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
physics.flu-dyn
When simulating multiscale systems, where some fields cannot be fully prescribed despite their effects on the simulation's accuracy, closure models are needed. This phenomenon is observed in turbulent fluid dynamics, where Large Eddy Simulations (LES) depict global behavior while turbulence modeling introduces dissipation correspondent to smaller sub-grid scales. Recently, scientific machine learning techniques have emerged to address this problem by integrating traditional (physics-based) equations with data-driven (machine-learned) models, typically coupling numerical solvers with neural networks. This work presents a comprehensive workflow, encompassing high-fidelity data generation and post-processing, a priori learning, and a posteriori testing, where data-driven models enrich differential equations.
cs.LG
Predicting the evolution of turbulent flows is central across science and engineering. Most studies rely on simulations with turbulence models, whose empirical simplifications introduce epistemic uncertainty. The Eigenspace Perturbation Method (EPM) is a widely used physics-based approach to quantify model-form uncertainty, but being purely physics-based it can overpredict uncertainty bounds. We propose a convolutional neural network (CNN)-based modulation of EPM perturbation magnitudes to improve calibration while preserving physical consistency. Across canonical cases, the hybrid ML-EPM framework yields substantially tighter, better-calibrated uncertainty estimates than baseline EPM alone.
physics.plasm-ph
Constructing reduced models for turbulent transport is essential for accelerating profile predictions and enabling many-query tasks such as parameter exploration and design optimization. This work investigates machine-learning-driven reduced models for Electron Temperature Gradient (ETG) turbulence in the Wendelstein 7-X (W7-X) stellarator. We develop physics-guided scaling laws to predict the ETG heat flux at seven radial locations as functions of three key plasma parameters: the normalized electron temperature gradient (), the ratio of normalized electron temperature and density gradients (), and the electron-to-ion temperature ratio (). The model coefficients are determined through regression combined with an active learning strategy. The procedure initializes the scaling laws using low-cardinality sparse-grid training data and iteratively enriches the training set by selecting maximally informative samples from an existing simulation database. The predictive performance of the models is assessed using out-of-sample datasets comprising more than points per radial location. Using the coefficients identified at the seven training radial locations, we further derive regression-based parameterizations for the scaling-law coefficients as functions of radial position. The resulting models are then evaluated at three additional radial locations not used during training, including both interpolation and moderate extrapolation cases. Overall, our reduced models demonstrate good predictive performance and achieve accuracy comparable to the original reference simulations, including in interpolation and moderate extrapolation regimes. An important finding is that a single radius-independent model cannot adequately describe ETG transport across the W7-X core, suggesting the presence of geometry-dependent physics not captured by the present formulation.
physics.flu-dyn
Fully resolving turbulent flows remains challenging due to turbulent systems' multiscale complexity. Existing data-driven approaches typically demand expensive retraining for each flow scenario and struggle to generalize beyond their training conditions. Leveraging the universality of small-scale turbulent motions (Kolmogorov's K41 theory), we propose a Scale-oriented Zonal Generative Adversarial Network (SoZoGAN) framework for high-fidelity, zero-shot turbulence generation across diverse domains. Unlike conventional methods, SoZoGAN is trained exclusively on a single dataset of moderate-Reynolds-number homogeneous isotropic turbulence (HIT). The framework employs a zonal decomposition strategy, partitioning turbulent snapshots into subdomains based on scale-sensitive physical quantities. Within each subdomain, turbulence is synthesized using scale-indexed models pre-trained solely on the HIT database. SoZoGAN demonstrates high accuracy, cross-domain generalizability, and robustness in zero-shot super-resolution of unsteady flows, as validated on untrained HIT, turbulent boundary layer, and channel flow. Its strong generalization, demonstrated for homogenous and inhomogenous turbulence cases, suggests potential applicability to a wider range of industrial and natural turbulent flows. The scale-oriented zonal framework is architecture-agnostic, readily extending beyond GANs to other deep learning models.
physics.flu-dyn
Fourier Neural Operators (FNOs) have demonstrated exceptional accuracy in mapping functional spaces by leveraging Fourier transforms to establish a connection with underlying physical principles. However, their opaque inner workings often constitute an obstacle to physical interpretability. This work introduces Hierarchical Fourier Neural Operators (HFNOs), a novel FNO-based architecture tailored for reduced-order modeling of turbulent fluid flows, designed to enhance interpretability by explicitly separating fluid behavior across scales. The proposed architecture processes wavenumber bins in parallel, enabling the approximation of dispersion relations and non-linear interactions. Inputs are lifted to a higher-dimensional space, Fourier-transformed, and partitioned into wavenumber bins. Each bin is processed by a Fully Connected Neural Network (FCNN), with outputs subsequently padded, summed, and inverse-transformed back into physical space. A final transformation refines the output in physical space as a correction model, by means of one of the following architectures: Convolutional Neural Network (CNN) and Echo State Network (ESN). We evaluate the proposed model on a series of increasingly complex dynamical systems: first on the one-dimensional Kuramoto-Sivashinsky equation, then on the two-dimensional Kolmogorov flow, and finally on the prediction of wall shear stress in turbulent channel flow, given the near-wall velocity field. In all test cases, the model demonstrates its ability to decompose turbulent flows across various scales, opening up the possibility of increased interpretability and multiscale modeling of such flows.
cs.LG
Computationally resolving turbulence remains a central challenge in fluid dynamics due to its multi-scale interactions. Fully resolving large-scale turbulence through direct numerical simulation (DNS) is computationally prohibitive, motivating data-driven machine learning alternatives. In this work, we propose EddyFormer, a Transformer-based spectral-element (SEM) architecture for large-scale turbulence simulation that combines the accuracy of spectral methods with the scalability of the attention mechanism. We introduce an SEM tokenization that decomposes the flow into grid-scale and subgrid-scale components, enabling capture of both local and global features. We create a new three-dimensional isotropic turbulence dataset and train EddyFormer to achieves DNS-level accuracy at 256^3 resolution, providing a 30x speedup over DNS. When applied to unseen domains up to 4x larger than in training, EddyFormer preserves accuracy on physics-invariant metrics-energy spectra, correlation functions, and structure functions-showing domain generalization. On The Well benchmark suite of diverse turbulent flows, EddyFormer resolves cases where prior ML models fail to converge, accurately reproducing complex dynamics across a wide range of physical conditions.
physics.flu-dyn
Variational data assimilation and machine-learning based super-resolution are two alternative approaches to state estimation in turbulent flows. The former is an optimisation problem featuring a time series of coarse observations, the latter usually requires a library of high-resolution 'ground truth' data. We show that the classic '4DVar' data assimilation algorithm can be used to train neural networks for super-resolution in three-dimensional isotropic turbulence without the need for high-resolution reference data. To do this, we adapt a pseudo-spectral version of the fully-differentiable JAX-CFD solver (Kochkov et al, Proc. Nat. Acad. Sci. 118, 2021) to three-dimensional flows and combine it with a convolutional neural network for super-resolution. As a result we are able to include entire trajectories in our loss function which is minimised with gradient-based optimisation to define the neural network weights. We show that the resulting neural networks outperform 4DVar for state estimation at initial time over a wide variety of metrics, though 4DVar leads to more robust predictions towards the end of its assimilation window. We also present a hybrid approach in which the trained neural network output is used to initialise 4DVar. The resulting performance is more than twice as accurate as other state estimation strategies for all times and performs well even beyond known limiting lengthscales, all without requiring access to high-resolution measurements at any point.
physics.flu-dyn
We train active neural-network flow controllers using a deep learning PDE augmentation method to optimize lift-to-drag ratios in turbulent airfoil flows at Reynolds number and Mach number 0.4. Direct numerical simulation and large eddy simulation are employed to model compressible, unconfined flow over two- and three-dimensional semi-infinite NACA 0012 airfoils at angles of attack , , and . Control actions, implemented through a blowing/suction jet at a fixed location and geometry on the upper surface, are adaptively determined by a neural network that maps local pressure measurements to optimal jet total pressure, enabling a sensor-informed control policy that responds spatially and temporally to unsteady flow conditions. The sensitivities of the flow to the neural network parameters are computed using the adjoint Navier-Stokes equations, which we construct using automatic differentiation applied to the flow solver. The trained flow controllers significantly improve the lift-to-drag ratios and reduce flow separation for both two- and three-dimensional airfoil flows, especially at and . The 2D-trained models remain effective when applied out-of-sample to 3D flows, which demonstrates the robustness of the adjoint-trained control approach. The 3D-trained models capture the flow dynamics even more effectively, which leads to better energy efficiency and comparable performance for both adaptive (neural network) and offline (simplified, constant-pressure) controllers. These results underscore the effectiveness of this learning-based approach in improving aerodynamic performance.
physics.ins-det
This paper presents a bio-inspired underwater whisker sensor for robust hydrodynamic disturbance detection and efficient signal analysis based on Physical Reservoir Computing (PRC). The design uses a tapered nylon spring with embedded accelerometers to achieve spatially distributed vibration sensing and frequency separation along the whisker. Towing-tank experiments and computational fluid dynamics simulations confirmed that the whisker effectively distinguishes vortex regimes across different fin angles and maintains Strouhal scaling with flow velocity, where higher speeds increase vibration intensity without affecting the dominant frequencies. Frequency-domain analysis, Shannon entropy, and machine learning further validated the sensing performance: vortex shedding frequencies were identified with less than 10% error, entropy captured the transition from coherent vortex streets to turbulence, and logistic regression achieved 86.0% classification accuracy with millisecond-level inference. These results demonstrate that structurally encoded whisker sensing provides a scalable and real-time solution for underwater perception, wake tracking, and turbulence-aware navigation in autonomous marine robots.
physics.flu-dyn
Near-surface turbulent flows beneath a free surface are reconstructed from sparse measurements of the surface height variation, by a neural network algorithm known as the SHallow REcurrent Decoder (SHRED). The reconstruction of turbulent flow fields from limited, partial, or indirect measurements remains a grand challenge in science and engineering. The central goal in such applications is to leverage easy-to-measure proxy variables in order to estimate quantities which have not been, and perhaps cannot in practice be, measured. In the application considered here, the aim is to use a sparse number of surface height point measurements of a flow field, or drone video footage of surface features, in order to infer the turbulent flow field beneath the surface. SHRED is a deep learning architecture that learns a delay-coordinate embedding from a few surface height (point) sensors and maps it, via a shallow decoder trained in a compressed basis, to full subsurface fields, enabling fast, robust training from minimal data. We demonstrate the SHRED sensing architecture on two types of turbulent data from recent studies [Aarnes et al. J. Fluid Mech. 1007, A38 (2025) and Babiker et al. Phys. Rev. Fluids 11, 054802 (2026), respectively]: fully resolved DNS data and PIV laboratory data from a turbulent water tank. SHRED is capable of robustly mapping surface height fluctuations to full-state flow fields up to about one integral length scale deep, with as few as three surface measurements.
physics.flu-dyn
Traditional Reynolds-averaged Navier-Stokes (RANS) closures, based on the Boussinesq eddy viscosity hypothesis and calibrated on canonical flows, often yield inaccurate predictions of both mean flow and turbulence statistics. Here, we consider flow past a circular cylinder over a range of Reynolds numbers (3,900-100,000) and Mach numbers (0-0.3), encompassing incompressible and weakly compressible regimes, with the goal of improving predictions of mean velocity and Reynolds forces. To this end, we assemble a cross-validated dataset comprising hydrodynamic particle image velocimetry (PIV) in a towing tank, aerodynamic PIV in a wind tunnel, and high-fidelity spectral element DNS and LES. Analysis of these data reveals a universal distribution of Reynolds stresses across the parameter space, which provides the foundation for a data-driven closure. We employ physics-informed neural networks (PINNs), trained with the unclosed RANS equations, to infer the velocity field and Reynolds-stress forcing from boundary information alone. The resulting closure, embedded in a forward PINN solver and the numerical solver OpenFOAM, significantly improves RANS predictions of both mean flow and turbulence statistics relative to conventional models.
physics.flu-dyn
We present a data-driven framework for turbulence modeling, applied to flow prediction in the FDA nozzle. In this study, the standard RANS equations have been modified using an implicit-explicit hybrid approach. New variables were introduced, and a solver was developed within the OpenFOAM framework, integrating a machine learning module to estimate these variables. The invariant input features were derived based on Hilbert's basis theorem, and the outputs of the machine learning model were obtained through eigenvalue-vector decomposition of the Reynolds stress tensor. Validation was performed using DNS data for turbulent flow in a square channel at various Reynolds numbers. A baseline MLP was first trained at and tested at to assess its ability to reproduce turbulence anisotropy and secondary flows. To further enhance generalization, three benchmark DNS datasets were transformed into images via the Deep-Insight method, enabling the use of convolutional neural networks. The trained Deep-Insight network demonstrated improved prediction of turbulence structures in the FDA blood nozzle, highlighting the promise of data-driven augmentation in turbulence modeling.
physics.flu-dyn
Turbulence governs the transport of momentum, energy, and scalars in many geophysical and engineering flows. In large-eddy simulations (LES), parameterizing subgrid-scale (SGS) stresses remains a central challenge, as unresolved physical processes strongly influence turbulent transport. Traditional SGS models, such as the Smagorinsky-type models and deep neural networks (DNNs), are deterministic and cannot capture the stochastic nature of turbulence. Despite its wide application in computer vision and natural language processing, generative artificial intelligence (AI) has not previously been applied to directly compute SGS stresses in three-dimensional turbulent boundary layers at high Reynolds numbers. Here we introduce a denoising diffusion probabilistic model (DDPM) to reconstruct SGS stresses from coarse-grained velocity fields in direct numerical simulations of the atmospheric boundary layer. The DDPM consistently outperforms Smagorinsky-type models and previous deep neural networks in terms of spatial correlations and probability distributions for deviatoric stresses, and can be applied to unseen convective stability conditions and resolutions. By learning conditional distributions rather than pointwise values, this generative approach opens a new direction for SGS turbulence modeling at high Reynolds numbers.
physics.plasm-ph
In this work, we introduce a non-local five-moment electron pressure tensor closure parametrized by a Fully Convolutional Neural Network (FCNN). Electron pressure plays an important role in generalized Ohm's law, competing with electron inertia. This model is used in the development of a surrogate model for a fully kinetic energy-conserving semi-implicit Particle-in-Cell simulation of decaying magnetosheath turbulence. We achieve this by training FCNN on a representative set of simulations with a smaller number of particles per cell and showing that our results generalise to a simulation with a large number of particles per cell. We evaluate the statistical properties of the learned equation of state, with a focus on pressure-strain interaction, which is crucial for understanding energy channels in turbulent plasmas. The resulting equation of state learned via FCNN significantly outperforms local closures, such as those learned by Multi-Layer Perceptron (MLP) or double adiabatic expressions. We report that the overall spatial distribution of pressure-strain and its conditional averages are reconstructed well. However, some small-scale features are missed, especially for the off-diagonal components of the pressure tensor. Nevertheless, the results are substantially improved with more training data, indicating favorable scaling and potential for improvement, which will be addressed in future work.
physics.flu-dyn
Developing reduced-order models applicable to fluid-dynamics problems involving complex geometries and different flow conditions remains a critical challenge for turbulent flows. This study introduces VIVALDy, a novel machine-learning framework that employs a hybrid -Variational Autoencoder-Generative Adversarial Network (-VAE-GAN) architecture with masked convolutions to extract dominant flow features into a compact latent space while preserving fidelity at solid-fluid interfaces. A bidirectional transformer then models the temporal evolution of these features, learning to predict flow trajectories from minimal sensor inputs. This two-stage approach enables the transformer to map sensor measurements to dominant flow variables identified by the autoencoder, advancing reduced-order modeling capabilities for real-time flow prediction. The effectiveness of the framework is demonstrated through application to a problem relevant to vortex-induced vibration (VIV) energy harvesting systems, reconstructing the turbulent flow around a one-degree-of-freedom moving cylinder. Validated against experimental data spanning fluid-structure interaction regimes of interest, VIVALDy accurately predicts different flow states using only the cylinder displacement. The framework demonstrates adequate performance in both reconstruction accuracy and statistical fidelity across diverse operating conditions, enabling efficient prediction of the turbulent flow phenomena governing vortex-induced vibration.
cs.LG
Accurately forecasting the long-term evolution of turbulence represents a grand challenge in scientific computing and is crucial for applications ranging from climate modeling to aerospace engineering. Existing deep learning methods, particularly neural operators, often fail in long-term autoregressive predictions, suffering from catastrophic error accumulation and a loss of physical fidelity. This failure stems from their inability to simultaneously capture the distinct mathematical structures that govern turbulent dynamics: local, dissipative effects and global, non-local interactions. In this paper, we propose the {\textbf{\underline{D}}}ifferential-{\textbf{\underline{I}}}ntegral {\textbf{\underline{N}}}eural {\textbf{\underline{O}}}perator (\method{}), a novel framework designed from a first-principles approach of operator decomposition. \method{} explicitly models the turbulent evolution through parallel branches that learn distinct physical operators: a local differential operator, realized by a constrained convolutional network that provably converges to a derivative, and a global integral operator, captured by a Transformer architecture that learns a data-driven global kernel. This physics-based decomposition endows \method{} with exceptional stability and robustness. Through extensive experiments on the challenging 2D Kolmogorov flow benchmark, we demonstrate that \method{} significantly outperforms state-of-the-art models in long-term forecasting. It successfully suppresses error accumulation over hundreds of timesteps, maintains high fidelity in both the vorticity fields and energy spectra, and establishes a new benchmark for physically consistent, long-range turbulence forecast.
physics.flu-dyn
The immense computational cost of simulating turbulence has motivated the use of machine learning approaches for super-resolving turbulent flows. A central challenge is ensuring that learned models respect physical symmetries, such as rotational equivariance. We show that standard convolutional neural networks (CNNs) can partially acquire this symmetry without explicit augmentation or specialized architectures, as turbulence itself provides implicit rotational augmentation in both time and space. Using 3D channel-flow subdomains with differing anisotropy, we find that models trained on more isotropic mid-plane data achieve lower equivariance error than those trained on boundary layer data, and that greater temporal or spatial sampling further reduces this error. We show a distinct scale-dependence of equivariance error that occurs regardless of dataset anisotropy that is consistent with Kolmogorov's local isotropy hypothesis. These results clarify when rotational symmetry must be explicitly incorporated into learning algorithms and when it can be obtained directly from turbulence, enabling more efficient and symmetry-aware super-resolution.
physics.flu-dyn
We studied the reconstruction of turbulent flow fields from trajectory data recorded by actively migrating Lagrangian agents. We propose a deep-learning model, track-to-flow (T2F), which employs a vision transformer as the encoder to capture the spatiotemporal features of a single agent trajectory, and a convolutional neural network as the decoder to reconstruct the flow field. To enhance the physical consistency of the T2F model, we further incorporate a physics-informed loss function inspired by the framework of physics-informed neural network (PINN), yielding a variant model referred to as T2F+PINN. We first evaluate both models in a laminar cylinder wake flow at a Reynolds number of as a proof of concept. The results show that the T2F model achieves velocity reconstruction accuracy comparable to that of existing flow reconstruction methods, while the T2F+PINN model reduces the normalised error in vorticity reconstruction relative to the T2F model. We then apply the models in a turbulent Rayleigh-Bénard convection at a Rayleigh number of and a Prandtl number of . The results show that the T2F model accurately reconstructs both the velocity and temperature fields, whereas the T2F+PINN model further improves the reconstruction accuracy of gradient-related physical quantities, such as temperature gradients, vorticity and the Q value, with a maximum improvement of approximately 60 % compared to the T2F model. Overall, the T2F model is better suited for reconstructing primitive flow variables, while the T2F+PINN model provides advantages in reconstructing gradient-related quantities. Our models open a promising avenue for accurate flow reconstruction from a single Lagrangian trajectory.
physics.flu-dyn
Solving the Reynolds-averaged Navier-Stokes equations (RANS) closed with an eddy viscosity computed through a turbulence model is still the leading approach for Computational Fluid Dynamics simulations. Unfortunately, universal models with good predictive capabilities over a wide range of flows are not available. In this work, we propose the use of machine learning to improve existing RANS models. The approach does not require high-fidelity training data. A convolutional neural network is used to identify and segment at runtime the flow field into different zones, each resembling one item of a predefined list of elementary flows. The turbulence model applied in each zone is taken from an equally predefined set of classic models, each specifically tuned to work best for one elementary flow, free from the requirement of universality. The idea is first presented in general terms, and then demonstrated via a preliminary implementation, where only three elementary flows are considered, and three turbulence models are used. Test cases show that, already in this oversimplified form, automated zonal modelling outperforms the baseline RANS models without computational overhead.
nlin.PS
Ventricular arrhythmias, like ventricular tachycardia (VT) and ventricular fibrillation (VF), precipitate sudden cardiac death (SCD), which is the leading cause of mortality in the industrialised world. Thus, the elimination of VT and VF is a problem of paramount importance, which is studied experimentally, theoretically, and numerically. Numerical studies use partial-differential-equation models, for cardiac tissue, which admit solutions with spiral- or broken-spiral-wave solutions that are the mathematical counterparts of VT and VF. In silico investigations of such mathematical models of cardiac tissue allow us not only to explore the properties of such spiral-wave turbulence, but also to develop mathematical analogues of low-amplitude defibrillation by the application of currents that can eliminate spiral waves. We develop an efficient deep-neural-network U-Net-based method for the control of spiral-wave turbulence in mathematical models of cardiac tissue. Specifically, we use the simple, two-variable Aliev-Panfilov and the ionically realistic TP06 mathematical models to show that the lower the correlation length ξ for spiral-turbulence patterns, the easier it is to eliminate them by the application of control currents on a mesh electrode. We then use spiral-turbulence patterns from the TP06 model to train a U-Net to predict the sodium current, which is most prominent along thin lines that track the propagating front of a spiral wave. We apply currents, in the vicinities of the predicted sodium-current lines to eliminate spiral waves efficiently. The amplitudes of these currents are adjusted automatically, so that they are small when ξ is large and vice versa. We show that our U-Net-aided elimination of spiral-wave turbulence is superior to earlier methods.