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
Physics-informed neural networks (PINNs) demonstrate promising potential in parameterized engineering turbulence optimization problems but face challenges, such as high data requirements and low computational accuracy when applied to engineering turbulence problems. This study proposes a framework that enhances the ability of PINNs to solve parametric turbulence problems without training datasets from experiments or CFD-Parametric Turbulence PINNs (PT-PINNs)). Two key methods are introduced to improve the accuracy and robustness of this framework. The first is a soft constraint method for turbulent viscosity calculation. The second is a pre-training method based on the conservation of flow rate in the flow field. The effectiveness of PT-PINNs is validated using a three-dimensional backward-facing step (BFS) turbulence problem with two varying parameters (Re = 3000-200000, ER = 1.1-1.5). PT-PINNs produce predictions that closely match experimental data and computational fluid dynamics (CFD) results across various conditions. Moreover, PT-PINNs offer a computational efficiency advantage over traditional CFD methods. The total time required to construct the parametric BFS turbulence model is 39 hours, one-sixteenth of the time required by traditional numerical methods. The inference time for a single-condition prediction is just 40 seconds-only 0.5% of a single CFD computation. These findings highlight the potential of PT-PINNs for future applications in engineering turbulence optimization problems.
physics.flu-dyn
This article sheds light on the late-time influence of initial conditions in Boussinesq Rayleigh-Taylor turbulence using an approach combining direct numerical simulations, machine learning and theory. The initial conditions are characterized by four non-dimensional numbers describing the statistical properties of random-phase multi-mode perturbations of an initial diffuse interface. Based on high-fidelity data, a surrogate physics-informed neural network is used to extrapolate the dynamics to very late times and unseen initial conditions, beyond the reach of simulations. This enables uncertainty and global sensitivity analyses to be carried out, revealing the influence of initial conditions in the late-time regime. While the results support the idea of a universal self-similar growth rate, the virtual time origin is found to be strongly sensitive to the initial Reynolds, perturbation steepness and bandwidth numbers. An analytical model based on the phenomenology of Rayleigh-Taylor mixing layers explains most of this dependency, and provide accurate predictions for the virtual time origin. It turns out that when the initial perturbation reaches nonlinear saturation earlier, the mixing layer also re-accelerates earlier, while the virtual time origin is larger.
physics.flu-dyn
Traditional Reynolds-averaged Navier-Stokes (RANS) equations often struggle to predict separated flows accurately. Recent studies have employed data-driven methods to enhance predictions by modifying baseline equations, such as field inversion and machine learning (FIML) with symbolic regression. However, data-driven turbulence models exhibit limited adaptability and are rarely applied to complex engineering problems. This study examines the application of data-driven turbulence models to complex three-dimensional high-lift configurations, extending their usability beyond previous applications. First, the generalizability of the SST-CND model, derived from conditioned field inversion and symbolic regression, is validated. Then, the spatially varying correction factor obtained through conditioned field inversion is transferred to the three-equation k-(v^2)-w model. The 30P30N three-element airfoil, the JAXA Standard Model (JSM), and the high-lift version of the NASA Common Research Model (CRM-HL) are numerically simulated. The results indicated that the SST-CND model significantly improves the prediction of stall characteristics, demonstrating satisfactory generalizability. The corrected k-(v^2 )-w-CND model accurately predicts the stall characteristics of CRM-HL, with a relative error of less than 5% compared to experimental results. This confirms the strong transferability of the model correction derived from conditioned field inversion across different turbulence models.
cs.LG
Thermoacoustic instability in annular combustors, essential to aero engines and modern gas turbines, can severely impair operational stability and efficiency, accurately recognizing and understanding various combustion modes is the prerequisite for understanding and controlling combustion instabilities. However, the high-dimensional spatial-temporal dynamics of turbulent flames typically pose considerable challenges to mode recognition. Based on the bidirectional temporal and nonlinear dimensionality reduction models, this study introduces a two-layer bidirectional long short-term memory variational autoencoder, Bi-LSTM-VAE model, to effectively recognize dynamical modes in annular combustion systems. Specifically, leveraging 16 pressure signals from a swirl-stabilized annular combustor, the model maps complex dynamics into a low-dimensional latent space while preserving temporal dependency and nonlinear behavior features through the recurrent neural network structure. The results show that the novel Bi-LSTM-VAE method enables a clear representation of combustion states in two-dimensional state space. Analysis of latent variable distributions reveals distinct patterns corresponding to a wide range of equivalence ratios and premixed fuel and air mass flow rates, offering novel insights into mode classification and transitions, highlighting this model's potential for deciphering complex thermoacoustic phenomena.
physics.flu-dyn
In recent years, sub-grid models for turbulent mixing have been developed by data-driven methods for large eddy simulation (LES). Super-resolution is a data-driven deconvolution technique in which deep convolutional neural networks are trained using direct numerical simulation (DNS) data to learn mappings between the input data from a low resolution domain to the super-resolved high resolution output domain. While the technique has been of a great success in a-priori tests, the assessment of its generalization capabilities is required for further a-posteriori applications. In this study we assess the generalization capability of a super-resolution generative adversarial network (GAN) in reconstructing scalars with different distributions. Forced turbulence mixing DNS data with a fixed Reynolds number but different bulk scalar distributions, are generated and used as training/testing datasets. The results show that the velocity vector field can be reconstructed well, but the model fails to super-resolve the scalars from out-of-sample distributions. Including two extreme mixture fraction distributions, namely double Pareto and semi-Gaussian, in the training dataset significantly improves the performance of the model, not only for those distributions, but also for previously unseen bimodal distributions.
physics.flu-dyn
Proper-orthogonal decomposition (POD) based reduced-order models (ROM) of structurally dominant fluid flow can support a wide range of engineering applications. Yet, although they perform well for unsteady laminar flows, their straightforward extension to turbulent flows fails to capture the effects of small scale eddies and often leads to divergent solutions. Several approaches to mimic nonlinear closure terms modeling techniques within ROM frameworks have been employed to include the effect of higher modes that are often neglected. Recent success of neural network based models show promising results in modeling the effects of turbulence. In this study, we augment POD-ROM with a recurrent neural network (RNN) to develop ROM for turbulent flows. We simulate a three dimensional flow past a circular cylinder at Reynolds number of 1000. We first compute the POD modes and project the Navier-Stokes equations onto the limited number of modes in a Galerkin approach to develop a conventional ROM and LES-inspired ROM for comparison. We then develop a hybrid model by integrating the output of Galerkin projection ROM and long short-term memory (LSTM) RNN and term it as a physics-guided machine learning (PGML) model. The novelty of this study is to introduce a hybrid model that integrates LES inspired ROM and RNN to achieve more accurate and reliable predictions of turbulent flows. The results demonstrate that PGML for higher temporal coefficients outperforms the conventional and LES-inspired ROM.
physics.flu-dyn
The design of fluid channel structures of reactors or separators of chemical processes is key to enhancing the mass transfer processes inside the devices. However, the systematic design of channel topological structures is difficult for complex turbulent flows. Here, we address this challenge by developing a machine learning framework to efficiently perform topology optimization of channel structures for turbulent mass transfer. We represent a topological structure using a neural network (referred to as `neural topology', which is optimized by employing pre-trained neural operators combined with a fine-tuning strategy with active data augmentation. The optimization is performed with two objectives: maximization of mass transfer efficiency and minimization of energy consumption, for the possible considerations of compromise between the two in real-world designs. The developed neural operator with active learning is data efficient in network training and demonstrates superior computational efficiency compared with traditional methods in obtaining optimal structures across a large design space. The optimization results are validated through experiments, proving that the optimized channel improves concentration uniformity by 37% compared with the original channel. We also demonstrate the variation of the optimal structures with changes in inlet velocity conditions, providing a reference for designing turbulent mass-transfer devices under different operating conditions.
physics.flu-dyn
Extending gradient-type turbulence closures to turbulent premixed flames is challenging due to the significant influence of combustion heat release. We incorporate a deep neural network (DNN) into Reynolds-averaged Navier–Stokes (RANS) models for the turbulent viscosity and thermal conductivity as nonlinear functions of the local flow state and thermochemical gradients. Our models are optimized over the RANS partial differential equations (PDEs) using an adjoint-based data assimilation procedure. Because we directly target the RANS solution, as opposed to the unclosed terms, successfully trained models are guaranteed to improve the in-sample accuracy of the DNN-augmented RANS predictions. We demonstrate the learned closures for in- and out-of-sample RANS predictions of compressible, premixed, turbulent jet flames with turbulent Damköhler numbers spanning the gradient- and counter-gradient transport regimes. The DNN-augmented RANS predictions have one to two orders of magnitude lower spatiotemporal mean-squared error than those using a baseline – model, even for Damköhler numbers far from those used for training. This demonstrates the accuracy, stability, and generalizability of the PDE-constrained modeling approach for turbulent jet flames over this relatively wide Damköhler number range.
physics.flu-dyn
This study aims to enhance the generalizability of Reynolds-averaged Navier-Stokes (RANS) turbulence models, which are crucial for engineering applications. Classic RANS turbulence models often struggle to predict separated flows accurately. Recently, Data-driven machine learning approaches for turbulence modeling have been explored to address this issue. However, these models are often criticized for their limited generalizability. In this study, we address this issue by incorporating non-local effects into data-driven turbulence modeling. Specifically, we introduce a transport equation for the correction term \b{eta} of the shear stress transport (SST) model to encode non-local information along the mean streamline. The coefficients of the equation are calibrated using high-fidelity data from the NASA hump and periodic hills. The resulting model, termed the \b{eta}-Transport model, demonstrates high accuracy across various separated flows outside the training set, including periodic hills with different geometries and Reynolds numbers, the curved backward-facing step, a two-dimensional bump, and a three-dimensional simplified car body. In all tested cases, the \b{eta}-Transport model yields smaller or equal prediction errors compared to those from classic local data-driven turbulence models using algebraic relations for \b{eta}. These results indicate improved generalizability for separated flows. Furthermore, the \b{eta}-Transport model shows similar accuracy to the baseline model in basic flows including the mixing layer and the channel flow. Therefore, the non-local modeling approach presented here offers a promising pathway for developing more generalizable data-driven turbulence models.
physics.flu-dyn
In this study, eXplainable Artificial Intelligence (XAI) methods are applied to analyze flow fields obtained through PIV measurements of an axisymmetric turbulent jet. A convolutional neural network (U-Net) was trained to predict velocity fields at subsequent time steps. Three XAI methods: SHapley Additive explanations (SHAP), Gradient-SHAP, and Grad-CAM were employed to identify the flow field regions relevant for prediction. SHAP requires predefined segmentation of the flow field into relevant regions, while Gradient-SHAP and Grad-CAM avoid this bias by generating gradient-based heatmaps. The results show that the most relevant structures do not necessarily coincide with regions of maximum vorticity but rather with those exhibiting moderate vorticity, highlighting the critical role of these regions in energy transfer and jet dynamics. Additionally, structures with high turbulent dissipation values are identified as the most significant. Gradient-SHAP and Grad-CAM methods reveal a uniform spatial distribution of relevant regions, emphasizing the contribution of nearly circular structures to turbulent mixing. This study advances the understanding of turbulent dynamics through XAI tools, providing an innovative approach to correlate machine learning models with physical phenomena.
cs.CV
Wake vortices - strong, coherent air turbulences created by aircraft - pose a significant risk to aviation safety and therefore require accurate and reliable detection methods. In this paper, we present an advanced, explainable machine learning method that utilizes Light Detection and Ranging (LiDAR) data for effective wake vortex detection. Our method leverages a dynamic graph CNN (DGCNN) with semantic segmentation to partition a 3D LiDAR point cloud into meaningful segments. Further refinement is achieved through clustering techniques. A novel feature of our research is the use of a perturbation-based explanation technique, which clarifies the model's decision-making processes for air traffic regulators and controllers, increasing transparency and building trust. Our experimental results, based on measured and simulated LiDAR scans compared against four baseline methods, underscore the effectiveness and reliability of our approach. This combination of semantic segmentation and clustering for real-time wake vortex tracking significantly advances aviation safety measures, ensuring that these are both effective and comprehensible.
cs.LG
We demonstrate that a deep learning emulator for chaotic systems can forecast phenomena absent from training data. Using the Kuramoto-Sivashinsky and beta-plane turbulence models, we evaluate the emulator through scenarios probing the fundamental phenomena of both systems: forecasting spontaneous relaminarisation, capturing initialisation of arbitrary chaotic states, zero-shot prediction of dynamics with parameter values outside of the training range, and characterisation of dynamical statistics from artificially restricted training datasets. Our results show that deep learning emulators can uncover emergent behaviours and rare events in complex systems by learning underlying mathematical rules, rather than merely mimicking observed patterns.
cs.LG
In recent years, augmentation of differentiable PDE solvers with neural networks has shown promising results, particularly in fluid simulations. However, most approaches rely on convolutional neural networks and custom solvers operating on Cartesian grids with efficient access to cell data. This particular choice poses challenges for industrial-grade solvers that operate on unstructured meshes, where access is restricted to neighboring cells only. In this work, we address this limitation using a novel architecture, named Transported Memory Networks. The architecture draws inspiration from both traditional turbulence models and recurrent neural networks, and it is fully compatible with generic discretizations. Our results show that it is point-wise and statistically comparable to, or improves upon, previous methods in terms of both accuracy and computational efficiency.
physics.flu-dyn
Entangled vortex filaments are essential to turbulence, serving as coherent structures that govern nonlinear fluid dynamics and support the reconstruction of fluid fields to reveal statistical properties. This study introduces an quantum implicit representation of vortex filaments in turbulence, employing a level-set method that models the filaments as the intersection of the real and imaginary zero iso-surfaces of a complex scalar field. Describing the fluid field via the scalar field offers distinct advantages in capturing complex structures, topological properties, and fluid dynamics, while opening new avenues for innovative solutions through quantum computing platforms. The representation is reformulated into an eigenvalue problem for Hermitian matrices, enabling the conversion of velocity fields into complex scalar fields that embed the vortex filaments. The resulting optimization is addressed using a variational quantum eigensolver, with Pauli operator truncation and deep learning techniques applied to improve efficiency and reduce noise. The proposed quantum framework achieves a near-linear time complexity and a exponential storage reduction while maintaining a balance of accuracy, robustness, and versatility, presenting a promising tool for turbulence analysis, vortex dynamics research, and machine learning dataset generation.
physics.flu-dyn
Turbulent flow remains a challenging subject, despite extensive efforts to find analytical descriptions. Modeling small scales of motion is crucial for saving time and resources in numerical simulations, particularly in industrial applications. Here we attempt to model small scales of motion by creating closures for a Shell model of turbulence, more specifically for Sabra. Shell models are infinite dimensional dynamical systems that retain most key properties of Navier-Stokes equation, such as energy cascade and intermittency, while being computationally treatable. To account for Sabra's intermittent fluctuations we employ a set of scaling relations that recover a hidden symmetry and leaves us with universal statistics across the inertial range. On data from these rescaled variables we then adapt and apply two machine learning tools, a variational auto-encoder and sparse identification of non-linear dynamics. We estimate the data's densities and dynamics in order to then generate new instances of data. Given a mid-inertial range cutoff scale, we evolve reduced models in time, resolving only scales of motion larger than the cutoff scale, closing the reduced model with data generated by the machine learning tools. We compare statistics of our reduced models against a Sabra's fully resolved simulation to evaluate each closure's performances. Our results show improvement regarding previous work, and all our closures are probabilistic and cutoff-independent.
physics.flu-dyn
We present a data-driven approach to Reynolds-averaged Navier-Stokes turbulence closure modelling in magnetohydrodynamic (MHD) flows. In these flows the magnetic field interacting with the conductive fluid induces unconventional turbulence states such as quasi two-dimensional (2D) turbulence, and turbulence suppression, which are poorly represented by standard Boussinesq models. Our data-driven approach uses time-averaged Large Eddy Simulation (LES) data of annular pipe flows, at different Hartmann numbers, to derive corrections for the - SST model. Correction fields are obtained by injecting time averaged LES fields into the MHD RANS equations, and examining the remaining residuals. The correction to the Reynolds-stress anisotropy is approximated with a modified Tensor Basis Neural Network (TBNN). We extend the generalised eddy hypothesis with a traceless antisymmetric tensor representation of the Lorentz force to obtain MHD flow features, thus keeping Galilean and frame invariance while including MHD effects in the turbulence model. The resulting data-driven models are shown to reduce errors in the mean flow, and to generalise to annular flow cases with different Hartmann numbers from those of the training cases.
physics.plasm-ph
Magnetic geometry has a significant effect on the level of turbulent transport in fusion plasmas. Here, we model and analyze this dependence using multiple machine learning methods and a dataset of > 200,000 nonlinear simulations of ion-temperature-gradient turbulence in diverse non-axisymmetric geometries. The dataset is generated using a large collection of both optimized and randomly generated stellarator equilibria. At fixed gradients, the turbulent heat flux varies between geometries by several orders of magnitude. Trends are apparent among the configurations with particularly high or low heat flux. Regression and classification techniques from machine learning are then applied to extract patterns in the dataset. Due to a symmetry of the gyrokinetic equation, the heat flux and regressions thereof should be invariant to translations of the raw features in the parallel coordinate, similar to translation invariance in computer vision applications. Multiple regression models including convolutional neural networks (CNNs) and decision trees can achieve reasonable predictive power for the heat flux in held-out test configurations, with highest accuracy for the CNNs. Using Spearman correlation, sequential feature selection, and Shapley values to measure feature importance, it is consistently found that the most important geometric lever on the heat flux is the flux surface compression in regions of bad curvature. The second most important feature relates to the magnitude of geodesic curvature. These two features align remarkably with surrogates that have been proposed based on theory, while the methods here allow a natural extension to more features for increased accuracy. The dataset, released with this publication, may also be used to test other proposed surrogates, and we find many previously published proxies do correlate well with both the heat flux and stability boundary.
physics.flu-dyn
This paper applies Bayesian-optimization-RANS (turbo-RANS) to improve Reynolds-averaged Navier-Stokes (RANS) turbulence models for a converging-diverging channel, a case with adverse pressure gradients and flow separation. Using Bayesian optimization, the Generalized - (GEKO) model was calibrated by tuning and with sparse direct numerical simulation (DNS) data at . The calibration followed the Generalized Error Distribution-based Calibration Procedure (GEDCP), optimizing coefficients based on pressure recovery () and skin friction (). The optimized model was evaluated beyond training data. Streamwise velocity () predictions at were compared to DNS to assess improvements in and . To test robustness, comparisons were made against large-eddy simulation (LES) data at for velocity and skin friction. Results show that optimized GEKO (turbo-RANS) improves wall quantity predictions, particularly reattachment. Improved velocity profiles at both Reynolds numbers suggest Bayesian-optimized coefficients enhance adverse pressure gradient modeling. The model retains accuracy across different , showing turbo-RANS' potential in turbulence model corrections that generalize across flows. While skin friction predictions showed limited improvement due to constraints of two-equation models, this study highlights the role of machine learning-assisted RANS calibration in improving predictive accuracy for complex flows. The results suggest optimized coefficients from a single dataset can be applied across moderate variations, improving turbo-RANS' applicability for turbulence model tuning.
physics.flu-dyn
In this work we present a framework to explain the prediction of the velocity fluctuation at a certain wall-normal distance from wall measurements with a deep-learning model. For this purpose, we apply the deep-SHAP method to explain the velocity fluctuation prediction in wall-parallel planes in a turbulent open channel at a friction Reynolds number . The explainable-deep-learning methodology comprises two stages. The first stage consists of training the estimator. In this case, the velocity fluctuation at a wall-normal distance of 15 wall units is predicted from the wall-shear stress and wall-pressure. In the second stage, the deep-SHAP algorithm is applied to estimate the impact each single grid point has on the output. This analysis calculates an importance field, and then, correlates the high-importance regions calculated through the deep-SHAP algorithm with the wall-pressure and wall-shear stress distributions. The grid points are then clustered to define structures according to their importance. We find that the high-importance clusters exhibit large pressure and shear-stress fluctuations, although generally not corresponding to the highest intensities in the input datasets. Their typical values averaged among these clusters are equal to one to two times their standard deviation and are associated with streak-like regions. These high-importance clusters present a size between 20 and 120 wall units, corresponding to approximately 100 and 600 for the case of a commercial aircraft.
physics.flu-dyn
Direct numerical simulation of turbulence at realistic Reynolds numbers is still beyond current computational capability, necessitating models that reduce the number of resolved spatial scales. Motivated by phenomenology and recent data-driven works based on universality of the smallest scales in fully developed turbulence, the statistical dynamics of the velocity gradient tensor (VGT) at the Kolmogorov scale become of critical importance in advancing turbulence models. Physics-informed machine learning has found considerable success in exploiting large datasets taken from direct numerical simulation of Navier-Stokes to improve models for the evolution of the VGT. In this work, we follow the long line of blending physical insight with data analysis to simultaneously advance both the modeling and understanding of the phenomenology of the VGT. Using the intimate connection between VGT evolution and fluid deformation, we develop the Lagrangian attention tensor network approach that significantly improves over current physics-informed machine learning methods. We demonstrate state-of-the-art performance in both a-priori and a-posteriori metrics, before interpreting the trained attention mechanisms to discover a surprising connection between the history of the strain-rate-tensor and the pressure Hessian.