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.plasm-ph
The Trapped Gyro-Landau Fluid (TGLF) model provides fast, accurate predictions of turbulent transport in tokamaks, but whole device simulations requiring thousands of evaluations remain computationally expensive. Neural network (NN) surrogates offer accelerated inference with fully differentiable approximations that enable gradient-based coupling but typically require large training datasets to capture transport flux variations across plasma conditions, creating significant training burden and limiting applicability to expensive gyrokinetic simulations. We propose TGLF-WINN (Wavenumber-Informed Neural Network) with three key innovations: (1) principled feature engineering that reduces target prediction range, simplifying the learning task; (2) physics-guided wavenumber-resolved regularization to improve generalization under sparse data; and (3) Bayesian Active Learning (BAL) to strategically select training samples based on model uncertainty, reducing data requirements while maintaining accuracy. Feature tuning and wavenumber regularization together deliver a 12.5% relative RMSLE reduction over TGLF-NN on the full dataset; under sparse, unfiltered training (approximately 1/9 the full size) they yield an order-of-magnitude smaller RMSLE degradation than TGLF-NN, with the wavenumber-informed regularization imposing a physics-guided constraint on per-mode fluxes. Adding Bayesian Active Learning, TGLF-WINN matches TGLF-NN's full-data offline accuracy using only 25% of the training data, within 2.8% of TGLF-NN's full-data baseline and 4.3% of our own full-data result. A downstream flux-matching workflow further shows practicality: the NN surrogate gives a 45x speedup over TGLF with comparable reconstruction accuracy.
physics.flu-dyn
When developing scientific machine learning (ML) approaches, it is often beneficial to embed knowledge of the physical system in question into the training process. One way to achieve this is by leveraging the specific characteristics of the data at hand. In the case of turbulent flows, fluid velocities can be measured and recorded as multi-component vectors at discrete points in space, using techniques such as particle image velocimetry (PIV) or computational fluid mechanics (CFD). However, the vectorised nature of the data is ignored by standard ML approaches, as widely-used loss functions such as the mean-square error treat each component of a velocity vector in isolation. Therefore, the aim of this work is to better preserve the physical characteristics of the data by introducing loss functions that utilise vector similarity metrics. To this end, vector-based loss functions are developed here and implemented alongside a U-Net model for a turbulent flow field inpainting problem, amounting to the prediction of velocity vectors inside large gaps in PIV images. The intention is for the inpainting task to pose a significant challenge for the ML models in order to shed light on their capabilities. The test case uses PIV data from the highly turbulent flow in the well-known Transparent Combustion Chamber III (TCC-III) engine. Loss functions based on the cosine similarity and vector magnitude differences are proposed; the results show that the vector-based loss functions lead to significantly improved predictions of multi-scale flow patterns, while a hybrid (vector and mean-square error) loss function enables a good compromise to be found between preserving multi-scale behaviour and pixel-wise accuracy.
physics.flu-dyn
Turbulence Models represent the workhorse for simulations used in engineering design and analysis. Despite their low computational cost and robustness, these models suffer from substantial predictive uncertainty, most of which is epistemic. At present, the Eigenspace Perturbation Method (EPM) is the only approach to estimate these turbulence model uncertainties, using physics based perturbation to the predicted Reynolds stresses. While the EPM address the question of how to perturb the Reynolds stresses for uncertainty estimation, it does not address how much to perturb. This shortcoming leads to very generous uncertainty bounds that result in sub-optimal designs. In this investigation, we use Convolutional Neural Networks (CNN) to predict the discrepancy between predicted and actual turbulent flows. These can be utilized to modulate the degree of the perturbations in the EPM leading to a Physics Constrained Deep Learning approach for Reynolds Averaged Navier Stokes model uncertainty quantification. We test this approach on turbulent flows over aero-foils and periodic hills to show the efficacy of our approach.
physics.flu-dyn
This study establishes a symmetry-based framework to quantify non-equilibrium processes in complex pressure gradient (PG) turbulent boundary layers (TBLs), using a Lie-group-informed dilation-symmetry-breaking formalism. We derive a universal multilayer defect scaling law for the evolution of total shear stress (TSS). The law shows that gradually varying adverse pressure gradients (APGs) break the dilation symmetry in the two-layer defect scaling of equilibrium TSS, leading to three-layer TSS structures. For abrupt PG transitions, we identify boundary-layer decoupling into: 1) an equilibrium internal boundary layer, and 2) a history-dependent outer flow, arising from disparate adaptation timescales. The framework introduces a unified velocity scale mapping non-equilibrium TSS to canonical zero-PG scaling. Validation spans different aerodynamic systems, including developing APG on airfoils, APG-to-favorable-PG transition on a Gaussian bump, and favorable PG to rapidly amplifying APG in a converging-diverging channel. The work enables improved prediction of non-equilibrium PG TBL behavior through unified characterization of stress evolution dynamics, providing new physics-based parameterizations that could promote machine learning of complex wall-bounded turbulent flows.
physics.flu-dyn
This study presents the development of a domain-responsive edge-aware multiscale Graph Neural Network for predicting steady, turbulent flow and thermal behavior in a two-dimensional channel containing arbitrarily shaped complex pin-fin geometries. The training dataset was constructed through an automated framework that integrated geometry generation, meshing, and flow-field solutions in ANSYS Fluent. The pin-fin geometry was parameterized using piecewise cubic splines, producing 1,000 diverse configurations through Latin Hypercube Sampling. Each simulation was converted into a graph structure, where nodes carried a feature vector containing spatial coordinates, a normalized streamwise position, one-hot boundary indicators, and a signed distance to the nearest boundary such as wall. This graph structure served as input to the newly developed Graph Neural Network, which was trained to predict temperature, velocity magnitude, and pressure at each node using data from ANSYS. The network predicted fields with outstanding accuracy, capturing boundary layers, recirculation, and the stagnation region upstream of the pin-fins while reducing wall time by 2-3 orders of magnitude. In conclusion, the novel graph neural network offered a fast and reliable surrogate for simulations in complex flow configurations.
cs.LG
Neural-Network (NN) based turbulence closures have been developed for being used as pre-trained surrogates for traditional turbulence closures, with the aim to increase computational efficiency and prediction accuracy of CFD simulations. The bottleneck to the widespread adaptation of these ML-based closures is the relative lack of uncertainty quantification (UQ) for these models. Especially, quantifying uncertainties associated with out-of-training inputs, that is when the ML-based turbulence closures are queried on inputs outside their training data regime. In the current paper, a published algebraic turbulence closure1 has been utilized to compare the quality of epistemic UQ between three NN-based methods and Gaussian Process (GP). The three NN-based methods explored are Deep Ensembles (DE), Monte-Carlo Dropout (MCD), and Stochastic Variational Inference (SVI). In the in-training results, we find the exact GP performs the best in accuracy with a Root Mean Squared Error (RMSE) of followed by the DE with an RMSE of . Next, the paper discusses the performance of the four methods for quantifying out-of-training uncertainties. For performance, the Exact GP yet again is the best in performance, but has similar performance to the DE in the out-of-training regions. In UQ accuracy for the out-of-training case, SVI and DE hold the best miscalibration error for one of the cases. However, the DE performs the best in Negative Log-Likelihood for both out-of-training cases. We observe that for the current problem, in terms of accuracy GP > DE > SV I > MCD. The DE results are relatively robust and provide intuitive UQ estimates, despite performing naive ensembling. In terms of computational cost, the GP is significantly higher than the NN-based methods with a computational complexity for each training step
cs.CE
We present a general framework to predict precursors to extreme events in turbulent dynamical systems. The approach combines phase-space reconstruction techniques with recurrence matrices and convolutional neural networks to identify precursors to extreme events. We evaluate the framework across three distinct testbed systems: a triad turbulent interaction model, a prototype stochastic anisotropic turbulent flow, and the Kolmogorov flow. This method offers three key advantages: (1) a threshold-free classification strategy that eliminates subjective parameter tuning, (2) efficient training using only recurrence matrices, and (3) ability to generalize to unseen systems. The results demonstrate robust predictive performance across all test systems: 96% detection rate for the triad model with a mean lead time of 1.8 time units, 96% for the anisotropic turbulent flow with a mean lead time of 6.1 time units, and 93% for the Kolmogorov flow with a mean lead time of 22.7 units.
physics.flu-dyn
The laminar-to-turbulent transition remains a fundamental and enduring challenge in fluid mechanics. Its complexity arises from the intrinsic nonlinearity and extreme sensitivity to external disturbances. This transition is critical in a wide range of applications, including aerospace, marine engineering, geophysical flows, and energy systems. While the governing physics can be well described by the Navier-Stokes equations, practical prediction efforts often fall short due to the lack of comprehensive models for perturbation initialization and turbulence generation in numerical simulations. To address the uncertainty introduced by unforeseeable environmental perturbations, we propose a fine-grained predictive framework that accurately predicts the transition location. The framework generates an extensive dataset using nonlinear parabolized stability equations (NPSE). NPSE simulations are performed over a wide range of randomly prescribed initial conditions for the generic zero-pressure-gradient flat-plate boundary-layer flow, resulting in a large dataset that captures the nonlinear evolution of instability waves across three canonical transition pathways (Type-K, -H, and -O). From a database of 3000 simulation cases, we extract diagnostic quantities (e.g., wall pressure signals and skin-friction coefficients) from each simulation to construct a feature set that links pre-transition flow characteristics to transition onset locations. Machine learning models are systematically evaluated, with ensemble methods-particularly XGBoost-demonstrating exceptional predictive accuracy (mean relative error of approximately 0.001). Compared to methods currently available (e.g., N-factor, transitional turbulence model), this approach accounts for the physical process and achieves transition prediction without relying on any empirical parameters.
physics.flu-dyn
Turbulence plays a crucial role in multiphysics applications, including aerodynamics, fusion, and combustion. Accurately capturing turbulence's multiscale characteristics is essential for reliable predictions of multiphysics interactions, but remains a grand challenge even for exascale supercomputers and advanced deep learning models. The extreme-resolution data required to represent turbulence, ranging from billions to trillions of grid points, pose prohibitive computational costs for models based on architectures like vision transformers. To address this challenge, we introduce a multiscale hierarchical Turbulence Transformer that reduces sequence length from billions to a few millions and a novel RingX sequence parallelism approach that enables scalable long-context learning. We perform scaling and science runs on the Frontier supercomputer. Our approach demonstrates excellent performance up to 1.1 EFLOPS on 32,768 AMD GPUs, with a scaling efficiency of 94%. To our knowledge, this is the first AI model for turbulence that can capture small-scale eddies down to the dissipative range.
physics.flu-dyn
The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly non-trivial statistical behavior, motivating the development of surrogate models that can reproduce these trajectories without incurring the high computational cost of direct numerical simulations of the full Eulerian field. This task is particularly challenging because reduced-order models typically lack access to the full set of interactions with the underlying turbulent field. Novel data-driven machine learning techniques can be powerful in capturing and reproducing complex statistics of the reduced-order/surrogate dynamics. In this work, we show how one can learn a surrogate dynamical system that is able to evolve a turbulent Lagrangian trajectory in a way that is point-wise accurate for short-time predictions (with respect to Kolmogorov time) and stable and statistically accurate at long times. This approach is based on the Mori-Zwanzig formalism, which prescribes a mathematical decomposition of the full dynamical system into resolved dynamics that depend on the current state and the past history of a reduced set of observables, and the unresolved orthogonal dynamics due to unresolved degrees of freedom of the initial state. We show how by training this reduced order model on a point-wise error metric on short time-prediction, we are able to correctly learn the dynamics of Lagrangian turbulence, such that also the long-time statistical behavior is stably recovered at test time. This opens up a range of new applications, for example, for the control of active Lagrangian agents in turbulence.
physics.flu-dyn
Large eddy simulation (LES) has become a central technique for simulating turbulent flows in engineering and applied sciences, offering a compromise between accuracy and computational cost by resolving large scale motions and modeling the effects of smaller, unresolved scales through a subgrid scale (SGS) model. The fidelity and robustness of LES depends critically on the SGS model, particularly in coarse simulations where much of the turbulence spectrum remains unresolved. In this work, we extend the tau-orthogonal (TO) method, a data-driven SGS modeling framework, to three-dimensional turbulent flows. The method reformulates the high-dimensional SGS closure problem as a low-dimensional prediction task focused on scale-aware quantities of interest (QoIs). We extend the model to incorporate QoI-state dependence and temporal correlations by combining regularized least-squares regression with a multivariate Gaussian residual model. This yields a simple yet effective stochastic time-series prediction model (the LRS model), with orders-of-magnitude fewer parameters than typical deep learning approaches which try to directly learn the high-dimensional SGS closure. We demonstrate the effectiveness of the TO LRS model in three-dimensional forced isotropic turbulence and turbulent channel flow. The model achieves accurate long-term QoI distributions, robust performance across hyperparameter settings, and good reproduction of key flow features such as kinetic energy spectra and coherent structures, despite being trained solely on QoI trajectories. Comparisons against classical SGS models, including Smagorinsky and WALE formulations, highlight the TO LRS model's balance of accuracy and computational efficiency.
cs.LG
This study explores the potential for predicting turbulent kinetic energy (TKE) from more readily acquired temperature data using temperature profiles and turbulence data collected concurrently at 10 Hz during a small experimental prescribed burn in the New Jersey Pine Barrens. Machine learning models, including Deep Neural Networks, Random Forest Regressor, Gradient Boosting, and Gaussian Process Regressor, were employed to assess the potential to predict TKE from temperature perturbations and explore temporal and spatial dynamics of correlations. Data visualization and correlation analyses revealed patterns and relationships between thermocouple temperatures and TKE, providing insight into the underlying dynamics. More accurate predictions of TKE were achieved by employing various machine learning models despite a weak correlation between the predictors and the target variable. The results demonstrate significant success, particularly from regression models, in accurately predicting the TKE. The findings of this study demonstrate a novel numerical approach to identifying new relationships between temperature and airflow processes in and around the fire environment. These relationships can help refine our understanding of combustion environment processes and the coupling and decoupling of fire environment processes necessary for improving fire operations strategy and fire and smoke model predictions. The findings of this study additionally highlight the valuable role of machine learning techniques in analyzing the complex large datasets of the fire environments, showcasing their potential to advance fire research and management practices.
cs.LG
Turbulent fluid flows are among the most computationally demanding problems in science, requiring enormous computational resources that become prohibitive at high flow speeds. Physics-informed neural networks (PINNs) represent a radically different approach that trains neural networks directly from physical equations rather than data, offering the potential for continuous, mesh-free solutions. Here we show that appropriately designed PINNs can successfully simulate fully turbulent flows in both two and three dimensions, directly learning solutions to the fundamental fluid equations without traditional computational grids or training data. Our approach combines several algorithmic innovations including adaptive network architectures, causal training, and advanced optimization methods to overcome the inherent challenges of learning chaotic dynamics. Through rigorous validation on challenging turbulence problems, we demonstrate that PINNs accurately reproduce key flow statistics including energy spectra, kinetic energy, enstrophy, and Reynolds stresses. Our results demonstrate that neural equation solvers can handle complex chaotic systems, opening new possibilities for continuous turbulence modeling that transcends traditional computational limitations.
physics.flu-dyn
Turbulence constitutes an exceptionally complex and irregular flow phenomenon that manifests in liquids, gases, and plasma, making it ubiquitous in both natural processes and engineering applications. Given the relatively modest advancements in classical turbulence models over the past half-century, data-driven approaches, such as machine learning, have recently gained considerable traction in turbulence model research. In this study, we introduce a symbolic regression-based implicit algebraic stress turbulence model that incorporates the production of non-dimensional Reynolds stress deviatoric tensor, thereby capturing the contribution of the shape of local turbulence produced by the mean flow field. We rigorously evaluate our model across five distinct characteristic flow cases and benchmark it against three alternative turbulence models. Our comprehensive analysis demonstrates that the proposed model exhibits robust performance and substantial generalizability across all test cases while manifesting notable advantages when compared with the reference turbulence models.
physics.flu-dyn
This paper introduces a deep learning-based super-resolution (SR) framework specifically developed for accurately reconstructing high-resolution velocity fields in two-way coupled particle-laden turbulent flows. Leveraging conditional generative adversarial networks (cGANs), the generator network architecture incorporates explicit conditioning on physical parameters, such as effective particle mass density and subgrid kinetic energy, while the discriminator network is conditioned on low-resolution data as well as high-frequency content of the input data. High-fidelity direct numerical simulation (DNS) datasets, covering a range of particle Stokes numbers, particle mass loadings, and carrier gas turbulence regimes, including forced- and decaying-turbulence, serve as training and testing datasets. Extensive validation studies, including detailed analyses of energy spectra, probability density functions (PDFs), vorticity distributions, and wavelet-based decomposition demonstrate the model's accuracy and generalization capabilities across different particle parameters. The results show that the network utilizes particle data, mainly in the reconstruction of high-frequency details modulated by particles. Additionally, systematic assessment of the model's performance in capturing previously unseen flow regimes further validates its predictive capabilities.
physics.flu-dyn
We present a hybrid machine learning framework that combines Physics-Informed Neural Operators (PINOs) with score-based generative diffusion models to simulate the full spatio-temporal evolution of two-dimensional, incompressible, resistive magnetohydrodynamic (MHD) turbulence across a broad range of Reynolds numbers (). The framework leverages the equation-constrained generalization capabilities of PINOs to predict coherent, low-frequency dynamics, while a conditional diffusion model stochastically corrects high-frequency residuals, enabling accurate modeling of fully developed turbulence. Trained on a comprehensive ensemble of high-fidelity simulations with , the approach achieves state-of-the-art accuracy in regimes previously inaccessible to deterministic surrogates. At and , the model faithfully reconstructs the full spectral energy distributions of both velocity and magnetic fields late into the simulation, capturing non-Gaussian statistics, intermittent structures, and cross-field correlations with high fidelity. At extreme turbulence levels (), it remains the first surrogate capable of recovering the high-wavenumber evolution of the magnetic field, preserving large-scale morphology and enabling statistically meaningful predictions.
physics.flu-dyn
The hybrid wall-modeled large-eddy simulation (WMLES) and immersed boundary (IB) method offers significant flexibility for simulating high Reynolds number flows involving complex boundaries. However, the approximate boundary conditions (e.g., the wall shear stress boundary condition) developed for body-fitted grids in the literature are not directly applicable to IB methods. In this work, we propose a features-embedded-learning-IB (FEL-IB) wall model to approximate IB boundaries in the hybrid WMLES-IB method, in which the velocity at the IB node (a grid node located in the fluid that has at least one neighbor in the solid) is reconstructed using the power law of the wall, and the momentum flux at the interface between the IB nodes and the fluid nodes is approximated using a neural network model. The neural network model for momentum flux is first pretrained using high-fidelity simulation data of the flow over periodic hills and the logarithmic law, and then learned in the WMLES environment using the ensemble Kalman method. The proposed model is evaluated using two challenging cases: the flow over a body of revolution and the DARPA Suboff submarine model. For the first case, good agreement with the reference data is obtained for the vertical profiles of the streamwise velocity. For the flow over the DARPA Suboff submarine model, WMLES cases with two Reynolds numbers and two grid resolutions are carried out. Overall good a posteriori performance is observed for predicting the mean and root mean square of velocity profiles at various streamwise locations, as well as the skin-friction and pressure coefficients.
physics.flu-dyn
Turbulence poses challenges for numerical simulation due to its chaotic, multiscale nature and high computational cost. Traditional turbulence modeling often struggles with accuracy and long-term stability. Recent scientific machine learning (SciML) models, such as Fourier Neural Operators (FNO), show promise in solving PDEs, but are typically limited to one-step-ahead predictions and often fail over long time horizons, especially in 3D turbulence. This study proposes a framework to assess the reliability of neural operator models in turbulent flows. Using three-dimensional forced homogeneous isotropic turbulence (HIT) as a benchmark, we evaluate models in terms of uncertainty quantification (UQ), error propagation, and sensitivity to initial perturbations. Statistical tools such as error distribution analysis and autocorrelation functions (ACF) are used to assess predictive robustness and temporal coherence. Our proposed model, the factorized-implicit FNO (F-IFNO), improves long-term stability and accuracy by incorporating implicit factorization into the prediction process. It outperforms conventional LES and other FNO-based models in balancing accuracy, stability, and efficiency. The results highlight the importance of prediction constraints, time interval selection, and UQ in developing robust neural operator frameworks for turbulent systems.
physics.flu-dyn
Turbulent flows and fluid-structure interactions (FSI) are ubiquitous in scientific and engineering applications, but their accurate and efficient simulation remains a major challenge due to strong nonlinearities, multiscale interactions, and high computational demands. Traditional CFD solvers, though effective, struggle with scalability and adaptability for tasks such as inverse modeling, optimization, and data assimilation. Recent advances in machine learning (ML) have inspired hybrid modeling approaches that integrate neural networks with physics-based solvers to enhance generalization and capture unresolved dynamics. However, realizing this integration requires solvers that are not only physically accurate but also differentiable and GPU-efficient. In this work, we introduce Diff-FlowFSI, a GPU-accelerated, fully differentiable CFD platform designed for high-fidelity turbulence and FSI simulations. Implemented in JAX, Diff-FlowFSI features a vectorized finite volume solver combined with the immersed boundary method to handle complex geometries and fluid-structure coupling. The platform enables GPU-enabled fast forward simulations, supports automatic differentiation for gradient-based inverse problems, and integrates seamlessly with deep learning components for hybrid neural-CFD modeling. We validate Diff-FlowFSI across a series of benchmark turbulence and FSI problems, demonstrating its capability to accelerate scientific computing at the intersection of physics and machine learning.
physics.flu-dyn
Deep autoencoder neural networks can generate highly accurate, low-order representations of turbulence. We design a new family of autoencoders which are a combination of a 'dense-block' encoder-decoder structure (Page et al, J. Fluid Mech. 991, 2024), an 'implicit rank minimization' series of linear layers acting on the embeddings (Zeng et al, Mach. Learn. Sci. Tech. 5, 2024) and a full discrete+continuous symmetry reduction. These models are applied to two-dimensional turbulence in Kolmogorov flow for a range of Reynolds numbers , and used to estimate the dimension of the chaotic attractor, . We find that the dimension scales like – much weaker than known bounds on the global attractor which grow like . In addition, two-dimensional maps of the latent space in our models reveal a rich structure not seen in previous studies, including multiple classes of high-dissipation events at lower which guide bursting trajectories. We visualize the embeddings of large numbers of "turbulent" unstable periodic orbits, which the model indicates are distinct (in terms of features) from any flow snapshot in a large turbulent dataset, suggesting their dynamical irrelevance. This is in sharp contrast to their appearance in more traditional low-dimensional projections, in which they appear to lie within the turbulent attractor.