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
We present UniFoil, a large publicly available universal airfoil dataset based on Reynolds-averaged Navier-Stokes (RANS) simulations. It contains over 500,000 samples spanning a wide range of Reynolds and Mach numbers, capturing both transitional and fully turbulent flows across incompressible to compressible regimes. UniFoil is designed to support machine learning research in fluid dynamics, particularly for modeling complex aerodynamic phenomena. Most existing datasets are limited to incompressible, fully turbulent flows with smooth field characteristics, overlooking the critical physics of laminar\-turbulent transition and shock\-wave interactions\-features that exhibit strong nonlinearity and sharp gradients. UniFoil addresses this limitation by offering a broad spectrum of realistic flow conditions. Turbulent simulations utilize the Spalart\-Allmaras (SA) model, while transitional flows are modeled using an e^N\-based transition prediction method coupled with the SA model. The dataset includes a comprehensive geometry set comprising over 4,800 natural laminar flow (NLF) airfoils and 30,000 fully turbulent (FT) airfoils, covering a diverse range of airfoil designs relevant to aerospace, wind energy, and marine applications. This dataset is also valuable for scientific machine learning, enabling the development of data-driven models that more accurately capture the transport processes associated with laminar-turbulent transition. UniFoil is freely available under a permissive CC\-BY\-SA license.
physics.flu-dyn
This study evaluates the generalization performance and representation efficiency (parsimony) of a previously introduced Tensor Basis Kolmogorov-Arnold Network (TBKAN) architecture for data-driven turbulence modeling. The TBKAN framework replaces the multi-layer perceptron (MLP) used in either the standard or modified Tensor Basis Neural Network (TBNN) with a Kolmogorov-Arnold network (KAN), which significantly reduces the model complexity while providing a structure that potentially can be used with symbolic regression to provide a physical interpretability that is not available in a 'black box' MLP. While some prior work demonstrated TBKAN's feasibility for modeling a 'simple' flat plate boundary layer flow, this study extends the TBKAN architecture to model more complex benchmark flows, in particular, square duct and periodic hills flows which exhibit strong turbulence anisotropy, secondary motion, and flow separation and reattachment. A realizability-informed loss function is employed to constrain the model predictions, and, for the first time, TBKAN predictions are stably injected into the Reynolds-averaged Navier-Stokes equations to provide it a posteriori predictions of the mean velocity field.
cs.LG
Accurately predicting the long-term evolution of turbulence is crucial for advancing scientific understanding and optimizing engineering applications. However, existing deep learning methods face significant bottlenecks in long-term autoregressive prediction, which exhibit excessive smoothing and fail to accurately track complex fluid dynamics. Our extensive experimental and spectral analysis of prevailing methods provides an interpretable explanation for this shortcoming, identifying Spectral Bias as the core obstacle. Concretely, spectral bias is the inherent tendency of models to favor low-frequency, smooth features while overlooking critical high-frequency details during training, thus reducing fidelity and causing physical distortions in long-term predictions. Building on this insight, we propose Turb-L1, an innovative turbulence prediction method, which utilizes a Hierarchical Dynamics Synthesis mechanism within a multi-grid architecture to explicitly overcome spectral bias. It accurately captures cross-scale interactions and preserves the fidelity of high-frequency dynamics, enabling reliable long-term tracking of turbulence evolution. Extensive experiments on the 2D turbulence benchmark show that Turb-L1 demonstrates excellent performance: (I) In long-term predictions, it reduces Mean Squared Error (MSE) by and increases Structural Similarity (SSIM) by over compared to the SOTA baseline, significantly improving prediction fidelity. (II) It effectively overcomes spectral bias, accurately reproducing the full enstrophy spectrum and maintaining physical realism in high-wavenumber regions, thus avoiding the spectral distortions or spurious energy accumulation seen in other methods.
physics.flu-dyn
In operational weather models, the effects of turbulence in the atmospheric boundary layer (ABL) on the resolved flow are modeled using turbulence parameterizations. These parameterizations typically use a predetermined set of model parameters that are tuned to limited data from canonical flows. Using these fixed parameters results in deterministic predictions that neglect uncertainty in the unresolved turbulence processes. In this study, we perform a machine learning-accelerated Bayesian inversion of a single-column model of the ABL. This approach is used to calibrate and quantify uncertainty in model parameters of Reynolds-averaged Navier-Stokes turbulence models. Following verification of the uncertainty quantification methodology, we learn the parameters and their uncertainties in two different turbulence models conditioned on scale-resolving large-eddy simulation data over a range of ABL stabilities. We show how Bayesian inversion of a numerical model improves flow predictions by investigating the underlying mean momentum budgets. Further, we show that uncertainty quantification based on neutral surface layer data recovers the relationships between parameters derived from theoretical modeling, but that learning the parameters based on stable ABL data or data from outside the surface layer can lead to different relationships than neutral surface layer theory. Systematic uncertainty reduction methods reveal that (1) sampling wind speed up to the ABL height can reduce uncertainty in key model parameters by up to 84%, and (2) assimilating fluid flow quantities beyond first-order moment statistics can further reduce uncertainty in ways that wind speed assimilation alone cannot achieve. The parameters learned using Bayesian uncertainty quantification generally yield lower error than standard deterministic parameters in out-of-sample tests and provide uncertainty intervals on predictions.
cs.LG
Despite decades of advancements, the simulation of fluids remains one of the most challenging areas of in scientific computing. Supported by the necessity of gradient information in deep learning, differentiable simulators have emerged as an effective tool for optimization and learning in physics simulations. In this work, we present our fluid simulator PICT, a differentiable pressure-implicit solver coded in PyTorch with Graphics-processing-unit (GPU) support. We first verify the accuracy of both the forward simulation and our derived gradients in various established benchmarks like lid-driven cavities and turbulent channel flows before we show that the gradients provided by our solver can be used to learn complicated turbulence models in 2D and 3D. We apply both supervised and unsupervised training regimes using physical priors to match flow statistics. In particular, we learn a stable sub-grid scale (SGS) model for a 3D turbulent channel flow purely based on reference statistics. The low-resolution corrector trained with our solver runs substantially faster than the highly resolved references, while keeping or even surpassing their accuracy. Finally, we give additional insights into the physical interpretation of different solver gradients, and motivate a physically informed regularization technique. To ensure that the full potential of PICT can be leveraged, it is published as open source: https://github.com/tum-pbs/PICT.
physics.flu-dyn
Amid growing interest in machine learning, numerous data-driven models have recently been developed for Reynolds-averaged turbulence modelling. However, their results generally show that they do not give accurate predictions for test cases that have different flow phenomena to the training cases. As these models have begun being applied to practical cases typically seen in industry such as in cooling and nuclear, improving or incorporating metrics to measure their reliability has become an important matter. To this end, a novel data-driven approach that uses mean-variance estimation networks (MVENs) is proposed in the present work. MVENs enable efficient computation as a key advantage over other uncertainty quantification (UQ) methods - during model training with maximum likelihood estimation, and UQ with a single forward propagation. Furthermore, the predicted standard deviation is also shown to be an appropriate proxy variable for the error in the mean predictions, thereby providing error quantification (EQ) capabilities. The new tensor-basis neural network with MVEN integration was compared with its popular underlying data-driven model by evaluating them on two test cases: a separated flow and a secondary flow. In both cases, the proposed approach preserved the predictive accuracy of the underlying data-driven model, while efficiently providing reliability metrics in the form of UQ and EQ. For the purposes of turbulence modelling, this work demonstrates that the UQ and EQ mechanisms in MVENs enable risk-informed predictions to be made and therefore can be insightful reliability measures in more complex cases, such as those found in industry.
physics.flu-dyn
Fluid thermodynamics underpins atmospheric dynamics, climate science, industrial applications, and energy systems. However, direct numerical simulations (DNS) of such systems can be computationally prohibitive. To address this, we present a novel physics-informed spatiotemporal surrogate model for Rayleigh-Benard convection (RBC), a canonical example of convective fluid flow. Our approach combines convolutional neural networks, for spatial dimension reduction, with an innovative recurrent architecture, inspired by large language models, to model long-range temporal dynamics. Inference is penalized with respect to the governing partial differential equations to ensure physical interpretability. Since RBC exhibits turbulent behavior, we quantify uncertainty using a conformal prediction framework. This model replicates key physical features of RBC dynamics while significantly reducing computational cost, offering a scalable alternative to DNS for long-term simulations.
astro-ph.SR
We compare the efficiency and ease-of-use of the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm and Sparse Physics-Informed Discovery of Empirical Relations (SPIDER) framework in recovering the relevant governing equations and boundary conditions from data generated by direct numerical simulations (DNS) of turbulent convective flows. In the former case, a weak-form implementation pySINDy is used. Time-dependent data for two- (2D) and three-dimensional (3D) DNS simulation of Rayleigh-Benard convection and convective plane Couette flow is generated using the Dedalus PDE framework for spectrally solving differential equations. Using pySINDy we are able to recover the governing equations of 2D models of Rayleigh-Benard convection at Rayleigh numbers, R, from laminar, through transitional to moderately turbulent flow conditions, albeit with increasing difficulty with larger Rayleigh number, especially in recovery of the diffusive terms (with coefficient magnitude proportional to 1/R^0.5). SPIDER requires a much smaller library of terms and we are able to recover more easily the governing equations for a wider range of R in 2D and 3D convection and plane flow models and go on to recover constraints (the incompressibility condition) and boundary conditions, demonstrating the benefits and capabilities of SPIDER to go beyond pySINDy for these fluid problems governed by second-order PDEs. [We] demonstrat[e] the potential of machine-learning methods to validate numerical solvers and solutions for such flow problems. We also find that properties of the flow, specifically the correlation time and spatial scales, should inform the initial selection of spatiotemporal subdomain sizes [abbreviated]
cs.LG
In this work, we introduce a new class of neural network operators designed to handle problems where memory effects and randomness play a central role. In this work, we introduce a new class of neural network operators designed to handle problems where memory effects and randomness play a central role. These operators merge symmetrized activation functions, Caputo-type fractional derivatives, and stochastic perturbations introduced via Itô type noise. The result is a powerful framework capable of approximating functions that evolve over time with both long-term memory and uncertain dynamics. We develop the mathematical foundations of these operators, proving three key theorems of Voronovskaya type. These results describe the asymptotic behavior of the operators, their convergence in the mean-square sense, and their consistency under fractional regularity assumptions. All estimates explicitly account for the influence of the memory parameter and the noise level . As a practical application, we apply the proposed theory to the fractional Navier-Stokes equations with stochastic forcing, a model often used to describe turbulence in fluid flows with memory. Our approach provides theoretical guarantees for the approximation quality and suggests that these neural operators can serve as effective tools in the analysis and simulation of complex systems. By blending ideas from neural networks, fractional calculus, and stochastic analysis, this research opens new perspectives for modeling turbulent phenomena and other multiscale processes where memory and randomness are fundamental. The results lay the groundwork for hybrid learning-based methods with strong analytical backing.
physics.flu-dyn
A data-driven algorithm is proposed that employs sparse data from velocity and/or scalar sensors to forecast the future evolution of three dimensional turbulent flows. The algorithm combines time-delayed embedding together with Koopman theory and linear optimal estimation theory. It consists of 3 steps; dimensionality reduction (currently POD), construction of a linear dynamical system for current and future POD coefficients and system closure using sparse sensor measurements. In essence, the algorithm establishes a mapping from current sparse data to the future state of the dominant structures of the flow over a specified time window. The method is scalable (i.e.\ applicable to very large systems), physically interpretable, and provides sequential forecasting on a sliding time window of prespecified length. It is applied to the turbulent recirculating flow over a surface-mounted cube (with more than degrees of freedom) and is able to forecast accurately the future evolution of the most dominant structures over a time window at least two orders of magnitude larger that the (estimated) Lyapunov time scale of the flow. Most importantly, increasing the size of the forecasting window only slightly reduces the accuracy of the estimated future states. Extensions of the method to include convolutional neural networks for more efficient dimensionality reduction and moving sensors are also discussed.
physics.flu-dyn
Learning symbolic turbulence models from indirect observation data is of significant interest as it not only improves the accuracy of posterior prediction but also provides explicit model formulations with good interpretability. However, it typically resorts to gradient-free evolutionary algorithms, which can be relatively inefficient compared to gradient-based approaches, particularly when the Reynolds-averaged Navier-Stokes (RANS) simulations are involved in the training process. In view of this difficulty, we propose a framework that uses neural networks and the associated feature importance analysis to improve the efficiency of symbolic turbulence modeling. In doing so, the gradient-based method can be used to efficiently learn neural network-based representations of Reynolds stress from indirect data, which is further transformed into simplified mathematical expressions with symbolic regression. Moreover, feature importance analysis is introduced to accelerate the convergence of symbolic regression by excluding insignificant input features. The proposed training strategy is tested in the flow in a square duct, where it correctly learns underlying analytic models from indirect velocity data. Further, the method is applied in the flow over the periodic hills, demonstrating that the feature importance analysis can significantly improve the training efficiency and learn symbolic turbulence models with satisfactory generalizability.
physics.flu-dyn
Velocity, pressure, and temperature are the key variables for understanding thermal convection, and measuring them all is a complex task. In this paper, we demonstrate a method to reconstruct temperature and pressure fields based on given Lagrangian velocity data. A physics-informed neural network (PINN) based on a multilayer perceptron architecture and a periodic sine activation function is used to reconstruct both the temperature and the pressure for two cases of turbulent Rayleigh-Bénard convection (Pr = 6.9, Ra = ). The first dataset is generated with DNS and it includes Lagrangian velocity data of 150000 tracer particles. The second contains a PTV experiment with the same system parameters in a water-filled cubic cell, and we observed about 50000 active particle tracks per time step with the open-source framework proPTV. A realistic temperature and pressure field could be reconstructed in both cases, which underlines the importance of PINNs also in the context of experimental data. In the case of the DNS, the reconstructed temperature and pressure fields show a 90% correlation over all particles when directly validated against the ground truth. Thus, the proposed method, in combination with particle tracking velocimetry, is able to provide velocity, temperature, and pressure fields in convective flows even in the hard turbulence regime. The PINN used in this paper is compatible with proPTV and is part of an open source project. It is available on request at https://github.com/DLR-AS-BOA.
cs.LG
This paper presents a new Computational Fluid Dynamics database, developed at ONERA, to support the advancement of machine learning techniques for aerodynamic field prediction. It contains 468 Reynolds-Averaged Navier-Stokes simulations using the Spalart-Allmaras turbulence model, performed on the NASA/Boeing Common Research Model wing-body-pylon-nacelle configuration. The database spans a wide range of flow conditions, varying Mach number (including transonic regimes), angle of attack (capturing flow separation), and Reynolds number (based on three stagnation pressures, with one setting matching wind tunnel experiments). The quality of the database is assessed, through checking the convergence level of each computation. Based on these data, a regression challenge is defined. It consists in predicting the wall distributions of pressure and friction coefficients for unseen aerodynamic conditions. The 468 simulations are split into training and testing sets, with the training data made available publicly on the Codabench platform. The paper further evaluates several classical machine learning regressors on this task. Tested pointwise methods include Multi-Layer Perceptrons, -DNNs, and Decision Trees, while global methods include Multi-Layer Perceptron, k-Nearest Neighbors, Proper Orthogonal Decomposition and IsoMap. Initial performance results, using scores and worst relative mean absolute error metrics, are presented, offering insights into the capabilities of these techniques for the challenge and references for future work.
physics.flu-dyn
This study explores the integration of machine learning (ML) techniques with large eddy simulation (LES) for predicting species mass fraction and flame characteristics in partially premixed turbulent jet flames. The LES simulations, conducted using STAR-CCM+ software, employed the Flamelet Generated Manifold (FGM) approach to effectively capture the interactions between the turbulence and chemical reactions, providing high-fidelity data on flame behaviour and pollutant formation. The simulation was based on the Sandia Flame D specification, utilizing a detailed mesh to accurately represent flow features and flame dynamics. To enhance real-time prediction capabilities, three ML models, Neural Networks (NN), Linear Regression (LR), and Decision Tree Regression (DTR), were trained on the LES data. Comparative analysis using metrics such as Mean Absolute Error (MAE), Mean Squared Error (MSE), Pearson Coefficient (PC), and R-squared (R2) identified the NN model as the most effective one. The NN model demonstrated high accuracy in predicting species mass fractions and flame patterns, significantly outperforming traditional LES solvers in terms of computational efficiency. The study also highlighted the considerable computational speedup achieved by the NN model, making it approximately 17.25 times faster than traditional LES solvers. Despite some limitations, such as handling large dataset fluctuations, the ML models have shown promise for future applications in combustion simulations.
cs.LG
Transfer learning (TL) is a powerful tool for enhancing the performance of neural networks (NNs) in applications such as weather and climate prediction and turbulence modeling. TL enables models to generalize to out-of-distribution data with minimal training data from the new system. In this study, we employ a 9-layer convolutional NN to predict the subgrid forcing in a two-layer ocean quasi-geostrophic system and examine which metrics best describe its performance and generalizability to unseen dynamical regimes. Fourier analysis of the NN kernels reveals that they learn low-pass, Gabor, and high-pass filters, regardless of whether the training data are isotropic or anisotropic. By analyzing the activation spectra, we identify why NNs fail to generalize without TL and how TL can overcome these limitations: the learned weights and biases from one dataset underestimate the out-of-distribution sample spectra as they pass through the network, leading to an underestimation of output spectra. By re-training only one layer with data from the target system, this underestimation is corrected, enabling the NN to produce predictions that match the target spectra. These findings are broadly applicable to data-driven parameterization of dynamical systems.
physics.flu-dyn
Reconstructing near-wall turbulence from wall-based measurements is a critical yet inherently ill-posed problem in wall-bounded flows, where limited sensing and spatially heterogeneous flow-wall coupling challenge deterministic estimation strategies. To address this, we introduce a novel generative modeling framework based on conditional flow matching for synthesizing instantaneous velocity fluctuation fields from wall observations, with explicit quantification of predictive uncertainty. Our method integrates continuous-time flow matching with a probabilistic forward operator trained using stochastic weight averaging Gaussian (SWAG), enabling zero-shot conditional generation without model retraining. We demonstrate that the proposed approach not only recovers physically realistic, statistically consistent turbulence structures across the near-wall region but also effectively adapts to various sensor configurations, including sparse, incomplete, and low-resolution wall measurements. The model achieves robust uncertainty-aware reconstruction, preserving flow intermittency and structure even under significantly degraded observability. Compared to classical linear stochastic estimation (LSE) and deterministic convolutional neural networks (CNN) methods, our stochastic generative learning framework exhibits superior generalization and resilience under measurement sparsity with quantified uncertainty. This work establishes a robust semi-supervised generative modeling paradigm for data-consistent flow reconstruction and lays the foundation for uncertainty-aware, sensor-driven modeling of wall-bounded turbulence.
physics.flu-dyn
Simulating massively separated turbulent flows over bodies is one of the major applications for large-eddy simulation (LES). In the current work, we propose a machine-learning-based LES framework for the rapid simulation of turbulent flows over periodic hills using a hybrid U-Net and Fourier neural operator (HUFNO) framework. The newly proposed HUFNO model integrates the strengths of both the convolutional neural network (CNN) and Fourier neural operator (FNO) in a novel way that the FNO is applied in the periodic directions of the flow field while the non-periodicity is handled by the CNN-based U-Net framework. In the numerical tests, compared to the original FNO and the U-Net framework, the HUFNO model shows a higher accuracy in the predictions of the velocity field and Reynolds stresses. Further numerical experiments in the LES show that the HUFNO framework outperforms the traditional Smagorinsky (SMAG) model and the wall-adapted local eddy-viscosity (WALE) model in the predictions of the turbulence statistics, the energy spectrum, the invariant characteristics of velocity gradients, the wall stresses and the flow separation structures, with much lower computational cost. Importantly, the accuracy and efficiency are transferable to unseen initial conditions, Reynolds number and hill shapes, underscoring its great potentials for the fast prediction of strongly separated turbulent flows over curved boundaries.
physics.flu-dyn
This work proposes a novel methodology for turbulence modeling in Large Eddy Simulation (LES) based on Graph Neural Networks (GNNs), which embeds the discrete rotational, reflectional and translational symmetries of the Navier-Stokes equations into the model architecture. In addition, suitable invariant input and output spaces are derived that allow the GNN models to be embedded seamlessly into the LES framework to obtain a symmetry-preserving simulation setup. The suitability of the proposed approach is investigated for two canonical test cases: Homogeneous Isotropic Turbulence (HIT) and turbulent channel flow. For both cases, GNN models are trained successfully in actual simulations using Reinforcement Learning (RL) to ensure that the models are consistent with the underlying LES formulation and discretization. It is demonstrated for the HIT case that the resulting GNN-based LES scheme recovers rotational and reflectional equivariance up to machine precision in actual simulations. At the same time, the stability and accuracy remain on par with non-symmetry-preserving machine learning models that fail to obey these properties. The same modeling strategy translates well to turbulent channel flow, where the GNN model successfully learns the more complex flow physics and is able to recover the turbulent statistics and Reynolds stresses. It is shown that the GNN model learns a zonal modeling strategy with distinct behaviors in the near-wall and outer regions. The proposed approach thus demonstrates the potential of GNNs for turbulence modeling, especially in the context of LES and RL.
physics.flu-dyn
Turbulence modeling remains a longstanding challenge in fluid dynamics. Recent advances in data-driven methods have led to a surge of novel approaches aimed at addressing this problem. This work builds upon our recent work [Phys. Rev. Fluids 10, 044602 (2025)], where we introduced a new closure for a shell model of turbulence using an a posteriori (or solver-in-the-loop) approach. Unlike most deep learning-based models, our method explicitly incorporates physical equations into the neural network framework, ensuring that the closure remains constrained by the underlying physics benefiting from enhanced stability and generalizability. In this paper, we further analyze the learned closure, probing its capabilities and limitations. In particular, we look at joint probability density functions between resolved and unresolved variables, as well as the scale invariance of multipliers (ratios between adjacent shells) within the inertial range. Although our model excels in reproducing high-order statistical moments, it breaks this known symmetry near the cutoff, indicating a fundamental limitation. We discuss the implications of these findings for subgrid-scale modeling in 3D turbulence and outline directions for future research.
physics.flu-dyn
Turbulent-flow control aims to develop strategies that effectively manipulate fluid systems, such as the reduction of drag in transportation and enhancing energy efficiency, both critical steps towards reducing global CO emissions. Deep reinforcement learning (DRL) offers novel tools to discover flow-control strategies, which we combine with our knowledge of the physics of turbulence. We integrate explainable deep learning (XDL) to objectively identify the coherent structures containing the most informative regions in the flow, with a DRL model trained to reduce them. The model trained with XDL targets the most relevant regions in the flow to sustain turbulence and produces a drag reduction which is higher than that of a model specifically trained to reduce the drag, resulting in a better net-energy saving. The XDL-based control remains the most effective control strategy when generalizing across Reynolds numbers and geometries. This demonstrates that combining DRL with XDL can produce causal control strategies that precisely target the most influential features of turbulence. By directly addressing the core mechanisms that sustain turbulence, our approach offers a powerful pathway towards its efficient control, which is a long-standing challenge in physics with profound implications for energy systems, climate modeling and aerodynamics.