Papers
Machine learning for physics, as it is published.
New work from arXiv on CFD surrogates, neural operators and physics-informed learning, refreshed every hour. Search it, filter by topic, or start with the papers we keep coming back to.
Papers
New work from arXiv on CFD surrogates, neural operators and physics-informed learning, refreshed every hour. Search it, filter by topic, or start with the papers we keep coming back to.
564 papers in Turbulence · newest first
math.NA
This study presents a hybrid reduced-order modeling (ROM) framework for incompressible flows on collocated finite-volume grids, combining a discretize-then-project consistent-flux formulation for velocity and pressure with a non-intrusive neural-network closure for turbulent viscosity. The intrusive formulation preserves discrete mass conservation and pressure-velocity coupling, while a reduced pressure reference-cell constraint fixes pressure gauge ambiguity. We evaluate Multilayer Perceptron (MLP), Transformer, and Long Short-Term Memory (LSTM) closures. For a three-dimensional lid-driven cavity at , the LSTM-based ROM achieves relative errors of 0.7% in velocity and 4% in turbulent viscosity. At , a mode-sensitivity study identifies POD modes as the best overall configuration, balancing accuracy, dimension, robustness, and cost. It yields a final relative velocity error of approximately 12.3% and an online wall-clock speedup of approximately over the full-order model; energy and enstrophy errors remain below 11% for all three architectures. This regime requires case-specific neural-network retraining and pressure reference-cell parameter retuning. In a time-extrapolation test trained on ,s and rolled out to ,s, the ROM remains bounded, although velocity and pressure errors increase beyond the training window. The LSTM turbulent-viscosity closure remains robust, identifying long-horizon pressure accuracy as the main limitation. These results demonstrate the potential of consistent projection-based modeling combined with data-driven turbulence closure for efficient reduced-order simulation.
physics.flu-dyn
This short note proposes a model-driven conditional Fourier neural operator (MD-CFNO) for synthetic turbulence generation. Spectrum-consistent synthetic turbulence is essential for inflow boundary construction in computational fluid dynamics and for broadband aeroacoustic noise prediction. Data-driven turbulence synthesis with neural networks has emerged as a promising direction. However, generating flow fields that match prescribed energy spectra across wide physical regimes remains challenging. Existing data-driven methods typically rely on expensive reliable datasets with limited generalization and are prone to regression-to-the-mean when trained in the spatial domain. To address these issues, the MD-CFNO is proposed with three components: a model-driven data construction strategy is adopted to improve interpretability and broaden the generalizable parameter regime; conditional stochastic generation is integrated into the Fourier neural operator architecture to alleviate regression-to-the-mean effects; and a composite loss is introduced to accelerate convergence and enhance spectral fidelity. Results show that the proposed MD-CFNO generates spectrum-consistent synthetic turbulence and achieves robust performance under both interpolation and out-of-distribution extrapolation conditions. This study provides a model-driven perspective on synthetic turbulence, showing the advantages of Fourier neural operators for conditional generation.
physics.flu-dyn
Solid aggregates in turbulent suspensions may break under the action of shear stresses. We explore the use of Graph Neural Networks (GNN) to infer aggregate fragmentation once the aggregate structure and flow velocity gradients are known. We consider two models: the first GNN is a classifier, trained to distinguish aggregates that break from those that do not; the second GNN is a regression model, trained to predict the maximal tensile force within each aggregate in a given flow condition. We show that both models complete their task with a high statistical accuracy, also generalizing to aggregates of different sizes, and generally performing better than the statistical prediction based on mean field quantities. This work paves the way for future use of GNN to quantify aggregate breakup in a large population of aggregates suspended in complex flow configurations, as it takes place in the wet production of fine powders and in the transport of sediments in environmental flows.
physics.flu-dyn
Physics-informed neural networks (PINNs) have recently emerged as a promising alternative for extracting unknown quantities from experimental data. Despite this potential, much of the recent literature has relied on sparse, high-fidelity data from direct numerical simulations (DNS) rather than experimental sources like particle image velocimetry (PIV), which are not suitable for validating all reconstructed quantities. In the case of PIV, for example, pressure is not directly measured and the data have imperfections such as noise contamination or a limited field of view. To overcome these limitations, we present a novel methodology where PINNs are first trained on a RANS simulation such that it learns all states at every location in the domain. We then apply transfer learning which updates the PINN using sub-sampled PIV data. The resulting predictions are in significantly better agreement with the full PIV dataset than PINNs which are trained on experimental data only. This work builds on the recent literature by integrating a Spalart-Allmaras turbulence model and applying hard constraints to the no-slip wall boundary condition. We apply this new methodology to a two-dimensional NACA 0012 airfoil inclined at an angle of attack, = 15 degrees, for two Reynolds numbers of Re = 10,000 and 75,000. The proposed methodology is initially validated using large eddy simulation (LES) data and then demonstrated on experimental PIV data. Our transfer learning approach results in improved predictions and a reduction in training time when compared to using a random network initialisation.
physics.comp-ph
Complex dynamical systems frequently encounter a recurrent structural instability: the collapse of the spectral gap, driving the system toward a low-dimensional "Zero-Mode Attractor" (e.g., spectral pile-up or over-smoothing). Building upon recent global well-posedness estimates [Hou, arXiv:2601.00638], this work generalizes the Multi-Scale Negative Coupled Information System (MNCIS) framework. We postulate that global stability requires an active topological operator - Adaptive Spectral Negative Coupling (ASNC) - functioning as a state-dependent high-pass filter that penalizes entropy accumulation at spectral boundaries. We validate this unified framework via three implementations: (1) Hydrodynamics: In 3D Navier-Stokes turbulence (), ASNC acts as a global-enstrophy adaptive sub-grid scale (SGS) model, stabilizing the inviscid limit and preserving the Kolmogorov inertial range without artificial hyper-viscosity. Crucially, we verify that the operator remains dormant () during the linear growth phase of physical instabilities, functioning strictly as a conditional topological clamp. (2) Artificial Intelligence: Addressing Over-smoothing in Graph Neural Networks (GNNs), we implement ASNC as a parameter-free topological constraint. Unlike baselines (e.g., DeepGCNs) relying on dense residual connections, our framework enables the training of ultra-deep 64-layer networks without residual connections, maintaining perfectly stationary feature variance () on the ogbn-arxiv benchmark. (3) Biological Physics: In reaction-diffusion morphogenesis, it stabilizes Turing patterns against diffusive washout in high-entropy regimes. Our results suggest that the MNCIS framework provides a base-independent topological condition for distinguishing viable complex systems from those collapsing into thermal equilibrium.
physics.flu-dyn
The spatiotemporal evolution of pulsating turbulent pipe flow was predicted by deep learning. A convolutional neural network (CNN) and long short-term memory (LSTM) were employed for long-term prediction by recursively predicting the local temporal evolution. To enhance prediction, physical components such as wall shear stress were informed into the training process. The datasets were obtained from direct numerical simulation (DNS). The model was trained exclusively on a limited set of sinusoidal pulsating flows driven by pressure gradients defined by their period and amplitude. Subsequently, 36 pulsating flows with arbitrary non-sinusoidal acceleration and deceleration were predicted to evaluate the generalization capability, defined as the predictive performance on unseen data during training. The model successfully predicted drag reduction rates ranging from to , with a mean absolute error of 9.2. This predictive performance for unseen pulsations indicates that local temporal prediction plays a central role, rather than learning the global profile of the pulsating waveforms. This implication was quantitatively verified by analyzing the differences in periodic – trajectories between the training and test datasets, demonstrating that flows exhibiting local similarity to the training data are more predictable. Furthermore, it was demonstrated that flows exhibiting intermittent laminar–turbulent transition and relaminarization become predictable when such regimes are incorporated into the training data. The results indicate that accurate prediction is achievable provided that the training data sufficiently cover the local flow-state space, highlighting the importance of appropriate training data selection for generalized flow prediction.
physics.optics
Atmospheric turbulence imposes a fundamental limitation across a broad range of applications, including optical imaging, remote sensing, and free-space optical communication. Recent advances in adaptive optics, wavefront shaping, and machine learning, driven by synergistic progress in fundamental theories, optoelectronic hardware, and computational algorithms, have demonstrated substantial potential in mitigating turbulence-induced distortions. Recently, active convolved illumination (ACI) was proposed as a versatile and physics-driven technique for transmitting structured light beams with minimal distortion through highly challenging turbulent regimes. While distinct in its formulation, ACI shares conceptual similarities with other physics-driven distortion correction approaches and stands to benefit from complementary integration with data-driven deep learning (DL) models. Inspired by recent work coupling deep learning with traditional turbulence mitigation strategies, the present work investigates the feasibility of integrating ACI with neural network-based methods. We outline a conceptual framework for coupling ACI with data-driven models and identify conditions under which learned representations can meaningfully support ACI's correlation-injection mechanism. As a representative example, we employ a convolutional neural network (CNN) together with a transfer-learning approach to examine how a learned model may operate in tandem with ACI. This exploratory study demonstrates feasible implementation pathways and establishes an early foundation for assessing the potential of future ACI-DL hybrid architectures, representing a step toward evaluating broader synergistic interactions between ACI and modern DL models.
physics.flu-dyn
This work proposes a data-driven explicit algebraic stress-based detached-eddy simulation (DES) method. Despite the widespread use of data-driven methods in model development for both Reynolds-averaged Navier-Stokes (RANS) and large-eddy simulations (LES), their applications to DES remain limited. The challenge mainly lies in the absence of modelled stress data, the requirement for proper length scales in RANS and LES branches, and the maintenance of a reasonable switching behaviour. The data-driven DES method is constructed based on the algebraic stress equation. The control of RANS/LES switching is achieved through the eddy viscosity in the linear part of the modelled stress, under the DES framework. Three model coefficients associated with the pressure-strain terms and the LES length scale are represented by a neural network as functions of scalar invariants of velocity gradient. The neural network is trained using velocity data with the ensemble Kalman method, thereby circumventing the requirement for modelled stress data. Moreover, the baseline coefficient values are incorporated as additional reference data to ensure reasonable switching behaviour. The proposed approach is evaluated on two challenging turbulent flows, i.e., the secondary flow in a square duct and the separated flow over a bump. The trained model achieves significant improvements in predicting mean flow statistics compared to the baseline model. This is attributed to improved predictions of the modelled stress. The trained model also exhibits reasonable switching behaviour, enlarging the LES region to resolve more turbulent structures. Furthermore, the model shows satisfactory generalization capabilities for both cases in similar flow configurations.
physics.flu-dyn
Computational fluid dynamics (CFD) has become a cornerstone of modern water engineering, providing quantitative tools for the analysis, prediction, and management of complex hydraulic systems across a wide range of spatial and temporal scales. This survey reviews the mathematical models and numerical methods that underpin CFD applications in water engineering, from depth-averaged formulations such as the shallow water equations to fully three-dimensional Navier-Stokes models, as well as selected alternative modeling approaches. We examine the historical development of these models, their mathematical structure, and the numerical discretization and solution strategies commonly employed in practice, including finite difference, finite volume, and finite element methods. Beyond core solver technology, the survey addresses practical modeling issues such as source-term treatment, wetting and drying, turbulence modeling, free-surface representation, and computational efficiency. The growing role of data integration is also discussed, encompassing data assimilation, uncertainty quantification, and emerging machine-learning-assisted approaches that complement physics-based solvers. To illustrate the impact of modeling and numerical choices on real-world applications, representative case studies from large-scale water management systems are reviewed. By integrating theory, numerical techniques, and applied perspectives, this survey provides a unified reference for researchers and practitioners seeking to understand both the foundational principles and contemporary challenges of CFD in water engineering.
physics.flu-dyn
Accurately autoregressive prediction of three-dimensional (3D) turbulence has been one of the most challenging problems for machine learning approaches. Diffusion models have demonstrated high accuracy in predicting two-dimensional (2D) turbulence, but their applications in 3D turbulence are relatively limited. To achieve reliable autoregressive predictions of 3D turbulence, we propose the DiAFNO model which integrates the implicit adaptive Fourier neural operator (IAFNO) with diffusion model. IAFNO can effectively capture the global frequency and structural features, which is crucial for global consistent reconstructions of the denoising process in diffusion models. Furthermore, based on conditional generation from diffusion models, we design an autoregressive framework in DiAFNO to achieve long-term stable predictions of 3D turbulence. The proposed DiAFNO model is systematically trained and tested separately with fixed hyperparameters in several types of 3D turbulence, including forced homogeneous isotropic turbulence (HIT) at Taylor Reynolds number 100, decaying HIT at initial Taylor Reynolds number at 100 and turbulent channel flow at friction Reynolds numbers 395 and 590 with case-specific training at each Reynolds number. The results in the \textit{a posteriori} tests demonstrate that DiAFNO exhibits a significantly higher prediction accuracy in most of the analyzed statistics (such as the velocity spectra, the root-mean-square (RMS) values of both velocity and vorticity, and Reynolds stresses), as compared to the elucidated diffusion model (EDM) and the traditional large-eddy simulation (LES) using dynamic Smagorinsky model (DSM). Although DiAFNO is not optimal in certain statistics, its overall performance is substantially better than all baseline models (EDM and DSM). Ignoring training costs, the well-trained DiAFNO achieves higher inference efficiency than EDM and LES with DSM.
cs.LG
Air turbulence refers to the disordered and irregular motion state generated by drastic changes in velocity, pressure, or direction during airflow. Various complex factors lead to intricate low-altitude turbulence outcomes. Under current observational conditions, especially when using only wind profile radar data, traditional methods struggle to accurately predict turbulence states. Therefore, this paper introduces a NeuTucker decomposition model utilizing discretized data. Designed for continuous yet sparse three-dimensional wind field data, it constructs a low-rank Tucker decomposition model based on a Tucker neural network to capture the latent interactions within the three-dimensional wind field data. Therefore, two core ideas are proposed here: 1) Discretizing continuous input data to adapt to models like NeuTucF that require discrete data inputs. 2) Constructing a four-dimensional Tucker interaction tensor to represent all possible spatio-temporal interactions among different elevations and three-dimensional wind speeds. In estimating missing observations in real datasets, this discretized NeuTucF model demonstrates superior performance compared to various common regression models.
physics.flu-dyn
Accurately predicting turbulent flows remains a central challenge in fluid dynamics due to their high dimensionality and intrinsic nonlinearity. Recent developments in quantum algorithms and machine learning offer new opportunities for overcoming the computational barriers inherent in turbulence modeling. Here we present a new hybrid quantum-classical framework that enables faster-than-real-time turbulence prediction by integrating machine learning, quantum computation, and fluid dynamics modeling, in particular, the reduced-order modeling. The novel framework combines quantum proper orthogonal decomposition (QPOD) with a quantum-enhanced deep kernel learning (QDKL) approach. QPOD employs quantum circuits to perform efficient eigenvalue decomposition for low-rank flow reconstruction, while QDKL exploits quantum entanglement and nonlinear mappings to enhance kernel expressivity and dynamic prediction accuracy. The new method is demonstrated on three benchmark turbulent flows, our architecture achieves significantly improved predictive accuracy at reduced model ranks, with training speeds up to 10 times faster and parameter counts reduced by a factor of 1/N compared to classical counterparts, where N is the input dimensionality. Although constrained by current noisy intermediate-scale quantum (NISQ) hardware, our results demonstrate the potential of quantum machine learning to transform turbulence simulation and lay a solid foundation for scalable, real-time quantum fluid modeling in future quantum computers.
physics.flu-dyn
While many existing machine learning studies have focused on augmenting Reynolds averaged Navier Stokes (RANS) turbulence models for steady or time averaged unsteady flows, this paper takes a first step toward extending such augmentation to time resolved unsteady flows. An unsteady field inversion and machine learning (FIML) method is developed, in which a temporally evolving correction field (beta) is incorporated into the production term of a RANS turbulence model. The inverse problem is solved by optimizing the spatial temporal distribution of beta to minimize the regularized prediction errors. The resulting optimized beta field is then used to train a multi layer neural network that learns the time dependent relationship between local flow features and beta. The approach is demonstrated using the unsteady flow over a NACA0012 airfoil undergoing dynamic stall. Results show that the unsteady FIML model, trained using only the time series of drag data at a given pitch rate, can accurately reproduce the spatial temporal evolution of reference drag, lift, pitching moment, surface pressure, and velocity fields at both identical and different pitch rates. The unsteady FIML is integrated into the open source DAFoam framework, enabling a pathway toward developing accurate and generalizable RANS turbulence models for time resolved unsteady flows.
physics.flu-dyn
This study proposes a rotationally invariant data-driven subgrid-scale (SGS) model for large-eddy simulation (LES) of wall-bounded turbulent flows. Building upon the multiscale convolutional neural network subgrid-scale model, which outputs SGS stress tensors () as the baseline, the deep neural network (DNN) architecture is modified to satisfy the principle of material objectivity by removing the bias terms and batch normalization layers while incorporating a spatial transformer network (STN) algorithm. The model was trained on a turbulent channel flow at and evaluated using both non-rotated and rotated inputs. The results show that the model performs well in predicting and key turbulence statistics, including dissipation, backscatter, and SGS transport. These quantities reflect the ability of the model to reproduce the energy transfer between the resolved scale and SGS. Moreover, it effectively generalizes to unseen rotated inputs, accurately predicting despite the input configurations not being encountered during the training. These findings highlight that modifying the DNN architecture and integrating the STN-based algorithm improves the ability to recognize and correctly respond to rotated inputs. The proposed data-driven SGS model addresses the key limitations of common data-driven SGS approaches, particularly their sensitivity to rotated input conditions. It also marks an important advancement in data-driven SGS modeling for LES, particularly in flow configurations where rotational effects are non-negligible.
physics.flu-dyn
Machine learning approaches to subgrid-scale (SGS) modelling are now well established in atmospheric and oceanic applications. Among these, online end-to-end learning, where the differentiable solver participates in the training, has shown particular promise. Yet, existing studies are largely restricted to idealised periodic domains, with no mechanical boundaries, precluding them from addressing the dynamics of bounded rotating flows relevant to planetary interiors. Here we consider two-dimensional quasi-geostrophic turbulence in a rapidly rotating annular bounded domain. We examine three configurations varying the geometry of the container and the rotation rate. The system exhibit key features such as zonal jets, Rossby waves, and, in the spherical shell geometry, a slow quasi-periodic inward drift of the jets. The spectral properties of the zonal and non-zonal flow can be understood in the framework of zonostrophic turbulence theory. We develop a differentiable solver for this system, which allows us to train SGS models online, over a time span of one turnover time, using coarse-grained data from direct numerical simulations. In all cases, a SGS model trained on a single turnover time accurately reproduce global integrated diagnostics, energy spectra as well as long-term dynamical behaviours —such as jet migration— occurring on timescales which exceed the training window by one order of magnitude. The online-trained model further outperforms classical hyperdiffusivity and Leith closure schemes, for which reducing the radial resolution is impractical. The resulting speed-up paves the way to further investigations of long-term geophysical fluid processes beyond the reach of direct numerical simulations.
physics.flu-dyn
Data-driven techniques have improved the accuracy of Reynolds-averaged Navier-Stokes (RANS) models in fluid dynamics. However, modeling separated flows remains challenging due to their complex physics and sensitivity to local conditions. Existing approaches often struggle with generalization beyond training cases and lack robust uncertainty quantification frameworks, limiting their utility in complex flow regimes. We propose a Bayesian neural network (BNN)-based framework specifically designed for two-dimensional separated flows. By focusing on flow zones near separated regions, we ensure targeted training and enhance predictive reliability. The BNN framework incorporates physics-guided, invariant inputs to maintain consistency with turbulence physics. Correction terms predicted by the BNN are selectively applied to specific regions of the flow domain using a novel classifier, improving accuracy. A key feature of this approach is propagating BNN-derived corrections to flow solutions, enabling uncertainty quantification in unseen test cases. This probabilistic characterization of modeling errors offers insights into the reliability of RANS predictions across geometries with similar topologies. Preliminary results demonstrate that this method accurately predicts correction terms for Reynolds stress anisotropy and turbulent kinetic energy production in separated flow regions, effectively addressing dominant modeling errors and advancing turbulence modeling through uncertainty quantification.
physics.flu-dyn
l flows and flat-plate boundary layers. However, it predicts too low a turbulent kinetic energy. This is a feature it shares with most other two-equation turbulence models. When comparing the terms in the k equations with DNS data it is found that the production and dissipation terms are well predicted but the turbulent diffusion is not. In the present work the poor modeling of the turbulent diffusion is improved using Physics Informed Neural Network (PINN) and Neural Network (NN).The k equation is turned into an ordinary differential equation for the turbulent viscosity in the k equation, nu_{t,PINN}, which is solved using PINN. A new turbulent Prandtl number is then computed as sigma_{k} = nu_{t}/nu_{t,PINN} where nu_t = k/omega.To compensate for the new, larger turbulent kinetic energy, three coefficients in the new k-omega model are computed using three NN models. The new turbulence model, called the k-omega-PINN-NN model, is shown to produce excellent velocity, skin friction and turbulent kinetic profiles in channel flow at Re_tau = 2 000, 5 200 and Re_tau = 10 000 as well as in flat-plate boundary layer flow (slightly too large a k for the latter case). The k-omega-PINN-NN model is also used for predicting the flow over a periodic hill and the agreement with DNS is very good. At the end of the Conclusions, we give an example on how a NN model can be replaced with a Python symbolic regression (pySR); the latter may conveniently be imported in commercial CFD codes. All Python PINN, NN and pySR scripts as well as the Python CFD code can be downloaded (Davidson, 2025a).
eess.SY
This study presents a novel deep learning approach aimed at enhancing stochastic Gust Load Alleviation (GLA) specifically for compliant wings. The approach incorporates the concept of smooth wing camber variation, where the camber of the wing's chord is actively adjusted during flight using a control signal to achieve the desired aerodynamic loading. The proposed method employs a deep learning-based model predictive controller designed for probability density shaping. This controller effectively solves the probability density evolution equation through a custom Physics-Informed Neural Network (PINN) and utilizes Automatic Differentiation for Model Predictive Control (MPC) optimization. Comprehensive numerical simulations were conducted on a compliant wing (CW) model, evaluating performance of the proposed approach against stochastic gust profiles. The evaluation involved stochastic aerodynamic loads generated from Band-Limited White Noise (BLWN) and Dryden gust models. The evaluation were conducted for two distinct Compliant Chord Fractions (CCF). The results demonstrate the effectiveness of the proposed probability density shaping model predictive control in alleviating stochastic gust load and reducing wing tip deflection.
physics.flu-dyn
Accurate and generalizable Reynolds-averaged Navier-Stokes (RANS) models for turbulent flows rely on effective closures, but currently available closures are notoriously unreliable. Kassinos et al. (J. Fluid Mechanics, 428, pp. 213-248, 2001) hypothesized that this unreliability of RANS models was due to an insufficient description of the statistical state of the turbulence and proposed a set of structure tensors as a candidate for a sufficiently rich description. To test this hypothesis for the rapid pressure-strain term, we introduce tensor-based, symmetry aware closures in terms of the structure tensors using equivariant neural networks (ENNs), and present an algorithm for enforcing algebraic contraction relations among tensor components. Using data from rapid distortion theory, experiments show that such ENNs can effectively learn relationships involving high-order tensors. The resulting ENN structure tensor models are orders of magnitude more accurate than existing models for the rapid pressure-strain correlation, effectively validating the Kassinos et al. hypothesis for this term. Results show that ENNs provide a physically consistent alternative to classical tensor basis models, enabling end-to-end learning of unclosed terms in RANS and other tensor modeling domains, and rapid exploration of model dependencies.
physics.optics
The stability of optical vortex structures in turbulent environments is critical for their applications in optical communication, quantum information, and structured light technologies. Although topological invariants, such as crossings and linking numbers, are fundamentally invariant, recent studies reveal that their observed values deteriorate considerably in turbulent conditions due to environmental effects. In this study, we introduce an alternative approach based on the geometric stability of three-dimensional singularity line shapes, demonstrating that shape-based tracing of singularities outperforms both topological and spectral methods in turbulence. To test this concept, we propose Flower Beams, a novel class of structured optical fields featuring controllable petal-like singularity morphologies. We construct an 81-element optical alphabet and classify these structures after turbulence using deep learning. Our findings reveal that shape-based tracing achieves classification accuracy exceeding 90% in the weaker turbulence regimes and remains highly competitive even in stronger turbulence, significantly outperforming spectral and topology-based approaches. Experimental results confirm that the predicted shape stability holds in real-world conditions. This study stablishes the shape of the singularities' lines as a scalable and resilient alternative for structured light tracing and transmission, opening new avenues for turbulence-robust-applications.