (ML) techniques across various fields. However, our ability to leverage ML methods for scientific discovery, {\it i.e.} to obtain fundamental and formalized knowledge about natural processes, is still in its infancy. In this review, we explore how the scientific community can increasingly leverage ML techniques to achieve scientific discoveries. We observe that the applicability and opportunity of ML depends strongly on the nature of the problem domain, and whether we have full ({\it e.g.}, turbulence), partial ({\it e.g.}, computational biochemistry), or no ({\it e.g.}, neuroscience) {\it a-priori} knowledge about the governing equations and physical properties of the system. Although challenges remain, principled use of ML is opening up new avenues for fundamental scientific discoveries. Throughout these diverse fields, there is a theme that ML is enabling researchers to embrace complexity in observational data that was previously intractable to classic analysis and numerical investigations.

We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data points (in some cases, our method can learn from a single full-state snapshot), it still achieves high accuracy and can predict the flow of PDEs over long time horizons. Moreover, we show how additional symmetries can be exploited to increase sample efficiency and to enforce equivariance.

Wall-scaled (attached) eddies play a significant role in the overall drag experienced in high-Reynolds-number turbulent boundary layers (TBLs). This study aims to delve into the underlying mechanisms driving this phenomenon by dissecting the active and inactive components of these attached eddies, as initially proposed by Townsend (1976). Employing a recently introduced energy-decomposition scheme, we analyze TBL datasets covering a wide range of Reynolds numbers ($Re_{\tau}$ $\sim$ $\mathcal{O}$(10$^{3}$)--$\mathcal{O}$(10$^{6}$)). This analysis provides empirical evidence of the distinct contributions of these components to drag generation, and reveals that while active motions are responsible solely for generating Reynolds shear stresses, inactive motions are crucial for transporting streamwise momentum from the logarithmic region to the wall, thus corroborating earlier hypotheses in the literature., Comment: Proceeding accepted for the Thirteenth International Symposium on Turbulence and Shear Flow Phenomena (TSFP13)

Neural-network models have been employed to predict the instantaneous flow close to the wall in a viscoelastic turbulent channel flow. Numerical simulation data at the wall is utilized to predict the instantaneous velocity-fluctuations and polymeric-stress-fluctuations at three different wall-normal positions in the buffer region. The ability of non-intrusive predictions has not been previously investigated in non-Newtonian turbulence. Our analysis shows that velocity-fluctuations are predicted well from wall measurements in viscoelastic turbulence. The models exhibit enhanced accuracy in predicting quantities of interest during the hibernation intervals, facilitating a deeper understanding of the underlying physics during low-drag events. The neural-network models also demonstrate a reasonably good accuracy in predicting polymeric-shear stress and the trace of the polymer stress at a given wall-normal location. This method could be used in flow control or when only wall information is available from experiments (for example, in opaque fluids). More importantly, only velocity and pressure information can be measured experimentally, while polymeric elongation and orientation cannot be directly measured despite their importance for turbulent dynamics. We therefore study the possibility to reconstruct the polymeric-stress fields from velocity or pressure measurements in viscoelastic turbulent flows. The results are promising but also underline that a lack of small scales in the input velocity fields can alter the rate of energy transfer from flow to polymers, affecting the prediction of the polymer-stress fluctuations. The present approach not only aids in extracting polymeric-stress information but also gives information about the link between polymeric-stress and velocity fields in viscoelastic turbulence., Comment: 26 pages, 16 figures

In this work, we study the causality of near-wall inner and outer turbulent motions. Here we define the inner motions as the self-sustained near-wall cycle and the outer motions as those living in the logarithmic layer exhibiting a footprint on the near-wall region. We perform causal analysis using two different methods: one is the transfer entropy, based on the information theory, and the other one is the Liang--Kleeman information-flow theory. The causal-analysis methods are applied to several scenarios, including a linear and a non-linear problem, a low-dimensional model of the near-wall cycle of turbulence, as well as the interaction between inner and outer turbulent motions in a channel at a friction Reynolds number of $Re_{\tau}=1000$. We find that both methods can well predict the causal links in the linear problem, and the information flow can identify more of the nonlinear problem. Despite richer causalities revealed by the transfer entropy for turbulent-flow problems, both methods can successfully identify the streak-vortex regeneration mechanism that majorly sustains the near-wall turbulence. It is also indicated that both bottom-up and top-down influences of inner and outer motions may coexist in addition to the multiscale self-sustaining mechanism. Lastly, we mention that the computation of the information flow is much more efficient than the transfer entropy. The present study suggests that the information flow can have great potential in causal inference for turbulent-flow problems besides the transfer entropy., Comment: 13th International Symposium on Turbulence and Shear Flow Phenomena (TSFP13), Montreal, Canada, June 25--28, 2024

The control efficacy of classical periodic forcing and deep reinforcement learning (DRL) is assessed for a turbulent separation bubble (TSB) at $Re_\tau=180$ on the upstream region before separation occurs. The TSB can resemble a separation phenomenon naturally arising in wings, and a successful reduction of the TSB can have practical implications in the reduction of the aviation carbon footprint. We find that the classical zero-net-mas-flux (ZNMF) periodic control is able to reduce the TSB by 15.7%. On the other hand, the DRL-based control achieves 25.3% reduction and provides a smoother control strategy while also being ZNMF. To the best of our knowledge, the current test case is the highest Reynolds-number flow that has been successfully controlled using DRL to this date. In future work, these results will be scaled to well-resolved large-eddy simulation grids. Furthermore, we provide details of our open-source CFD-DRL framework suited for the next generation of exascale computing machines., Comment: 19 pages, 14 figures, 3 tables

Feature selection is a crucial task in settings where data is high-dimensional or acquiring the full set of features is costly. Recent developments in neural network-based embedded feature selection show promising results across a wide range of applications. Concrete Autoencoders (CAEs), considered state-of-the-art in embedded feature selection, may struggle to achieve stable joint optimization, hurting their training time and generalization. In this work, we identify that this instability is correlated with the CAE learning duplicate selections. To remedy this, we propose a simple and effective improvement: Indirectly Parameterized CAEs (IP-CAEs). IP-CAEs learn an embedding and a mapping from it to the Gumbel-Softmax distributions' parameters. Despite being simple to implement, IP-CAE exhibits significant and consistent improvements over CAE in both generalization and training time across several datasets for reconstruction and classification. Unlike CAE, IP-CAE effectively leverages non-linear relationships and does not require retraining the jointly optimized decoder. Furthermore, our approach is, in principle, generalizable to Gumbel-Softmax distributions beyond feature selection., Comment: ICML 2024

The wake topology developing behind a wall-mounted square cylinder in a turbulent boundary layer has been investigated using a high-resolution large-eddy simulation (LES). The boundary-layer thickness at the obstacle location is fixed, the Reynolds number based on the cylinder h and the incoming free-stream velocity $u_\infty$ is 10,000 while the aspect ratio (AR), defined as obstacle height divided by its width, ranges from 1 to 4. The Reynolds stresses, anisotropy-invariant maps (AIM) and the turbulent kinetic energy (TKE) budget are analyzed to investigate the influence of AR on the wake structures and on the turbulence production and transport. In particular, the transition from a dipole configuration for low AR to a quadrupole wake is extensively discussed and examined. The necessity of more data to express this critical AR as a function of the momentum-thickness-based Reynolds number $Re_{\theta}$ is thus highlighted. As an effect of the AR, the wake is deformed in both streamwise and spanwise directions. This contraction of the wake, attributed to the occurrence of the base vortices for the cases AR = 3 and 4, impacts the size of the positive production region that stretches from the roof and the flank of the obstacle to the wake core. The AIMs confirm the wake three-dimensionality and are used to describe the redistribution of the turbulent kinetic energy (TKE) along the three normal directions, in agreement with the literature [A. J. Simonsen and P. Krogstad, Phys. Fluids 17, 088103, (2005)]. The present analysis on the TKE budget displays a stronger turbulence production for the cases AR = 3 and 4, demonstrating the strong influence of the tip and base vortices in generating turbulence at the wall location behind the cylinder.

This research focuses on the identification and causality analysis of coherent structures that arise in turbulent flows in square and rectangular ducts. Coherent structures are first identified from direct numerical simulation data via proper orthogonal decomposition (POD), both by using all velocity components, and after separating the streamwise and secondary components of the flow. The causal relations between the mode coefficients are analysed using pairwise-conditional Granger causality analysis. We also formulate a nonlinear Granger causality analysis that can account for nonlinear interactions between modes. Focusing on streamwise-constant structures within a duct of short streamwise extent, we show that the causal relationships are highly sensitive to whether the mode coefficients or their squared values are considered, whether nonlinear effects are explicitly accounted for, and whether streamwise and secondary flow structures are separated prior to causality analyses. We leverage these sensitivities to determine that linear mechanisms underpin causal relationships between modes that share the same symmetry or anti-symmetry properties about the corner bisector, while nonlinear effects govern the causal interactions between symmetric and antisymmetric modes. In all cases, we find that the secondary flow fluctuations (manifesting as streamwise vorticial structures) are the primary cause of both the presence and movement of near-wall streaks towards and away from the duct corners.

Two sets of measurements utilizing hot-wire anemometry and oil film interferometry for flat-plate turbulent boundary layers, exposed to various controlled adverse and favorable pressure gradients, are used to evaluate history effects of the imposed and varying freestream gradients. The results are from the NDF wind tunnel at ILLINOIS TECH (IIT) and the MTL wind tunnel at KTH, over the range $800 < Re_\tau < 22,000$ (where $Re_{\tau}$ is the friction Reynolds number). The streamwise pressure-gradient parameter $\beta \equiv (-\ell/\tau_{w}) \cdot (\partial P_{e}/\partial x)$ varied between $-2 < \beta < 7$, where $\ell$ is an outer length scale for boundary layers equivalent to the half height of channel flow and the radius of pipe flow, and is estimated for each boundary-layer profile. Extracting from each profile the three parameters of the overlap region, following the recent work of \cite{mon23} that led to an overlap region of combined logarithmic and linear parts, we find minimum history effects in the overlap region. Thus, the overlap region in this range of pressure-gradient boundary layers appears to be in ``quasi equilibrium"., Comment: 10 pages, 6 figures

Direct Numerical Simulations (DNSs) are one of the most powerful tools for studying turbulent flows. Even if achievable Reynolds numbers are lower than those obtained with experimental means, there is a clear advantage since the entire velocity field is known, and any desired quantity can be evaluated. This also includes the computation of derivatives of all relevant terms. One such derivative provides the indicator function, which is the product of wall distance by wall-normal derivative of the mean streamwise velocity. This derivative may depend on mesh spacing and distribution. However, it is extremely affected by the convergence of the simulation. The indicator function is a cornerstone to understanding inner and outer interactions in wall-bounded flows and describing the overlap region between them. We find a clear dependence of this indicator function on mesh distributions we examined, raising questions about classical mesh and convergence requirements for DNS and achievable accuracy. Within the framework of the logarithmic plus linear overlap region, coupled with a parametric study of channel flows and some pipe flows, sensitivities of extracted overlap parameters are examined, and a path is revealed to establishing their high-$Re_\tau$ or near-asymptotic values at modest Reynolds numbers accessible by high-quality DNS with reasonable ``cost''.

High-fidelity simulations are conducted to investigate the turbulent boundary layers around a finite-span NACA0012 wing with a rounded wing-tip geometry at a chord-based Reynolds number of $Re_c=200\,000$ and at various angles of attack up to $10^\circ$. The study aims to discern the differences between the boundary layers on the finite-span wing and those on infinite-span wings at equivalent angles of attack. The finite-span boundary layers exhibit: (i) an altered streamwise and a non-zero spanwise pressure gradient as a result of the variable downwash induced by the wing-tip vortices (an inviscid effect typical of finite-span wings); (ii) differences in the flow history at different wall-normal distances, caused by the variable flow angle in the wall-normal direction (due to constant pressure gradients and variable momentum normal to the wall); (iii) laminar flow entrainment into the turbulent boundary layers near the wing tip (due to a laminar/turbulent interface); and (iv) variations in boundary layer thickness across the span, attributed to the variable wall-normal velocity in that direction (a primarily inviscid effect). These physical effects are then used to explain the differences in the Reynolds stress profiles and other boundary layer quantities, including the reduced near-wall peak of the streamwise Reynolds stress and the elevated Reynolds stress levels near the boundary layer edge, both observed in the finite-span wings. Other aspects of the flow, such as the downstream development of wing-tip vortices and their interactions with the surrounding flow, are reserved for future investigations.

The current revolution in the field of machine learning (ML) is leading to many interesting developments in a wide range of areas, including fluid mechanics. Here we review recent and emerging possibilities in the context of predictions, simulations and control of fluid flows, focusing on wall-bounded turbulence. A number of important areas are benefiting from ML, and it is important to identify the synergies with the existing pillars of scientific discovery, i.e. theory, experiments and simulations. It is essential to adopt a balanced approach as a community in order to harness all the positive potential of these novel methods.

The present study proposes an active flow control (AFC) approach based on deep reinforcement learning (DRL) to optimize the performance of multiple plasma actuators on a square cylinder. The investigation aims to modify the control inputs of the plasma actuators to reduce the drag and lift forces affecting the cylinder while maintaining a stable flow regime. The environment of the proposed model is represented by a two-dimensional direct numerical simulation (DNS) of a flow past a square cylinder. The control strategy is based on the regulation of the supplied alternating current (AC) voltage at three distinct configurations of the plasma actuators. The effectiveness of the designed strategy is first investigated for Reynolds number, $Re_{D} = 100$, and further applied for $Re_{D} = 180$. The applied active flow control strategy is able to reduce the mean drag coefficient by 97\% at $Re_{D} = 100$ and by 99\% at $Re_D=180$. Furthermore, the results from this study show that with the increase in Reynolds number, it becomes more challenging to eliminate vortex shedding with plasma actuators located only on the rear surface of the cylinder. Nevertheless, the proposed control scheme is able to completely suppress it with an optimized configuration of the plasma actuators., Comment: 30 pages, 17 figures

To improve the robustness of transformer neural networks used for temporal-dynamics prediction of chaotic systems, we propose a novel attention mechanism called easy attention which we demonstrate in time-series reconstruction and prediction. While the standard self attention only makes use of the inner product of queries and keys, it is demonstrated that the keys, queries and softmax are not necessary for obtaining the attention score required to capture long-term dependencies in temporal sequences. Through the singular-value decomposition (SVD) on the softmax attention score, we further observe that self attention compresses the contributions from both queries and keys in the space spanned by the attention score. Therefore, our proposed easy-attention method directly treats the attention scores as learnable parameters. This approach produces excellent results when reconstructing and predicting the temporal dynamics of chaotic systems exhibiting more robustness and less complexity than self attention or the widely-used long short-term memory (LSTM) network. We show the improved performance of the easy-attention method in the Lorenz system, a turbulence shear flow and a model of a nuclear reactor., Comment: 15 pages and 6 figures

The widest spanwise scales in turbulent channel flows are studied through the use of three periodic channel-flow simulations at friction Reynolds number $\mathrm{Re}_{\tau}=550$. The length and height of the channels are the same in all cases ($L_x/h=8\pi$ and $L_y/h=2$ respectively), while the width is progressively doubled: $L_z/h = \{4\pi, 8\pi, 16\pi\}$. The effects of increasing the domain can not be determined with statistical significance in our simulations, since the difference in the statistics between the simulations is of the same order as the errors of convergence. A channel flow similar to the smaller one ($\textit{J. Fluid Mech.}$, vol. 500, 2004, pp. 135--144), which was averaged over a very long time, was used as a reference. The one-dimensional spanwise spectrum of the streamwise velocity is computed with the aim of assessing the domain-size effect on the widest scales. Our results indicate that $90\%$ of the total streamwise energetic fluctuations is recovered without a significant influence of the size of the domain. The remaining $10\%$ of the energy reflects that the widest scales in the outer layer are the ones most significantly affected by the spanwise length of the domain. The power-spectral density for $k_z = 0$ remains constant even if the size of the domain in the spanwise direction is increased up to 4 times the standard spanwise length, indicating that wide, spanwise coherent structures are not an artifact of domain truncation.

Physics is a field of science that has traditionally used the scientific method to answer questions about why natural phenomena occur and to make testable models that explain the phenomena. Discovering equations, laws and principles that are invariant, robust and causal explanations of the world has been fundamental in physical sciences throughout the centuries. Discoveries emerge from observing the world and, when possible, performing interventional studies in the system under study. With the advent of big data and the use of data-driven methods, causal and equation discovery fields have grown and made progress in computer science, physics, statistics, philosophy, and many applied fields. All these domains are intertwined and can be used to discover causal relations, physical laws, and equations from observational data. This paper reviews the concepts, methods, and relevant works on causal and equation discovery in the broad field of Physics and outlines the most important challenges and promising future lines of research. We also provide a taxonomy for observational causal and equation discovery, point out connections, and showcase a complete set of case studies in Earth and climate sciences, fluid dynamics and mechanics, and the neurosciences. This review demonstrates that discovering fundamental laws and causal relations by observing natural phenomena is being revolutionised with the efficient exploitation of observational data, modern machine learning algorithms and the interaction with domain knowledge. Exciting times are ahead with many challenges and opportunities to improve our understanding of complex systems., Comment: 137 pages

We study the Reynolds-number effects on the outer region of moderate adverse-pressure-gradient (APG) turbulent boundary layers (TBLs) and find that their small scale energy reduces with increasing friction Reynolds-number ($Re_{\tau}$). The trend is based on analyzing APG TBL data across 600 $\lesssim$ $Re_{\tau}$ $\lesssim$ 7000, and contrasts with the negligible variation in small scale energy noted for canonical wall flows. The datasets considered include those from a well-resolved numerical simulation (Pozuelo et al. 2022), which provides access to an APG TBL maintained at near-equilibrium conditions across 1000 $\lesssim$ $Re_{\tau}$ $\lesssim$ 2000, with a well-defined flow history, and a new high-$Re_{\tau}$ ($\sim$ 7000) experimental study from the large Melbourne wind tunnel, with its long test section modified to permit development of an APG TBL from a 'canonical' upstream condition. The decrease in small scale energy with $Re_{\tau}$ is revealed via decomposing the streamwise normal stresses into small and large scale contributions, based on a sharp spectral cut-off. The origin for this trend is traced back to the production of turbulent kinetic energy in an APG TBL, the small scale contribution to which is also found to decrease with $Re_{\tau}$ in the outer region. The conclusion is reaffirmed by investigating attenuation of streamwise normal stresses due to changing spatial-resolutions of the numerical grid/hotwire sensors, which reduces with increasing $Re_{\tau}$ and is found to be negligible at $Re_{\tau}$ $\sim$ 7000 in this study. The results emphasize that new scaling arguments and spatial-resolution correction schemes should be tested rigorously across a broad $Re_{\tau}$ range, particularly for the outer region of pressure gradient TBLs., Comment: Manuscript accepted in Physical Review Fluids, with 20 pages and 13 figures

Variational autoencoder (VAE) architectures have the potential to develop reduced-order models (ROMs) for chaotic fluid flows. We propose a method for learning compact and near-orthogonal ROMs using a combination of a $\beta$-VAE and a transformer, tested on numerical data from a two-dimensional viscous flow in both periodic and chaotic regimes. The $\beta$-VAE is trained to learn a compact latent representation of the flow velocity, and the transformer is trained to predict the temporal dynamics in latent space. Using the $\beta$-VAE to learn disentangled representations in latent-space, we obtain a more interpretable flow model with features that resemble those observed in the proper orthogonal decomposition, but with a more efficient representation. Using Poincar\'e maps, the results show that our method can capture the underlying dynamics of the flow outperforming other prediction models. The proposed method has potential applications in other fields such as weather forecasting, structural dynamics or biomedical engineering.

Rayleigh-B\'enard convection (RBC) is a recurrent phenomenon in several industrial and geoscience flows and a well-studied system from a fundamental fluid-mechanics viewpoint. However, controlling RBC, for example by modulating the spatial distribution of the bottom-plate heating in the canonical RBC configuration, remains a challenging topic for classical control-theory methods. In the present work, we apply deep reinforcement learning (DRL) for controlling RBC. We show that effective RBC control can be obtained by leveraging invariant multi-agent reinforcement learning (MARL), which takes advantage of the locality and translational invariance inherent to RBC flows inside wide channels. The MARL framework applied to RBC allows for an increase in the number of control segments without encountering the curse of dimensionality that would result from a naive increase in the DRL action-size dimension. This is made possible by the MARL ability for re-using the knowledge generated in different parts of the RBC domain. We show in a case study that MARL DRL is able to discover an advanced control strategy that destabilizes the spontaneous RBC double-cell pattern, changes the topology of RBC by coalescing adjacent convection cells, and actively controls the resulting coalesced cell to bring it to a new stable configuration. This modified flow configuration results in reduced convective heat transfer, which is beneficial in several industrial processes. Therefore, our work both shows the potential of MARL DRL for controlling large RBC systems, as well as demonstrates the possibility for DRL to discover strategies that move the RBC configuration between different topological configurations, yielding desirable heat-transfer characteristics. These results are useful for both gaining further understanding of the intrinsic properties of RBC, as well as for developing industrial applications., Comment: 34 pages, 11 figures submitted to Physics of Fluids

The field of machine learning has rapidly advanced the state of the art in many fields of science and engineering, including experimental fluid dynamics, which is one of the original big-data disciplines. This perspective will highlight several aspects of experimental fluid mechanics that stand to benefit from progress advances in machine learning, including: 1) augmenting the fidelity and quality of measurement techniques, 2) improving experimental design and surrogate digital-twin models and 3) enabling real-time estimation and control. In each case, we discuss recent success stories and ongoing challenges, along with caveats and limitations, and outline the potential for new avenues of ML-augmented and ML-enabled experimental fluid mechanics.

Innovation is a key component to equip our society with tools to adapt to new climatic conditions. The development of research-action interfaces shifts useful ideas into operationalized knowledge allowing innovation to flourish. In this paper we quantify the existing gap between climate research and innovation action in Europe using a novel framework that combines artificial intelligence (AI) methods and network science. We compute the distance between key topics of research interest from peer review publications and core issues tackled by innovation projects funded by the most recent European framework programmes. Our findings reveal significant differences exist between and within the two layers. Economic incentives, agricultural and industrial processes are differently connected to adaptation and mitigation priorities. We also find a loose research-action connection in bioproducts, biotechnologies and risk assessment practices, where applications are still too few compared to the research insights. Our analysis supports policy-makers to measure and track how research funding result in innovation action, and to adjust decisions if stated priorities are not achieved., Comment: 21 pages; methods at the end of the manuscript; submitted to ECCA2023 conference

The objective of this study is to assess the capability of convolution-based neural networks to predict wall quantities in a turbulent open channel flow. The first tests are performed by training a fully-convolutional network (FCN) to predict the 2D velocity-fluctuation fields at the inner-scaled wall-normal location $y^{+}_{\rm target}$, using the sampled velocity fluctuations in wall-parallel planes located farther from the wall, at $y^{+}_{\rm input}$. The predictions from the FCN are compared against the predictions from a proposed R-Net architecture. Since the R-Net model is found to perform better than the FCN model, the former architecture is optimized to predict the 2D streamwise and spanwise wall-shear-stress components and the wall pressure from the sampled velocity-fluctuation fields farther from the wall. The dataset is obtained from DNS of open channel flow at $Re_{\tau} = 180$ and $550$. The turbulent velocity-fluctuation fields are sampled at various inner-scaled wall-normal locations, along with the wall-shear stress and the wall pressure. At $Re_{\tau}=550$, both FCN and R-Net can take advantage of the self-similarity in the logarithmic region of the flow and predict the velocity-fluctuation fields at $y^{+} = 50$ using the velocity-fluctuation fields at $y^{+} = 100$ as input with about 10% error in prediction of streamwise-fluctuations intensity. Further, the R-Net is also able to predict the wall-shear-stress and wall-pressure fields using the velocity-fluctuation fields at $y^+ = 50$ with around 10% error in the intensity of the corresponding fluctuations at both $Re_{\tau} = 180$ and $550$. These results are an encouraging starting point to develop neural-network-based approaches for modelling turbulence near the wall in large-eddy simulations., Comment: 33 pages, 10 figures. arXiv admin note: substantial text overlap with arXiv:2107.07340

Despite its great scientific and technological importance, wall-bounded turbulence is an unresolved problem in classical physics that requires new perspectives to be tackled. One of the key strategies has been to study interactions among the energy-containing coherent structures in the flow. Such interactions are explored in this study for the first time using an explainable deep-learning method. The instantaneous velocity field obtained from a turbulent channel flow simulation is used to predict the velocity field in time through a U-net architecture. Based on the predicted flow, we assess the importance of each structure for this prediction using the game-theoretic algorithm of SHapley Additive exPlanations (SHAP). This work provides results in agreement with previous observations in the literature and extends them by revealing that the most important structures in the flow are not necessarily the ones with the highest contribution to the Reynolds shear stress. We also apply the method to an experimental database, where we can identify completely new structures based on their importance score. This framework has the potential to shed light on numerous fundamental phenomena of wall-bounded turbulence, including novel strategies for flow control.

The objective of the present study is to provide a numerical database of thermal boundary layers and to contribute to the understanding of the dynamics of passive scalars at different Prandtl numbers. In this regard, a direct numerical simulation (DNS) of an incompressible zero-pressure-gradient turbulent boundary layer is performed with the Reynolds number based on momentum thickness $Re_{\theta}$ up to $1080$. Four passive scalars, characterized by the Prandtl numbers $Pr = 1,2,4,6$ are simulated with constant Dirichlet boundary conditions, using the pseudo-spectral code SIMSON (Chevalier et al. 2007). To the best of our knowledge, the present direct numerical simulation provides the thermal boundary layer with the highest Prandtl number available in the literature. It corresponds to that of water at $\sim$24$^{o}C$, when the fluid temperature is considered as a passive scalar. Turbulence statistics for the flow and thermal fields are computed and compared with available numerical simulations at similar Reynolds numbers. The mean flow and temperature profiles, root-mean squared (RMS) velocity and temperature fluctuations, turbulent heat flux, turbulent Prandtl number and higher-order statistics agree well with the numerical data reported in the literature. Furthermore, the pre-multiplied two-dimensional spectra of the velocity and of the passive scalars are computed, providing a quantitative description of the energy distribution at the different lengthscales for various wall-normal locations. The energy distribution of the heat flux fields at the wall is concentrated on longer temporal structures and exhibits different footprint at the wall, with increasing Prandtl number.

Deep reinforcement learning (DRL) has been applied to a variety of problems during the past decade, and has provided effective control strategies in high-dimensional and non-linear situations that are challenging to traditional methods. Flourishing applications now spread out into the field of fluid dynamics, and specifically of active flow control (AFC). In the community of AFC, the encouraging results obtained in two-dimensional and chaotic conditions have raised interest to study increasingly complex flows. In this review, we first provide a general overview of the reinforcement-learning (RL) and DRL frameworks, as well as their recent advances. We then focus on the application of DRL to AFC, highlighting the current limitations of the DRL algorithms in this field, and suggesting some of the potential upcoming milestones to reach, as well as open questions that are likely to attract the attention of the fluid-mechanics community.

The renewed interest from the scientific community in machine learning (ML) is opening many new areas of research. Here we focus on how novel trends in ML are providing opportunities to improve the field of computational fluid dynamics (CFD). In particular, we discuss synergies between ML and CFD that have already shown benefits, and we also assess areas that are under development and may produce important benefits in the coming years. We believe that it is also important to emphasize a balanced perspective of cautious optimism for these emerging approaches

Deep artificial neural networks (ANNs) used together with deep reinforcement learning (DRL) are receiving growing attention due to their capabilities to control complex problems. This technique has been recently used to solve problems related to flow control. In this work, an ANN trained through a DRL agent is used to perform active flow control. Two-dimensional simulations of the flow around a cylinder are conducted and an active control based on two jets located on the walls of the cylinder is considered. By gathering information from the flow surrounding the cylinder, the ANN agent is able to learn effective control strategies for the jets, leading to a significant drag reduction. In the present work, a Reynolds-number range beyond those previously considered is studied and compared with results obtained using classical flow-control methods. Significantly different nature in the control strategies is identified by the DRL as the Reynolds number Re increases. For Re <= 1000 the classical control strategy based on an opposition control relative to the wake oscillation is obtained. For Re = 2000 the new strategy consists of an energisation of the boundary layers and the separation area, which modulate the flow separation and reduce drag in a fashion similar to that of the drag crisis, through a high frequency actuation. A cross-application of agents is performed for a flow at Re = 2000, obtaining similar results in terms of drag reduction with the agents trained at Re = 1000 and 2000. The fact that two different strategies yield the same performance make us question whether this Reynolds number regime (Re = 2000) belongs to a transition towards a nature-different flow which would only admit a high-frequency actuation strategy to obtain drag reduction. This finding allows the application of ANNs trained at lower Reynolds numbers but comparable in nature, saving computational resources., Comment: 26 pages, 5 figures, submitted to MDPI