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
astro-ph.SR
Molecular clouds exhibit complex, multi-scale dynamics driven by the interplay of turbulence, self-gravity, and gas pressure. Modelling these systems with conventional grid-based methods becomes increasingly expensive as spatial resolution and dimensionality increase. Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative by incorporating the governing equations directly into the training objective, but their ability to model realistic turbulent self-gravitating flows remains largely unexplored. We apply PINNs to isothermal molecular clouds initialized with astrophysically motivated turbulent velocity fields, considering subsonic and supersonic evolution in two and three dimensions. We benchmark the predicted density and velocity fields against the finite-volume code Athena++. PINNs accurately recover the global evolution of the flow over multiple free-fall times across turbulent realizations, Mach numbers, and dimensionalities. Their training cost also exhibits weak dependence on spatial resolution, increasing by less than 25% from 128^3 to 1024^3 in our experiments. These results demonstrate that PINNs can model substantially more realistic self-gravitating turbulent flows than previously explored and provide a promising complementary framework for studying these systems.
physics.flu-dyn
The three-dimensional Navier-Stokes equations govern fluid turbulence, a chaotic and non-linear physical phenomenon characterized by complex eddies interacting across vast spatial and temporal scales. A numerically accurate modeling of this multi-scale energy cascade requires fully resolving both the fine spatial structures and the continuous temporal evolution of the flow field. In this paper, we leverage massive, time-resolved direct numerical simulations, which exceed 28 TB per run, to assess how numerical choices govern the resolved (3+1)-dimensional physics of turbulent flows. Building on this analysis, we study how neural networks represent the recorded turbulent motion. Our results highlight that spatial and temporal assessments can disagree for both numerical records and learned representations. We therefore call on the machine learning community to treat (3+1)-dimensional turbulence as a four-dimensional phenomenon.
physics.flu-dyn
This work presents the development and assessment of a hybrid framework coupling numerical simulation, experimental samples, data assimilation (DA) and machine learning (ML) to investigate the flow within an axial compressor stage. The methodology first implements a Multi-Fidelity Ensemble Kalman Filter (MFEnKF) which integrates experimental PIV data with a two-fidelity numerical simulation setup, combining steady-state RANS on a fixed grid with unsteady hybrid RANS/LES simulations on a moving grid. This data assimilation step successfully reduces discrepancies between experiments and CFD realizations. Besides, it provides additional high fidelity samples when compared with the available PIV data. This enriched database is used to train machine learning (ML) tools, with the objective to obtain black-box forcing terms to be included in the discretized form of the Navier-Stokes equations. These models are expected to preserve the accuracy of the DA results while not longer requiring the input of experimental data. The neural network architecture used here maps local physical features such as the velocity, the velocity gradients and the turbulent viscosity, to obtain the volume forcing terms. The analysis of the performance of such ML models shows that global accuracy is preserved but localized increased errors in specific regions of the compressor, such as close to the blade tips, can exceed those observed from the baseline RANS simulations. To resolve this issue, a Mixture of Experts (MoE) method is employed, which classifies and combines the trained ML tools for different flow regions. The discrepancy with experimental data of this method is systematically lower than the one observed for the baseline RANS solution and very similar to the one obtained with the MFEnKF.
physics.flu-dyn
Despite widespread enthusiasm, applying artificial intelligence and machine learning (AI/ML) to turbulence modeling has yielded only modest progress, primarily due to a lack of situation-aware deployment. Data-driven Reynolds-averaged Navier–Stokes (ML-RANS) closures frequently fail to generalize across diverse flow regimes, while scale-resolving simulations (SRS) remain computationally prohibitive. As a result, ML-RANS is often misapplied outside its domain of validity, and ML-SRS is unnecessarily deployed on flows fully amenable to RANS. To guide optimal AI/ML deployment, we propose a turbulence taxonomy map parameterized by degrees of freedom () and the degree of non-equilibrium (). By applying Weaver's well-recognized complexity framework, we classify turbulence into distinct physical regimes. This categorization identifies where local ML-RANS surrogates can generalize, clarifies where explicit scale resolution is physically mandatory, and highlights where physics-informed neural networks (PINNs) are most effective. Ultimately, this perspective establishes a physics-grounded framework for the flow-aware, successful deployment of AI/ML in turbulence.
physics.flu-dyn
Standard convolutional neural networks for turbulence super-resolution are restricted to uniform structured grids, preventing their direct application to the non-uniform and non-orthogonal meshes commonly used in wall-bounded flows and complex geometries. We introduce a finite-volume convolution unit (FVCU) that removes this restriction. The key idea is to construct convolutional layers using finite-volume operators that are applicable to non-uniform and unstructured meshes. To this end, we use an exact representation of a 3D convolution as a linear combination of successive axis-wise convolutions. We adopt axis-wise gradient, averaging, and identity operators, as they can be evaluated on arbitrary polyhedral cells using finite-volume discretization. The resulting FVCU is well-defined on general meshes, serving as a drop-in replacement for conventional convolution layers. The FVCU is embedded in a super-resolution neural network and trained to reconstruct 3D velocity fields from coarsened low-resolution fields in turbulent channel flow on a non-uniform mesh, and in circular-pipe flow on a non-orthogonal O-grid mesh. Inspired by the role of the Van Driest damping function in near-wall subgrid-scale modelling in large-eddy simulations, this function is supplied as a conditional input to encode wall proximity. An ablation study confirms that the network interprets this input in a physically consistent manner. In both configurations, the model accurately reconstructs instantaneous velocity fields, Reynolds-stresses and their anisotropy, and energy spectra beyond the Nyquist limit of the low-resolution mesh. On an elliptic pipe unseen during training, the model reproduces the main flow features and local statistics, with a modest overprediction of small-scale energy. These results demonstrate a framework for extending CNN-based super-resolution to general finite-volume grids.
physics.plasm-ph
Machine learning surrogate models offer a promising path toward accelerating plasma turbulence simulations. We present PreVAE-Turb, a surrogate modeling framework that leverages pre-trained variational autoencoders (VAEs) from the Stable Diffusion image generation model for efficient spatial compression of turbulence fields. The pre-trained VAE is fine-tuned on turbulence data using a physics-informed loss function that includes a spectral loss operating in Fourier space to enforce spectral accuracy across scales. The VAE is combined with convolutional long short-term memory (ConvLSTM) networks to learn temporal dynamics in latent space, with a manifold consistency error metric that monitors encode–decode consistency during autoregressive rollouts. We validate the framework on two-dimensional Hasegawa-Wakatani drift-wave turbulence and extend it to gyrokinetic turbulence from the GENE code, where a four-channel adaptation simultaneously predicts electrostatic potential, density, and parallel/perpendicular temperature fluctuations without requiring architecture redesign. Once trained, inference generates thousands of time steps in seconds on a single GPU, providing substantial computational acceleration compared to direct numerical simulation. The pre-trained approach offers a transferable methodology broadly applicable to various turbulence simulation codes.
physics.flu-dyn
The derivative-free loss method (DFLM) is a mesh-free neural network approach for solving partial differential equations by simulating stochastic walkers rather than computing derivatives directly. Although DFLM has previously been applied to the Navier–Stokes equations, extending it to turbulent flows reveals two limitations of its simplest implementation. The walkers do not account for the swirling, directionally stretching motion of the flow, and randomly sampling the walkers used to evaluate the target introduces noise into the learned solution. We address both limitations with an analytic approximation of the walkers' local motion that captures directional stretching and eliminates this sampling noise, while remaining computationally efficient. We study the resulting method as a non-intrusive multiscale solver capable of learning macroscopic flow behavior without resolving every scale on a fine grid or explicitly coupling coarse- and fine-scale models. For two turbulent two-dimensional flows, the proposed method reproduces the macroscopic energy spectrum of fully resolved reference simulations more accurately than the standard method, particularly where directional stretching is strongest, confirming DFLM's efficacy as a multiscale solver for turbulent fluid systems.
physics.flu-dyn
The three-dimensional organization of coherent structures in the turbulent flow over aircraft wings remains elusive, limiting our ability to reduce fuel consumption. Here, we use explainable artificial intelligence to characterize these structures by predicted flow evolution rather than classical predefined kinematic criteria. After training a deep neural network to predict the short-term evolution of the flow, we identify the highest-relevance flow regions using Shapley-value attribution methods. We have found that as the flow decelerates towards the trailing edge, predictive importance shifts from near-wall low-speed structures to three-dimensional pairs of high- and low-speed fluid regions. Matching no single classical structure family, these pairs progressively dominate the dynamically relevant flow. Most stand spanwise side-by-side, enclosing a near-vertical momentum interface with the strongest velocity jump. Their geometry remains invariant in viscous units while their volume expands when approaching separation. Our results reveal a predictive organization that traditional paradigms overlook, opening new ways to control turbulent flows.
physics.flu-dyn
Inertial particle dynamics in turbulence are commonly interpreted in terms of the instantaneous particle Stokes number, as supported by studies in statistically stationary homogeneous isotropic turbulence. But in freely decaying turbulence the Kolmogorov time scale evolves continuously, causing the effective Stokes number, St, to vary even though particle properties remain unchanged. Whether preferential concentration remains uniquely determined by this instantaneous St or depends on the flow's previous evolution has remained largely unexplored. We investigate inertial-particle clustering during the decay of homogeneous isotropic turbulence using direct numerical simulations of heavy point particles in the one-way coupling limit. Clustering is quantified through 3D Voronoï tessellations for populations evolving either from statistically stationary clustered states or initially random distributions. We consider both conventionally forced homogeneous isotropic turbulence and velocity fields reconstructed using physics-informed neural networks. We show that preferential concentration cannot be described solely by the instantaneous St. While particle slip velocity follows the classical steady-state dependence on the instantaneous St, clustering statistics retain a measurable history dependence throughout decay. Existing stationary scaling laws remain applicable to cluster-size evolution, but only through history-dependent prefactors. Particle distributions evolving from different initial conditions rapidly converge towards similar large-scale spatial organisation, indicating that the carrier flow determines the geometry of preferential concentration while finer clustering statistics preserve imprints of the previous evolution. These results demonstrate that preferential concentration in non-stationary turbulence is governed jointly by the instantaneous flow state and its initial state.
physics.flu-dyn
Predictive simulation of turbulent combustion remains challenging because stiff chemical kinetics, turbulent transport, molecular mixing, and heat release interact nonlinearly across unresolved scales. In the filtered or averaged formulations, reaction rate is unclosed, and the integration of detailed chemistry constitutes the dominant computational cost. Conventional closures such as mixing-limited models, flamelet and manifold methods, conditional moment closure, and transported probability/filtered density function (PDF/FDF) formulations, encode substantial physical insight, but rely on structural assumptions that may lose validity outside their calibrated regimes. Machine learning offers a complementary approach because of its ability to approximate complex nonlinear functions. In turbulent combustion, this capability can be used to relax restrictive closure assumptions, learn unresolved nonlinear mappings from data, and accelerate expensive computations such as detailed chemistry computation. However, purely data-driven models may violate conservation laws and thermochemical consistency. They may also extrapolate poorly outside the training domain and destabilize the CFD solvers in which they are embedded. Physics-guided machine learning (PGML) addresses these failure modes by incorporating prior knowledge throughout the modeling pipeline: in the training data and input features, the model architecture, the loss function, the hybrid closure structure, and the solver-aware validation protocol. This article reviews PGML for turbulence-chemistry interaction (TCI) modeling within this framework.
physics.flu-dyn
A physics-embedded training framework is used to close the sub-grid-scale dynamics of turbulent premixed flames. The trained model augments the resolved flow equations and is trained to match its predicted flow field to trusted data. An end-to-end optimization of the coupled resolved equations and embedded model leads to a model that is robust and effective for a freely propagating premixed flame in turbulence, modeled by a single-species, single-step, and irreversible chemical reaction. Important constraints are built into the training formulation for conservation, scalar boundedness, and equivariance. The model is scaled based on the residual of the resolved flow equations to focus its influence where the closure is needed. It outperforms other cases considered — no-model, dynamic closure, and the same machine learning model trained directly to fit the residual data — for a long-time simulation, correcting the turbulence dissipation and flame kinematics. Finally, it is shown how the prediction-based training better informs the model than the precise residual data.
physics.flu-dyn
Turbulence modeling in porous media can be greatly improved by combining high-resolution numerical methods with modern data-driven techniques. The development of accurate macroscale models (length scale greater than the pore size) will enable real-time systemic simulations of porous media flow. We consider the case of turbulent flow in homogeneous porous media, typically encountered in engineered porous media (heat exchangers, metamaterials, combustors, etc.). The underlying microscale flow field is inhomogeneous and determined by the geometry of the porous medium. Neural Networks are able to resolve the geometry-dependence and the non-linearity of porous media turbulent flow. We are proposing to separate the macroscale model into individual blocks that predict a unique aspect of the microscale flow, such as microscale spatial flow distribution and vortex dynamics. In the present work, we determine the feasibility of the prediction of the Reynolds-averaged microscale flow patterns by using Convolutional Neural Networks (CNN). The porous medium is represented by using a square lattice arrangement of circular cylinder solid obstacles. The pore-scale Reynolds number of the flow is 300. The porosity of the porous medium is varied from 0.45 to 0.92 with 60 steps. The microscale flow field is simulated by using Large Eddy Simulation (LES) with a compact sixth-order finite difference method. We demonstrate satisfactory prediction of the microscale flow field using the CNN with a global error less than 10%. We vary the number of training samples to study the deterioration of the model accuracy. The CNN model offers a O(106) speedup over LES with only 10% loss in accuracy.
physics.flu-dyn
Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly. However, most existing studies remain in 2D, while 3D turbulence has fundamentally different physics and is far more costly to simulate. Existing 3D resources also typically provide only one realization per configuration, making it difficult to distinguish learning the dynamics from fitting the statistics of a single flow. In this paper, we introduce TIDE (Turbulent Incompressible DNS Ensembles), a 256^3 DNS corpus and benchmark for 3D incompressible turbulence, with 15 configurations on eight controlled axes, independent ensembles, pressure fields, and equation-level verification. The benchmark includes five tasks, standardized learned baselines, controlled generalization splits, and physical-fidelity metrics alongside pointwise error. Across the main forecasting configurations, current learned models barely outperform persistence and still make about twice the error of a spectral solver given the true equations. Moreover, lower pointwise error can coincide with severely distorted small-scale dynamics, showing that accuracy alone does not ensure physical fidelity. Generalization results further show that most regime shifts reflect limited training coverage, whereas forced-to-decay transfer exposes a missing conditioning variable: operators trained under forcing continue to predict driven evolution when the external drive is removed. Closing these accuracy, fidelity, and conditioning gaps is the central open problem made measurable by TIDE.
physics.flu-dyn
In fluid engineering, the turbulence problem is the longstanding challenge of obtaining accurate predictions of engineering quantities at affordable computational cost. Viewed through computational complexity, a practical algorithm requires cost growth no worse than , where denotes problem size. For turbulent flows, the problem size may be approximated by the number of dynamically relevant scales and hence by the Reynolds number . We propose a multi-fidelity, physics-constrained, data-driven framework designed to meet this criterion under stated assumptions. We augment the Spalart–Allmaras model through field inversion and machine learning using a constrained formulation that preserves the law of the wall. The model is trained at a low Reynolds number, where high-fidelity data are affordable, and deployed at higher Reynolds numbers. For a mean-flow-aligned grid in a wall-bounded flow, fixed spanwise resolution, and steady-solver cost linear in grid-point count, the low-fidelity RANS prediction scales as . The high-fidelity calculation and learning stage each contribute relative to the target Reynolds number, giving an overall formal cost of . In plane channel flow, a model trained at corrects the wake-layer error of the baseline model and retains the improvement at . In the periodic hill, a model trained at is tested at , , and . The constrained formulation preserves separation and recovery behavior as Reynolds number increases, yields the lowest root-mean-square error across all tests, and exhibits nearly Reynolds-number-independent error, indicating robust extrapolation.
physics.flu-dyn
Although a complete characterisation of the probability distribution in the phase space of turbulent flows remains elusive, accurately sampling this distribution is essential for both synthetic turbulence generation and turbulent flow reconstruction. Motivated by these applications, we examine to what extent a machine-learned distribution can approximate the physical invariant distribution of turbulent channel flow at . We assess three important properties of the approximation: physical ensemble statistics, consistent conditional sampling, and dynamical invariance. To this end, a flow-based generative model is trained on a minimal conditional flow unit, which we define as the smallest domain outside which conditional fields, given a single observation at the domain centre, are indistinguishable from unconditional fields in terms of mean-square discrepancy to other conditional fields. We also introduce a consistent procedure for sampling from the conditional learned distribution. Comparisons with direct numerical simulation show that synthetic turbulent fields reproduce key statistical and dynamical features of turbulence, including intermittency and nonlinear energy transfer. The consistency of conditional sampling is demonstrated in a flow reconstruction problem, and subsequently used to generate synthetic turbulent velocity fields on a large domain. When adopted as initial conditions in direct numerical simulations, these fields yield physical and statistically stationary ensemble statistics, indicating that the learned distribution provides a good approximation to the natural distribution of the turbulent dynamical system.
physics.flu-dyn
Large-eddy simulation (LES) turbulence models often fail to capture the effects of chemical heat release and the resulting modulation of turbulence in premixed flames, underscoring the need for a framework that remains accurate across a broad range of physical regimes. We develop an augmented eddy-viscosity closure, based on deep neural networks calibrated jointly with the LES solution using adjoint-based optimization and differentiable programming, ensuring consistency with the governing partial differential equations (PDEs). Several objective functions and training methods are examined, and each model is assessed for its capability to interpolate and extrapolate across a wide range of Damköhler numbers. Relative to the Smagorinsky-model baseline, the best neural network model improves a posteriori errors in the LES primitive variables by 25-50% and in the resolved Reynolds stress and scalar flux by more than 60%. Crucially, the model generalizes across Damköhler number regimes, maintaining stability and accuracy even for out-of-sample conditions. These results demonstrate that PDE-consistent deep learning closures can recover both mean fields and resolved turbulence statistics in LES of turbulent premixed flames and can therefore provide a broadly applicable framework for turbulent combustion modeling.
physics.flu-dyn
Wall-modelled large-eddy simulation (WMLES) treats the subgrid-scale (SGS) closure, wall closure and numerical discretization as independent components, although their effects are coupled through the same resolved field. We present a differentiable hybrid neural–CFD framework in which the SGS and wall closures are learned jointly, end-to-end, within a differentiable flow solver, using only low-order statistics as training targets. Each closure is a composed neural operator: a trainable neural network followed by a fixed differentiable layer that preserves the structure of its conventional counterpart, so that the network learns only the functions left undetermined by the conventional form. Because every operation is differentiable, gradients of the training loss are back-propagated through the coupled solver, allowing both neural closures to be optimized consistently against the flow field, rather than fitted offline or in isolation. We demonstrate the framework, denoted Hybrid-Joint, on a zero-pressure-gradient turbulent boundary layer across a posteriori tests spanning Re_θ= 600–6500, computational domains and mesh resolutions. The model outperforms WMLES baselines, extrapolates to more than four times the highest training Reynolds number, and transfers to grids and domains absent from training. It recovers a logarithmic mean-velocity region, not imposed by the wall closure, and reproduces the resolved energy spectra accurately, although spectral information is excluded from the training objective. Ablation studies show that learning either closure alone is insufficient and that only joint optimization recovers the full set of statistics, confirming that SGS closure, wall closure and discretization are coupled and must be trained jointly. Once trained, the closures are reused without retraining across all cases, so that training cost is amortized over repeated deployment.
physics.flu-dyn
In this study, a conditional diffusion model – a class of generative machine learning models – is developed to generate synthetic, experimental data-based trajectories of turbulent flames. Generated experimental data corresponds to simultaneous field measurements, namely OH planar laser-induced fluorescence (OH-PLIF) fields and multi-component particle image velocimetry (PIV) fields, for attached and detached flame states in a swirl combustor configuration. This is done using an x-prediction flow matching framework combined with a pixel-based spatiotemporal transformer, which is capable of generating entire spatiotemporal slabs containing synthetic flame evolution at inference time, conditioned on the flame regime. Using this framework, synthetic flames were found to preserve key flame features and statistical consistency across space and time, particularly at the large scales – deviations at high temporal frequencies and small spatial length scales were found to depend on the time-span of the generated space-time slabs. An extrapolation task of transition synthesis is also conducted, in which the conditional diffusion model is used to synthesize spatiotemporally coherent flame transitions (flame liftoff and reattachment) unseen by the model during training. This was accomplished using a model for the denoising transition velocity that relies on time-varying linear combinations of attached and detached denoising velocities, leading to an approach that (a) allows for control of the generated transition directions and timescales, and (b) retains sample-to-sample variability in the generated transitions in the process. Overall, this study provides a promising pathway for the utilization of experimental data-based generative models as a new means of data exploration in data-sparse environments, complementing both experiments and computational fluid dynamics-based approaches.
astro-ph.SR
Numerical modeling of solar plasma dynamics is affected by the resolution of the computational grid. This often requires the estimation of subgrid processes related to the small-scale flow turbulence, as these processes play a critical role in momentum transport and energy dissipation. In this work, we investigate the use of deep learning techniques as surrogate models for subgrid turbulent transport in realistic hydrodynamic simulations of the quiet Sun. We describe the development of a 3D Convolutional Neural Network (CNN) to capture spatial dependencies in 3D velocity fields, leveraging different activation functions, as well as different architectural designs. We specifically focus on the prediction of Reynolds stress tensor components. The resultant model integrates velocity vector components and scalar features, such as plasma density, to enhance prediction accuracy. We compare the 3DCNN model to other types of models, such as a Multilayer Perceptron (MLP) and physics-based Gradient and Smagorinsky models, and show that the final model design reconstructs the Reynolds stress tensor components more accurately. Specifically, a 3DCNN model achieves an average improvement of ~31% on diagonal components and ~8% on the off-diagonal components of the stress tensor. Additionally, we show that applying a logarithmic data transformation of the target stress tensor components, to handle heavily skewed data, improves model performance. Results demonstrate the potential of deep learning, particularly CNNs, to approximate Reynolds stress tensor components for the upper solar convection zone and lower atmosphere, making them a viable candidate for modeling subgrid processes and a promising alternative to traditional turbulence models.
astro-ph.SR
Turbulence in the solar interior and atmosphere plays a crucial role in energy transport, yet modeling its subgrid-scale effects remains a major challenge. This study leverages machine learning (ML) models to predict components of the Reynolds stress tensor using high-resolution StellarBox simulations of the quiet Sun. Previously, we have compared a Multi-Layer Perceptron (MLP) and a 3D Convolutional Neural Network (CNN) against physics-based baselines to achieve a lower Mean Squared Error (MSE) and better generalization across various heights and depths in the solar atmosphere. To enhance learning, in this work, we investigate cluster-weighted training using K-Means and Hierarchical Agglomerative Clustering (HAC). By weighing the loss function based on cluster-specific prediction errors, we direct the model's attention to high-error regions. It significantly improves CNN performance, achieving 34% lower MSE and a significantly higher R2 score indicating that integrating deterministic clustering with ML is a promising technique for modeling subgrid turbulence, in particular, and regression in diverse environments, in general.