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
The applicability of computational fluid dynamics (CFD) based design tools depend on the accuracy and complexity of the physical models, for example turbulence models, which remains an unsolved problem in physics, and rotor models that dictates the computational cost of rotorcraft and wind/hydro turbine farm simulations. The research focuses on investigation of the ability of neural networks to learn correlation between desired modeling variables and flow parameters, thereby providing surrogate models. For the turbulence modeling, the machine learned turbulence model is developed for unsteady boundary layer flow, and the predictions are validated against DNS data and compared with one-equation unsteady Reynolds Averaged NavierStokes (URANS) predictions. The machine-learned model performs much better than the URANS model due to its ability to incorporate the non-linear correlation between turbulent stresses and rate-of-strain. The development of the surrogate rotor model builds on the hypothesis that if a model can mimic the axial and tangential momentum deficit generated by a blade resolved model, then it should produce a qualitatively and quantitatively similar wake recovery. An initial validation of the hypothesis was performed, which showed encouraging results.
cs.LG
The immense computational cost of traditional numerical weather and climate models has sparked the development of machine learning (ML) based emulators. Because ML methods benefit from long records of training data, it is common to use datasets that are temporally subsampled relative to the time steps required for the numerical integration of differential equations. Here, we investigate how this often overlooked processing step affects the quality of an emulator's predictions. We implement two ML architectures from a class of methods called reservoir computing: (1) a form of Nonlinear Vector Autoregression (NVAR), and (2) an Echo State Network (ESN). Despite their simplicity, it is well documented that these architectures excel at predicting low dimensional chaotic dynamics. We are therefore motivated to test these architectures in an idealized setting of predicting high dimensional geophysical turbulence as represented by Surface Quasi-Geostrophic dynamics. In all cases, subsampling the training data consistently leads to an increased bias at small spatial scales that resembles numerical diffusion. Interestingly, the NVAR architecture becomes unstable when the temporal resolution is increased, indicating that the polynomial based interactions are insufficient at capturing the detailed nonlinearities of the turbulent flow. The ESN architecture is found to be more robust, suggesting a benefit to the more expensive but more general structure. Spectral errors are reduced by including a penalty on the kinetic energy density spectrum during training, although the subsampling related errors persist. Future work is warranted to understand how the temporal resolution of training data affects other ML architectures.
physics.flu-dyn
Generally, reduced order models of fluid flows are obtained by projecting the Navier-Stokes equations onto a reduced subspace spanned by vector functions that carry the meaningful information of the dynamics. A common method to generate such subspace is the Proper Orthogonal Decomposition. This projection strategy is intrusive since it assumes that the approximation model used to solve the high fidelity flow problem is known and accessible. In the present article, we propose a non-intrusive paradigm based on Machine Learning to build Closed Parametric Reduced Order Models (ML-PROM) relevant to fluid dynamics. With no prior knowledge requirement of the approximation model, this method is purely data-driven as it operates directly on data regardless their origin, DNS, RANS simulations or experiment. The key idea to build the ML-CPROM is to use the generally known form of Galerkin ROMs and assimilate the time variations of the temporal POD modes to a nonlinear quadratic form taking a closure right hand side member. This last term is introduced to account for uncaptured dynamics due to data noise, POD truncation errors and time integration schemes. For parameter variation, the ML-CPROM is updated by interpolation on the quotient manifold of the set of fixed rank matrices by the orthogonal group. The predicted closure term is afterwards calculated by a Long-Short-Term-Memory neural network. We assess the potential of the proposed approach on the parametric examples of the lid-driven cavity flow and the flow past a cylinder by varying the Reynolds number through the viscosity, and the Ahmed-Body flow by varying the geometry through the rear slant angle. We show on these examples that our method enables to recover the dynamics with a good accuracy, not only for the training parameter points, but also for unseen parameter values for which the model was not priory trained.
physics.flu-dyn
The convective heat transfer in a turbulent boundary layer (TBL) on a flat plate is enhanced using an artificial intelligence approach based on linear genetic algorithms control (LGAC). The actuator is a set of six slot jets in crossflow aligned with the freestream. An open-loop optimal periodic forcing is defined by the carrier frequency, the duty cycle and the phase difference between actuators as control parameters. The control laws are optimised with respect to the unperturbed TBL and to the actuation with a steady jet. The cost function includes the wall convective heat transfer rate and the cost of the actuation. The performance of the controller is assessed by infrared thermography and characterised also with particle image velocimetry measurements. The optimal controller yields a slightly asymmetric flow field. The LGAC algorithm converges to the same frequency and duty cycle for all the actuators. It is noted that such frequency is strikingly equal to the inverse of the characteristic travel time of large-scale turbulent structures advected within the near-wall region. The phase difference between multiple jet actuation has shown to be very relevant and the main driver of flow asymmetry. The results pinpoint the potential of machine learning control in unravelling unexplored controllers within the actuation space. Our study furthermore demonstrates the viability of employing sophisticated measurement techniques together with advanced algorithms in an experimental investigation.
physics.ao-ph
Turbulent fluctuations of the atmospheric refraction index, so-called optical turbulence, can significantly distort propagating laser beams. Therefore, modeling the strength of these fluctuations () is highly relevant for the successful development and deployment of future free-space optical communication links. In this letter, we propose a physics-informed machine learning (ML) methodology, -ML, based on dimensional analysis and gradient boosting to estimate . Through a systematic feature importance analysis, we identify the normalized variance of potential temperature as the dominating feature for predicting . For statistical robustness, we train an ensemble of models which yields high performance on the out-of-sample data of .
physics.flu-dyn
Simulating turbulence is critical for many societally important applications in aerospace engineering, environmental science, the energy industry, and biomedicine. Large eddy simulation (LES) has been widely used as an alternative to direct numerical simulation (DNS) for simulating turbulent flows due to its reduced computational cost. However, LES is unable to capture all of the scales of turbulent transport accurately. Reconstructing DNS from low-resolution LES is critical for many scientific and engineering disciplines, but it poses many challenges to existing super-resolution methods due to the spatio-temporal complexity of turbulent flows. In this work, we propose a new physics-guided neural network for reconstructing the sequential DNS from low-resolution LES data. The proposed method leverages the partial differential equation that underlies the flow dynamics in the design of spatio-temporal model architecture. A degradation-based refinement method is also developed to enforce physical constraints and further reduce the accumulated reconstruction errors over long periods. The results on two different types of turbulent flow data confirm the superiority of the proposed method in reconstructing the high-resolution DNS data and preserving the physical characteristics of flow transport.
physics.flu-dyn
Turbulence modeling within the RANS equations' framework is essential in engineering due to its high efficiency. Field inversion and machine learning (FIML) techniques have improved RANS models' predictive capabilities for separated flows. However, FIML-generated models often lack interpretability, limiting physical understanding and manual improvements based on prior knowledge. Additionally, these models may struggle with generalization in flow fields distinct from the training set. This study addresses these issues by employing symbolic regression (SR) to derive an analytical relationship between the correction factor of the baseline turbulence model and local flow variables, enhancing the baseline model's ability to predict separated flow across diverse test cases. The shear-stress-transport (SST) model undergoes field inversion on a curved backward-facing step (CBFS) case to obtain the corrective factor field beta, and SR is used to derive a symbolic map between local flow features and beata. The SR-derived analytical function is integrated into the original SST model, resulting in the SST-SR model. The SST-SR model's generalization capabilities are demonstrated by its successful predictions of separated flow on various test cases, including 2D-bump cases with varying heights, periodic hill case where separation is dominated by geometric features, and the three-dimensional Ahmed-body case. In these tests, the model accurately predicts flow fields, showing its effectiveness in cases completely different from the training set. The Ahmed-body case, in particular, highlights the model's ability to predict the three-dimensional massively separated flows. When applied to a turbulent boundary layer with Re_L=1.0E7, the SST-SR model predicts wall friction coefficient and log layer comparably to the original SST model, maintaining the attached boundary layer prediction performance.
physics.flu-dyn
Turbulent flows consist of a wide range of interacting scales. Since the scale range increases as some power of the flow Reynolds number, a faithful simulation of the entire scale range is prohibitively expensive at high Reynolds numbers. The most expensive aspect concerns the small scale motions; thus, major emphasis is placed on understanding and modeling them, taking advantage of their putative universality. In this work, using physics-informed deep learning methods, we present a modeling framework to capture and predict the small scale dynamics of turbulence, via the velocity gradient tensor. The model is based on obtaining functional closures for the pressure Hessian and viscous Laplacian contributions as functions of velocity gradient tensor. This task is accomplished using deep neural networks that are consistent with physical constraints and incorporate Reynolds number dependence explicitly to account for small-scale intermittency. We then utilize a massive direct numerical simulation database, spanning two orders of magnitude in the large-scale Reynolds number, for training and validation. The model learns from low to moderate Reynolds numbers, and successfully predicts velocity gradient statistics at both seen and higher (unseen) Reynolds numbers. The success of our present approach demonstrates the viability of deep learning over traditional modeling approaches in capturing and predicting small scale features of turbulence.
physics.flu-dyn
In this study, an efficient deep-learning model is developed to predict unavailable parameters, e.g., streamwise velocity, temperature, and pressure from available velocity components. This model, termed mapping generative adversarial network (M-GAN), consists of a label information generator (LIG) and an enhanced super-resolution generative adversarial network (ESRGAN). LIG can generate label information helping the model to predict different parameters. The GAN-based model receives the label information from LIG and existing velocity data to generate the unavailable parameters. Two-dimensional (2D) Rayleigh-B{é}nard flow and turbulent channel flow are used to evaluate the performance of M-GAN. Firstly, M-GAN is trained and evaluated by 2D direct numerical simulation (DNS) data of a Rayleigh-B{é}nard flow. From the results, it can be shown that M-GAN can predict temperature distribution from the two-dimensional velocities. Furthermore, DNS data of turbulent channel flow at two different friction Reynolds numbers = 180 and 550 are applied simultaneously to train the M-GAN and examine its predicting ability for the pressure fields and the streamwise velocity from the other two velocity components. The instantaneous and statistical results of the predicted data agree well with the DNS data, even for the flow at = 395, indicating that M-GAN can be trained to learn the mapping function of the unknown fields with good interpolation capability.
physics.flu-dyn
We parameterize sub-grid scale (SGS) fluxes in sinusoidally forced two-dimensional turbulence on the -plane at high Reynolds numbers (Re25000) using simple 2-layer Convolutional Neural Networks (CNN) having only O(1000)parameters, two orders of magnitude smaller than recent studies employing deeper CNNs with 8-10 layers; we obtain stable, accurate, and long-term online or a posteriori solutions at 16X downscaling factors. Our methodology significantly improves training efficiency and speed of online Large Eddy Simulations (LES) runs, while offering insights into the physics of closure in such turbulent flows. Our approach benefits from extensive hyperparameter searching in learning rate and weight decay coefficient space, as well as the use of cyclical learning rate annealing, which leads to more robust and accurate online solutions compared to fixed learning rates. Our CNNs use either the coarse velocity or the vorticity and strain fields as inputs, and output the two components of the deviatoric stress tensor. We minimize a loss between the SGS vorticity flux divergence (computed from the high-resolution solver) and that obtained from the CNN-modeled deviatoric stress tensor, without requiring energy or enstrophy preserving constraints. The success of shallow CNNs in accurately parameterizing this class of turbulent flows implies that the SGS stresses have a weak non-local dependence on coarse fields; it also aligns with our physical conception that small-scales are locally controlled by larger scales such as vortices and their strained filaments. Furthermore, 2-layer CNN-parameterizations are more likely to be interpretable and generalizable because of their intrinsic low dimensionality.
physics.flu-dyn
The present study represents a data-driven turbulent model with Galilean invariance preservation based on machine learning algorithm. The fully connected neural network (FCNN) and tensor basis neural network (TBNN) [Ling et al. (2016)] are established. The models are trained based on five kinds of flow cases with Reynolds Averaged Navier-Stokes (RANS) and high-fidelity data. The mappings between two invariant sets, mean strain rate tensor and mean rotation rate tensor as well as additional consideration of invariants of turbulent kinetic energy gradients, and the Reynolds stress anisotropy tensor are trained. The prediction of the Reynolds stress anisotropy tensor is treated as user's defined RANS turbulent model with a modified turbulent kinetic energy transport equation. The results show that both FCNN and TBNN models can provide more accurate predictions of the anisotropy tensor and turbulent state in square duct flow and periodic flow cases compared to the RANS model. The machine learning based turbulent model with turbulent kinetic energy gradient related invariants can improve the prediction precision compared with only mean strain rate tensor and mean rotation rate tensor based models. The TBNN model is able to predict a better flow velocity profile compared with FCNN model due to a prior physical knowledge.
physics.flu-dyn
A machine-learned (ML) model is developed to enhance the accuracy of turbulence transport equations of Reynolds Averaged Navier Stokes (RANS) solver and applied for periodic hill test case, which involves complex flow regimes, such as attached boundary layer, shear-layer, and separation and reattachment. The accuracy of the model is investigated in extrapolation modes, i.e., the test case has much larger separation bubble and higher turbulence than the training cases. A parametric study is also performed to understand the effect of network hyperparameters on training and model accuracy and to quantify the uncertainty in model accuracy due to the non-deterministic nature of the neural network training. The study revealed that, for any network, less than optimal mini-batch size results in overfitting, and larger than optimal batch size reduces accuracy. Data clustering is found to be an efficient approach to prevent the machine-learned model from over-training on more prevalent flow regimes, and results in a model with similar accuracy using almost one-third of the training dataset. Feature importance analysis reveals that turbulence production is correlated with shear strain in the free-shear region, with shear strain and wall-distance and local velocity-based Reynolds number in the boundary layer regime, and with streamwise velocity gradient in the accelerating flow regime. The flow direction is found to be key in identifying flow separation and reattachment regime. Machine-learned models perform poorly in extrapolation mode, wherein the prediction shows less than 10% correlation with Direct Numerical Simulation (DNS). A priori tests reveal that model predictability improves significantly as the hill dataset is partially added during training in a partial extrapolation model, e.g., with the addition of only 5% of the hill data increases correlation with DNS to 80%.
physics.flu-dyn
This paper focuses on the use of reinforcement learning (RL) as a machine-learning (ML) modeling tool for near-wall turbulence. RL has demonstrated its effectiveness in solving high-dimensional problems, especially in domains such as games. Despite its potential, RL is still not widely used for turbulence modeling and is primarily used for flow control and optimization purposes. A new RL wall model (WM) called VYBA23 is developed in this work, which uses agents dispersed in the flow near the wall. The model is trained on a single Reynolds number () and does not rely on high-fidelity data, as the back-propagation process is based on a reward rather than output error. The states of the RLWM, which are the representation of the environment by the agents, are normalized to remove dependence on the Reynolds number. The model is tested and compared to another RLWM (BK22) and to an equilibrium wall model, in a half-channel flow at eleven different Reynolds numbers (). The effects of varying agents' parameters such as actions range, time-step, and spacing are also studied. The results are promising, showing little effect on the average flow field but some effect on wall-shear stress fluctuations and velocity fluctuations. This work offers positive prospects for developing RLWMs that can recover physical laws, and for extending this type of ML models to more complex flows in the future.
cs.LG
Estimating fluid dynamics is classically done through the simulation and integration of numerical models solving the Navier-Stokes equations, which is computationally complex and time-consuming even on high-end hardware. This is a notoriously hard problem to solve, which has recently been addressed with machine learning, in particular graph neural networks (GNN) and variants trained and evaluated on datasets of static objects in static scenes with fixed geometry. We attempt to go beyond existing work in complexity and introduce a new model, method and benchmark. We propose EAGLE, a large-scale dataset of 1.1 million 2D meshes resulting from simulations of unsteady fluid dynamics caused by a moving flow source interacting with nonlinear scene structure, comprised of 600 different scenes of three different types. To perform future forecasting of pressure and velocity on the challenging EAGLE dataset, we introduce a new mesh transformer. It leverages node clustering, graph pooling and global attention to learn long-range dependencies between spatially distant data points without needing a large number of iterations, as existing GNN methods do. We show that our transformer outperforms state-of-the-art performance on, both, existing synthetic and real datasets and on EAGLE. Finally, we highlight that our approach learns to attend to airflow, integrating complex information in a single iteration.
physics.flu-dyn
Despite its great scientific and technological importance, wall-bounded turbulence is an unresolved problem in classical physics that requires new perspectives to be tackled. One of the key strategies has been to study interactions among the energy-containing coherent structures in the flow. Such interactions are explored in this study for the first time using an explainable deep-learning method. The instantaneous velocity field obtained from a turbulent channel flow simulation is used to predict the velocity field in time through a U-net architecture. Based on the predicted flow, we assess the importance of each structure for this prediction using the game-theoretic algorithm of SHapley Additive exPlanations (SHAP). This work provides results in agreement with previous observations in the literature and extends them by revealing that the most important structures in the flow are not necessarily the ones with the highest contribution to the Reynolds shear stress. We also apply the method to an experimental database, where we can identify completely new structures based on their importance score. This framework has the potential to shed light on numerous fundamental phenomena of wall-bounded turbulence, including novel strategies for flow control.
math.NA
In turbulence modeling, we are concerned with finding closure models that represent the effect of the subgrid scales on the resolved scales. Recent approaches gravitate towards machine learning techniques to construct such models. However, the stability of machine-learned closure models and their abidance by physical structure (e.g. symmetries, conservation laws) are still open problems. To tackle both issues, we take the `discretize first, filter next' approach. In this approach we apply a spatial averaging filter to existing fine-grid discretizations. The main novelty is that we introduce an additional set of equations which dynamically model the energy of the subgrid scales. Having an estimate of the energy of the subgrid scales, we can use the concept of energy conservation to derive stability. The subgrid energy containing variables are determined via a data-driven technique. The closure model is used to model the interaction between the filtered quantities and the subgrid energy. Therefore the total energy should be conserved. Abiding by this conservation law yields guaranteed stability of the system. In this work, we propose a novel skew-symmetric convolutional neural network architecture that satisfies this law. The result is that stability is guaranteed, independent of the weights and biases of the network. Importantly, as our framework allows for energy exchange between resolved and subgrid scales it can model backscatter. To model dissipative systems (e.g. viscous flows), the framework is extended with a diffusive component. The introduced neural network architecture is constructed such that it also satisfies momentum conservation. We apply the new methodology to both the viscous Burgers' equation and the Korteweg-De Vries equation in 1D. The novel architecture displays superior stability properties when compared to a vanilla convolutional neural network.
physics.flu-dyn
Turbulence is characterised by chaotic dynamics and a high-dimensional state space, which make this phenomenon challenging to predict. However, turbulent flows are often characterised by coherent spatiotemporal structures, such as vortices or large-scale modes, which can help obtain a latent description of turbulent flows. However, current approaches are often limited by either the need to use some form of thresholding on quantities defining the isosurfaces to which the flow structures are associated or the linearity of traditional modal flow decomposition approaches, such as those based on proper orthogonal decomposition. This problem is exacerbated in flows that exhibit extreme events, which are rare and sudden changes in a turbulent state. The goal of this paper is to obtain an efficient and accurate reduced-order latent representation of a turbulent flow that exhibits extreme events. Specifically, we employ a three-dimensional multiscale convolutional autoencoder (CAE) to obtain such latent representation. We apply it to a three-dimensional turbulent flow. We show that the Multiscale CAE is efficient, requiring less than 10% degrees of freedom than proper orthogonal decomposition for compressing the data and is able to accurately reconstruct flow states related to extreme events. The proposed deep learning architecture opens opportunities for nonlinear reduced-order modeling of turbulent flows from data.
physics.flu-dyn
Dynamical systems with extreme events are difficult to capture with data-driven modeling, due to the relative scarcity of data within extreme events compared to the typical dynamics of the system, and the strong dependence of the long-time occurrence of extreme events on short-time conditions.A recently developed technique [Floryan, D. & Graham, M. D. Data-driven discovery of intrinsic dynamics. Nat Mach Intell , 1113-1120 (2022)], here denoted as , or CANDyMan, overcomes these difficulties by decomposing the time series into separate charts based on data similarity, learning dynamical models on each chart via individual time-mapping neural networks, then stitching the charts together to create a single atlas to yield a global dynamical model. We apply CANDyMan to a nine-dimensional model of turbulent shear flow between infinite parallel free-slip walls under a sinusoidal body force [Moehlis, J., Faisst, H. & Eckhardt, B. A low-dimensional model for turbulent shear flows. New J Phys , 56 (2004)], which undergoes extreme events in the form of intermittent quasi-laminarization and long-time full laminarization. We demonstrate that the CANDyMan method allows the trained dynamical models to more accurately forecast the evolution of the model coefficients, reducing the error in the predictions as the model evolves forward in time. The technique exhibits more accurate predictions of extreme events, capturing the frequency of quasi-laminarization events and predicting the time until full laminarization more accurately than a single neural network.
physics.flu-dyn
A model based on a convolutional neural network (CNN) is designed to reconstruct the three-dimensional turbulent flows beneath a free surface using surface measurements, including the surface elevation and surface velocity. Trained on datasets obtained from the direct numerical simulation (DNS) of turbulent open-channel flows with a deformable free surface, the proposed model can accurately reconstruct the near-surface flow field and capture the characteristic large-scale flow structures away from the surface. The reconstruction performance of the model, measured by metrics such as the normalised mean squared reconstruction errors and scale-specific errors, is considerably better than that of the traditional linear stochastic estimation (LSE) method. We further analyse the saliency maps of the CNN model and the kernels of the LSE model and obtain insights into how the two models utilise surface features to reconstruct subsurface flows. The importance of different surface variables is analysed based on the saliency map of the CNN, which reveals knowledge about the surface-subsurface relations. The CNN is also shown to have a good generalization capability with respect to the Froude number if a model trained for a flow with a high Froude number is applied to predict flows with lower Froude numbers. The results presented in this work indicate that the CNN is effective regarding the detection of subsurface flow structures and by interpreting the surface-subsurface relations underlying the reconstruction model, the CNN can be a promising tool for assisting with the physical understanding of free-surface turbulence.
cs.LG
The lacking of analytic solutions of diverse partial differential equations (PDEs) gives birth to a series of computational techniques for numerical solutions. Although numerous latest advances are accomplished in developing neural operators, a kind of neural-network-based PDE solver, these solvers become less accurate and explainable while learning long-term behaviors of non-linear PDE families. In this paper, we propose the Koopman neural operator (KNO), a new neural operator, to overcome these challenges. With the same objective of learning an infinite-dimensional mapping between Banach spaces that serves as the solution operator of the target PDE family, our approach differs from existing models by formulating a non-linear dynamic system of equation solution. By approximating the Koopman operator, an infinite-dimensional operator governing all possible observations of the dynamic system, to act on the flow mapping of the dynamic system, we can equivalently learn the solution of a non-linear PDE family by solving simple linear prediction problems. We validate the KNO in mesh-independent, long-term, and5zero-shot predictions on five representative PDEs (e.g., the Navier-Stokes equation and the Rayleigh-B{é}nard convection) and three real dynamic systems (e.g., global water vapor patterns and western boundary currents). In these experiments, the KNO exhibits notable advantages compared with previous state-of-the-art models, suggesting the potential of the KNO in supporting diverse science and engineering applications (e.g., PDE solving, turbulence modelling, and precipitation forecasting).