Ricardo Vinuesa, Steven L. Brunton, Beverley J. McKeon
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.
Soledad Le Clainche, Esteban Ferrer, Sam Gibson et al.
This review covers the new developments in machine learning (ML) that are impacting the multi-disciplinary area of aerospace engineering, including fundamental fluid dynamics (experimental and numerical), aerodynamics, acoustics, combustion and structural health monitoring. We review the state of the art, gathering the advantages and challenges of ML methods across different aerospace disciplines and provide our view on future opportunities. The basic concepts and the most relevant strategies for ML are presented together with the most relevant applications in aerospace engineering, revealing that ML is improving aircraft performance and that these techniques will have a large impact in the near future.
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
Giuseppe Borrelli, Luca Guastoni, Hamidreza Eivazi et al.
The success of recurrent neural networks (RNNs) has been demonstrated in many applications related to turbulence, including flow control, optimization, turbulent features reproduction as well as turbulence prediction and modeling. With this study we aim to assess the capability of these networks to reproduce the temporal evolution of a minimal turbulent channel flow. We first obtain a data-driven model based on a modal decomposition in the Fourier domain (which we denote as FFT-POD) of the time series sampled from the flow. This particular case of turbulent flow allows us to accurately simulate the most relevant coherent structures close to the wall. Long-short-term-memory (LSTM) networks and a Koopman-based framework (KNF) are trained to predict the temporal dynamics of the minimal-channel-flow modes. Tests with different configurations highlight the limits of the KNF method compared to the LSTM, given the complexity of the flow under study. Long-term prediction for LSTM show excellent agreement from the statistical point of view, with errors below 2% for the best models with respect to the reference. Furthermore, the analysis of the chaotic behaviour through the use of the Lyapunov exponents and of the dynamic behaviour through Poincaré maps emphasizes the ability of the LSTM to reproduce the temporal dynamics of turbulence. Alternative reduced-order models (ROMs), based on the identification of different turbulent structures, are explored and they continue to show a good potential in predicting the temporal dynamics of the minimal channel.
Andres Cremades, Sergio Hoyas, Rahul Deshpande et al.
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.
Rayleigh-Bénard 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.
Alberto Solera-Rico, Carlos Sanmiguel Vila, M. A. Gómez et al.
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 $β$-VAE and a transformer, tested on numerical data from a two-dimensional viscous flow in both periodic and chaotic regimes. The $β$-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 $β$-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 Poincaré 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.
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.
Joongoo Jeon, Juhyeong Lee, Ricardo Vinuesa et al.
While a big wave of artificial intelligence (AI) has propagated to the field of computational fluid dynamics (CFD) acceleration studies, recent research has highlighted that the development of AI techniques that reconciles the following goals remains our primary task: (1) accurate prediction of unseen (future) time series in long-term CFD simulations (2) acceleration of simulations (3) an acceptable amount of training data and time (4) within a multiple PDEs condition. In this study, we propose a residual-based physics-informed transfer learning (RePIT) strategy to achieve these four objectives using ML-CFD hybrid computation. Our hypothesis is that long-term CFD simulation is feasible with the hybrid method where CFD and AI alternately calculate time series while monitoring the first principle's residuals. The feasibility of RePIT strategy was verified through a CFD case study on natural convection. In a single training approach, a residual scale change occurred around 100th timestep, resulting in predicted time series exhibiting non-physical patterns as well as a significant deviations from the ground truth. Conversely, RePIT strategy maintained the residuals within the defined range and demonstrated good accuracy throughout the entire simulation period. The maximum error from the ground truth was below 0.4 K for temperature and 0.024 m/s for x-axis velocity. Furthermore, the average time for 1 timestep by the ML-GPU and CFD-CPU calculations was 0.171 s and 0.015 s, respectively. Including the parameter-updating time, the simulation was accelerated by a factor of 1.9. In conclusion, our RePIT strategy is a promising technique to reduce the cost of CFD simulations in industry. However, more vigorous optimization and improvement studies are still necessary.
Joel Vasanth, Jean Rabault, Francisco Alcántara-Ávila et al.
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-Bénard 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.
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-Bénard 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.
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.
Sai Bharath Chandra Gutha, Ricardo Vinuesa, Hossein Azizpour
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.
Hans Harder, Abhijeet Vishwasrao, Luca Guastoni et al.
This paper is concerned with probabilistic techniques for forecasting dynamical systems described by partial differential equations (such as, for example, the Navier-Stokes equations). In particular, it is investigating and comparing various extensions to the flow matching paradigm that reduce the number of sampling steps. In this regard, it compares direct distillation, progressive distillation, adversarial diffusion distillation, Wasserstein GANs and rectified flows. Moreover, experiments are conducted on a set of challenging systems. In particular, we also address the challenge of directly predicting 2D slices of large-scale 3D simulations, paving the way for efficient inflow generation for solvers.
Parthiban Loganathan, Elias Zea, Ricardo Vinuesa et al.
Rapid changes and increasing climatic variability across the widely varied Koppen-Geiger regions of northern Europe generate significant needs for adaptation. Regional planning needs high-resolution projected temperatures. This work presents an integrative downscaling framework that incorporates Vision Transformer (ViT), Convolutional Long Short-Term Memory (ConvLSTM), and Geospatial Spatiotemporal Transformer with Attention and Imbalance-Aware Network (GeoStaNet) models. The framework is evaluated with a multicriteria decision system, Deep Learning-TOPSIS (DL-TOPSIS), for ten strategically chosen meteorological stations encompassing the temperate oceanic (Cfb), subpolar oceanic (Cfc), warm-summer continental (Dfb), and subarctic (Dfc) climate regions. Norwegian Earth System Model (NorESM2-LM) Coupled Model Intercomparison Project Phase 6 (CMIP6) outputs were bias-corrected during the 1951-2014 period and subsequently validated against earlier observations of day-to-day temperature metrics and diurnal range statistics. The ViT showed improved performance (Root Mean Squared Error (RMSE): 1.01 degrees C; R^2: 0.92), allowing for production of credible downscaled projections. Under the SSP5-8.5 scenario, the Dfc and Dfb climate zones are projected to warm by 4.8 degrees C and 3.9 degrees C, respectively, by 2100, with expansion in the diurnal temperature range by more than 1.5 degrees C. The Time of Emergence signal first appears in subarctic winter seasons (Dfc: approximately 2032), signifying an urgent need for adaptation measures. The presented framework offers station-based, high-resolution estimates of uncertainties and extremes, with direct uses for adaptation policy over high-latitude regions with fast environmental change.
Active flow control of compressible transonic shock-boundary layer interactions over a two-dimensional RAE2822 airfoil at Re = 50,000 is investigated using deep reinforcement learning (DRL). The flow field exhibits highly unsteady dynamics, including complex shock-boundary layer interactions, shock oscillations, and the generation of Kutta waves from the trailing edge. A high-fidelity CFD solver, employing a fifth-order spectral discontinuous Galerkin scheme in space and a strong-stability-preserving Runge-Kutta (5,4) method in time, together with adaptive mesh refinement capability, is used to obtain the accurate flow field. Synthetic jet actuation is employed to manipulate these unsteady flow features, while the DRL agent autonomously discovers effective control strategies through direct interaction with high-fidelity compressible flow simulations. The trained controllers effectively mitigate shock-induced separation, suppress unsteady oscillations, and manipulate aerodynamic forces under transonic conditions. In the first set of experiments, aimed at both drag reduction and lift enhancement, the DRL-based control reduces the average drag coefficient by 13.78% and increases lift by 131.18%, thereby improving the lift-to-drag ratio by 121.52%, which underscores its potential for managing complex flow dynamics. In the second set, targeting drag reduction while maintaining lift, the DRL-based control achieves a 25.62% reduction in drag and a substantial 196.30% increase in lift, accompanied by markedly diminished oscillations. In this case, the lift-to-drag ratio improves by 220.26%.
Parthiban Loganathan, Elias Zea, Ricardo Vinuesa et al.
Accurate regional climate forecast calls for high-resolution downscaling of Global Climate Models (GCMs). This work presents a deep-learning-based multi-model evaluation and downscaling framework ranking 32 Coupled Model Intercomparison Project Phase 6 (CMIP6) models using a Deep Learning-TOPSIS (DL-TOPSIS) mechanism and so refines outputs using advanced deep-learning models. Using nine performance criteria, five Köppen-Geiger climate zones -- Tropical, Arid, Temperate, Continental, and Polar -- are investigated over four seasons. While TaiESM1 and CMCC-CM2-SR5 show notable biases, ranking results show that NorESM2-LM, GISS-E2-1-G, and HadGEM3-GC31-LL outperform other models. Four models contribute to downscaling the top-ranked GCMs to 0.1$^{\circ}$ resolution: Vision Transformer (ViT), Geospatial Spatiotemporal Transformer with Attention and Imbalance-Aware Network (GeoSTANet), CNN-LSTM, and CNN-Long Short-Term Memory (ConvLSTM). Effectively capturing temperature extremes (TXx, TNn), GeoSTANet achieves the highest accuracy (Root Mean Square Error (RMSE) = 1.57$^{\circ}$C, Kling-Gupta Efficiency (KGE) = 0.89, Nash-Sutcliffe Efficiency (NSE) = 0.85, Correlation ($r$) = 0.92), so reducing RMSE by 20% over ConvLSTM. CNN-LSTM and ConvLSTM do well in Continental and Temperate zones; ViT finds fine-scale temperature fluctuations difficult. These results confirm that multi-criteria ranking improves GCM selection for regional climate studies and transformer-based downscaling exceeds conventional deep-learning methods. This framework offers a scalable method to enhance high-resolution climate projections, benefiting impact assessments and adaptation plans.
Francisco Giral, Ignacio Gómez, Ricardo Vinuesa et al.
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.
Alfred Nilsson, Klas Wijk, Sai bharath chandra Gutha et al.
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.
Abhijeet Vishwasrao, Sai Bharath Chandra Gutha, Andres Cremades et al.
Rapid urbanization demands accurate and efficient monitoring of turbulent wind patterns to support air quality, climate resilience and infrastructure design. Traditional sparse reconstruction and sensor placement strategies face major accuracy degradations under practical constraints. Here, we introduce Diff-SPORT, a diffusion-based framework for high-fidelity flow reconstruction and optimal sensor placement in urban environments. Diff-SPORT combines a generative diffusion model with a maximum a posteriori (MAP) inference scheme and a Shapley-value attribution framework to propose a scalable and interpretable solution. Compared to traditional numerical methods, Diff-SPORT achieves significant speedups while maintaining both statistical and instantaneous flow fidelity. Our approach offers a modular, zero-shot alternative to retraining-intensive strategies, supporting fast and reliable urban flow monitoring under extreme sparsity. Diff-SPORT paves the way for integrating generative modeling and explainability in sustainable urban intelligence.
Ricardo Vinuesa, Paola Cinnella, Jean Rabault et al. · uw
As modern scientific instruments generate vast amounts of data and the volume of information in the scientific literature continues to grow, machine learning (ML) has become an essential tool for organising, analysing, and interpreting these complex datasets. This paper explores the transformative role of ML in accelerating breakthroughs across a range of scientific disciplines. By presenting key examples -- such as brain mapping and exoplanet detection -- we demonstrate how ML is reshaping scientific research. We also explore different scenarios where different levels of knowledge of the underlying phenomenon are available, identifying strategies to overcome limitations and unlock the full potential of ML. Despite its advances, the growing reliance on ML poses challenges for research applications and rigorous validation of discoveries. We argue that even with these challenges, ML is poised to disrupt traditional methodologies and advance the boundaries of knowledge by enabling researchers to tackle increasingly complex problems. Thus, the scientific community can move beyond the necessary traditional oversimplifications to embrace the full complexity of natural systems, ultimately paving the way for interdisciplinary breakthroughs and innovative solutions to humanity's most pressing challenges.
Sai Bharath Chandra Gutha, Ricardo Vinuesa, Hossein Azizpour
A pre-trained unconditional diffusion model, combined with posterior sampling or maximum a posteriori (MAP) estimation techniques, can solve arbitrary inverse problems without task-specific training or fine-tuning. However, existing posterior sampling and MAP estimation methods often rely on modeling approximations and can also be computationally demanding. In this work, we propose a new MAP estimation strategy for solving inverse problems with a pre-trained unconditional diffusion model. Specifically, we introduce the variational mode-seeking loss (VML) and show that its minimization at each reverse diffusion step guides the generated sample towards the MAP estimate (modes in practice). VML arises from a novel perspective of minimizing the Kullback-Leibler (KL) divergence between the diffusion posterior $p(\mathbf{x}_0|\mathbf{x}_t)$ and the measurement posterior $p(\mathbf{x}_0|\mathbf{y})$, where $\mathbf{y}$ denotes the measurement. Importantly, for linear inverse problems, VML can be analytically derived without any modeling approximations. Based on further theoretical insights, we propose VML-MAP, an empirically effective algorithm for solving inverse problems via VML minimization, and validate its efficacy in both performance and computational time through extensive experiments on diverse image-restoration tasks across multiple datasets.
Oliver Welin Odeback, Arivazhagan Geetha Balasubramanian, Jonas Schollenberger et al.
4D Flow Magnetic Resonance Imaging (4D Flow MRI) enables non-invasive quantification of blood flow and hemodynamic parameters. However, its clinical application is limited by low spatial resolution and noise, particularly affecting near-wall velocity measurements. Machine learning-based super-resolution has shown promise in addressing these limitations, but challenges remain, not least in recovering near-wall velocities. Generative adversarial networks (GANs) offer a compelling solution, having demonstrated strong capabilities in restoring sharp boundaries in non-medical super-resolution tasks. Yet, their application in 4D Flow MRI remains unexplored, with implementation challenged by known issues such as training instability and non-convergence. In this study, we investigate GAN-based super-resolution in 4D Flow MRI. Training and validation were conducted using patient-specific cerebrovascular in-silico models, converted into synthetic images via an MR-true reconstruction pipeline. A dedicated GAN architecture was implemented and evaluated across three adversarial loss functions: Vanilla, Relativistic, and Wasserstein. Our results demonstrate that the proposed GAN improved near-wall velocity recovery compared to a non-adversarial reference (vNRMSE: 6.9% vs. 9.6%); however, that implementation specifics are critical for stable network training. While Vanilla and Relativistic GANs proved unstable compared to generator-only training (vNRMSE: 8.1% and 7.8% vs. 7.2%), a Wasserstein GAN demonstrated optimal stability and incremental improvement (vNRMSE: 6.9% vs. 7.2%). The Wasserstein GAN further outperformed the generator-only baseline at low SNR (vNRMSE: 8.7% vs. 10.7%). These findings highlight the potential of GAN-based super-resolution in enhancing 4D Flow MRI, particularly in challenging cerebrovascular regions, while emphasizing the need for careful selection of adversarial strategies.
Arnau Igualde Sáez, Lamyae Rhomrasi, Yusef Ahsini et al.
Multimodal Large Language Models (MLLMs) promise advanced vision language capabilities, yet their effectiveness in visually presented mathematics remains underexplored. This paper analyzes the development and evaluation of MLLMs for mathematical problem solving, focusing on diagrams, multilingual text, and symbolic notation. We then assess several models, including GPT 4o, Pixtral, Qwen VL, Llama 3.2 Vision variants, and Gemini 2.0 Flash in a multilingual Kangaroo style benchmark spanning English, French, Spanish, and Catalan. Our experiments reveal four key findings. First, overall precision remains moderate across geometry, visual algebra, logic, patterns, and combinatorics: no single model excels in every topic. Second, while most models see improved accuracy with questions that do not have images, the gain is often limited; performance for some remains nearly unchanged without visual input, indicating underutilization of diagrammatic information. Third, substantial variation exists across languages and difficulty levels: models frequently handle easier items but struggle with advanced geometry and combinatorial reasoning. Notably, Gemini 2.0 Flash achieves the highest precision on image based tasks, followed by Qwen VL 2.5 72B and GPT 4o, though none approach human level performance. Fourth, a complementary analysis aimed at distinguishing whether models reason or simply recite reveals that Gemini and GPT 4o stand out for their structured reasoning and consistent accuracy. In contrast, Pixtral and Llama exhibit less consistent reasoning, often defaulting to heuristics or randomness when unable to align their outputs with the given answer options.
Jonah Ekelund, Ricardo Vinuesa, Yuri Khotyaintsev et al.
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.
Pol Suárez, Francisco Alcántara-Ávila, Arnau Miró et al.
This paper presents for the first time successful results of active flow control with multiple independently controlled zero-net-mass-flux synthetic jets. The jets are placed on a three-dimensional cylinder along its span with the aim of reducing the drag coefficient. The method is based on a deep-reinforcement-learning framework that couples a computational-fluid-dynamics solver with an agent using the proximal-policy-optimization algorithm. We implement a multi-agent reinforcement-learning framework which offers numerous advantages: it exploits local invariants, makes the control adaptable to different geometries, facilitates transfer learning and cross-application of agents and results in significant training speedup. In this contribution we report significant drag reduction after applying the DRL-based control in three different configurations of the problem.
Gustau Camps-Valls, Andreas Gerhardus, Urmi Ninad et al.
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.
The sustainability of urban environments is an increasingly relevant problem. Air pollution plays a key role in the degradation of the environment as well as the health of the citizens exposed to it. In this chapter we provide a review of the methods available to model air pollution, focusing on the application of machine-learning methods. In fact, machine-learning methods have proved to importantly increase the accuracy of traditional air-pollution approaches while limiting the development cost of the models. Machine-learning tools have opened new approaches to study air pollution, such as flow-dynamics modelling or remote-sensing methodologies.
Machine learning is rapidly becoming a core technology for scientific computing, with numerous opportunities to advance the field of computational fluid dynamics. In this Perspective, we highlight some of the areas of highest potential impact, including to accelerate direct numerical simulations, to improve turbulence closure modeling, and to develop enhanced reduced-order models. We also discuss emerging areas of machine learning that are promising for computational fluid dynamics, as well as some potential limitations that should be taken into account.
We use Gaussian stochastic weight averaging (SWAG) to assess the model-form uncertainty associated with neural-network-based function approximation relevant to fluid flows. SWAG approximates a posterior Gaussian distribution of each weight, given training data, and a constant learning rate. Having access to this distribution, it is able to create multiple models with various combinations of sampled weights, which can be used to obtain ensemble predictions. The average of such an ensemble can be regarded as the `mean estimation', whereas its standard deviation can be used to construct `confidence intervals', which enable us to perform uncertainty quantification (UQ) with regard to the training process of neural networks. We utilize representative neural-network-based function approximation tasks for the following cases: (i) a two-dimensional circular-cylinder wake; (ii) the DayMET dataset (maximum daily temperature in North America); (iii) a three-dimensional square-cylinder wake; and (iv) urban flow, to assess the generalizability of the present idea for a wide range of complex datasets. SWAG-based UQ can be applied regardless of the network architecture, and therefore, we demonstrate the applicability of the method for two types of neural networks: (i) global field reconstruction from sparse sensors by combining convolutional neural network (CNN) and multi-layer perceptron (MLP); and (ii) far-field state estimation from sectional data with two-dimensional CNN. We find that SWAG can obtain physically-interpretable confidence-interval estimates from the perspective of model-form uncertainty. This capability supports its use for a wide range of problems in science and engineering.
Hamidreza Eivazi, Soledad Le Clainche, Sergio Hoyas et al.
We propose a deep probabilistic-neural-network architecture for learning a minimal and near-orthogonal set of non-linear modes from high-fidelity turbulent-flow-field data useful for flow analysis, reduced-order modeling, and flow control. Our approach is based on $β$-variational autoencoders ($β$-VAEs) and convolutional neural networks (CNNs), which allow us to extract non-linear modes from multi-scale turbulent flows while encouraging the learning of independent latent variables and penalizing the size of the latent vector. Moreover, we introduce an algorithm for ordering VAE-based modes with respect to their contribution to the reconstruction. We apply this method for non-linear mode decomposition of the turbulent flow through a simplified urban environment, where the flow-field data is obtained based on well-resolved large-eddy simulations (LESs). We demonstrate that by constraining the shape of the latent space, it is possible to motivate the orthogonality and extract a set of parsimonious modes sufficient for high-quality reconstruction. Our results show the excellent performance of the method in the reconstruction against linear-theory-based decompositions. Moreover, we compare our method with available AE-based models. We show the ability of our approach in the extraction of near-orthogonal modes that may lead to interpretability.
We discuss our insights into interpretable artificial-intelligence (AI) models, and how they are essential in the context of developing ethical AI systems, as well as data-driven solutions compliant with the Sustainable Development Goals (SDGs). We highlight the potential of extracting truly-interpretable models from deep-learning methods, for instance via symbolic models obtained through inductive biases, to ensure a sustainable development of AI.
Hamidreza Eivazi, Mojtaba Tahani, Philipp Schlatter et al.
Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations (PDEs). We employ PINNs for solving the Reynolds-averaged Navier$\unicode{x2013}$Stokes (RANS) equations for incompressible turbulent flows without any specific model or assumption for turbulence, and by taking only the data on the domain boundaries. We first show the applicability of PINNs for solving the Navier$\unicode{x2013}$Stokes equations for laminar flows by solving the Falkner$\unicode{x2013}$Skan boundary layer. We then apply PINNs for the simulation of four turbulent-flow cases, i.e., zero-pressure-gradient boundary layer, adverse-pressure-gradient boundary layer, and turbulent flows over a NACA4412 airfoil and the periodic hill. Our results show the excellent applicability of PINNs for laminar flows with strong pressure gradients, where predictions with less than 1% error can be obtained. For turbulent flows, we also obtain very good accuracy on simulation results even for the Reynolds-stress components.
A. G. Balasubramanian, L. Guastoni, A. Güemes et al.
Modelling the near-wall region of wall-bounded turbulent flows is a widespread practice to reduce the computational cost of large-eddy simulations (LESs) at high Reynolds number. As a first step towards a data-driven wall-model, a neural-network-based approach to predict the near-wall behaviour in a turbulent open channel flow is investigated. The fully-convolutional network (FCN) proposed by Guastoni et al. [preprint, arXiv:2006.12483] is trained to predict the two-dimensional velocity-fluctuation fields at $y^{+}_{\rm target}$, using the sampled fluctuations in wall-parallel planes located farther from the wall, at $y^{+}_{\rm input}$. The data for training and testing is obtained from a direct numerical simulation (DNS) at friction Reynolds numbers $Re_τ = 180$ and $550$. The turbulent velocity-fluctuation fields are sampled at various wall-normal locations, i.e. $y^{+} = \{15, 30, 50, 80, 100, 120, 150\}$. At $Re_τ=550$, the FCN 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 less than 20% error in prediction of streamwise-fluctuations intensity. These results are an encouraging starting point to develop a neural-network based approach for modelling turbulence at the wall in numerical simulations.
Urban areas are not only one of the biggest contributors to climate change, but also they are one of the most vulnerable areas with high populations who would together experience the negative impacts. In this paper, we address some of the opportunities brought by satellite remote sensing imaging and artificial intelligence (AI) in order to measure climate adaptation of cities automatically. We propose a framework combining AI and simulation which may be useful for extracting indicators from remote-sensing images and may help with predictive estimation of future states of these climate-adaptation-related indicators. When such models become more robust and used in real life applications, they may help decision makers and early responders to choose the best actions to sustain the well-being of society, natural resources and biodiversity. We underline that this is an open field and an on-going area of research for many scientists, therefore we offer an in-depth discussion on the challenges and limitations of data-driven methods and the predictive estimation models in general.
The digital revolution has brought ethical crossroads of technology, behavior and truth. However, the need of a comprehensive and constructive ethical framework is emerging as digital platforms have been used to build a global chaotic and truth-agnostic system. The unequal structure of the global system leads to dynamic changes and systemic problems, which have a more significant impact on those that are most vulnerable. Ethical frameworks based only on the individual level are no longer sufficient as they lack the necessary articulation to provide solutions to the new challenges. A new ethical vision must comprise the understanding of the scales and complex interconnections, as well as the causal chains of modern social systems. Many of these systems are internally fragile and very sensitive to external factors and threats, which lead to unethical situations that require systemic solutions still centered on individuals. Furthermore, the multi-layered net-like social tissue generates clusters of power that prevent certain communities from proper development. Digital technology has also impacted at the individual level posing the risk of a more homogeneous, predictable and ultimately controllable humankind. To preserve the core of humanity and the aspiration of common truth, a new ethical framework must empower individuals and uniqueness, as well as cultural heterogeneity, tackling the negative outcomes of digitalization. Only combining human-centered and collectiveness-oriented digital development will it be possible to construct new social models and interactions that are ethical. This vision requires science to enhance ethical frameworks and principles using computational tools to support truth-grounded actions, so as to transform and configure properties of the social systems.
Two models based on convolutional neural networks are trained to predict the two-dimensional velocity-fluctuation fields at different wall-normal locations in a turbulent open channel flow, using the wall-shear-stress components and the wall pressure as inputs. The first model is a fully-convolutional neural network (FCN) which directly predicts the fluctuations, while the second one reconstructs the flow fields using a linear combination of orthonormal basis functions, obtained through proper orthogonal decomposition (POD), hence named FCN-POD. Both models are trained using data from two direct numerical simulations (DNS) at friction Reynolds numbers $Re_τ = 180$ and $550$. Thanks to their ability to predict the nonlinear interactions in the flow, both models show a better prediction performance than the extended proper orthogonal decomposition (EPOD), which establishes a linear relation between input and output fields. The performance of the various models is compared based on predictions of the instantaneous fluctuation fields, turbulence statistics and power-spectral densities. The FCN exhibits the best predictions closer to the wall, whereas the FCN-POD model provides better predictions at larger wall-normal distances. We also assessed the feasibility of performing transfer learning for the FCN model, using the weights from $Re_τ=180$ to initialize those of the $Re_τ=550$ case. Our results indicate that it is possible to obtain a performance similar to that of the reference model up to $y^{+}=50$, with $50\%$ and $25\%$ of the original training data. These non-intrusive sensing models will play an important role in applications related to closed-loop control of wall-bounded turbulence.
Ricardo Vinuesa, Andreas Theodorou, Manuela Battaglini et al.
In their efforts to tackle the COVID-19 crisis, decision makers are considering the development and use of smartphone applications for contact tracing. Even though these applications differ in technology and methods, there is an increasing concern about their implications for privacy and human rights. Here we propose a framework to evaluate their suitability in terms of impact on the users, employed technology and governance methods. We illustrate its usage with three applications, and with the European Data Protection Board (EDPB) guidelines, highlighting their limitations.
Hamidreza Eivazi, Luca Guastoni, Philipp Schlatter et al.
The capabilities of recurrent neural networks and Koopman-based frameworks are assessed in the prediction of temporal dynamics of the low-order model of near-wall turbulence by Moehlis et al. (New J. Phys. 6, 56, 2004). Our results show that it is possible to obtain excellent reproductions of the long-term statistics and the dynamic behavior of the chaotic system with properly trained long-short-term memory (LSTM) networks, leading to relative errors in the mean and the fluctuations below $1\%$. Besides, a newly developed Koopman-based framework, called Koopman with nonlinear forcing (KNF), leads to the same level of accuracy in the statistics at a significantly lower computational expense. Furthermore, the KNF framework outperforms the LSTM network when it comes to short-term predictions. We also observe that using a loss function based only on the instantaneous predictions of the chaotic system can lead to suboptimal reproductions in terms of long-term statistics. Thus, we propose a model-selection criterion based on the computed statistics which allows to achieve excellent statistical reconstruction even on small datasets, with minimal loss of accuracy in the instantaneous predictions.
Luca Guastoni, Prem A. Srinivasan, Hossein Azizpour et al.
In this paper, the prediction capabilities of recurrent neural networks are assessed in the low-order model of near-wall turbulence by Moehlis {\it et al.} (New J. Phys. {\bf 6}, 56, 2004). Our results show that it is possible to obtain excellent predictions of the turbulence statistics and the dynamic behavior of the flow with properly trained long short-term memory (LSTM) networks, leading to relative errors in the mean and the fluctuations below $1\%$. We also observe that using a loss function based only on the instantaneous predictions of the flow may not lead to the best predictions in terms of turbulence statistics, and it is necessary to define a stopping criterion based on the computed statistics. Furthermore, more sophisticated loss functions, including not only the instantaneous predictions but also the averaged behavior of the flow, may lead to much faster neural network training.
Ricardo Vinuesa, Hossein Azizpour, Iolanda Leite et al.
The emergence of artificial intelligence (AI) and its progressively wider impact on many sectors across the society requires an assessment of its effect on sustainable development. Here we analyze published evidence of positive or negative impacts of AI on the achievement of each of the 17 goals and 169 targets of the 2030 Agenda for Sustainable Development. We find that AI can support the achievement of 128 targets across all SDGs, but it may also inhibit 58 targets. Notably, AI enables new technologies that improve efficiency and productivity, but it may also lead to increased inequalities among and within countries, thus hindering the achievement of the 2030 Agenda. The fast development of AI needs to be supported by appropriate policy and regulation. Otherwise, it would lead to gaps in transparency, accountability, safety and ethical standards of AI-based technology, which could be detrimental towards the development and sustainable use of AI. Finally, there is a lack of research assessing the medium- and long-term impacts of AI. It is therefore essential to reinforce the global debate regarding the use of AI and to develop the necessary regulatory insight and oversight for AI-based technologies.