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
Turbulent flow control has numerous applications and building reduced-order models (ROMs) of the flow and the associated feedback control laws is extremely challenging. Despite the complexity of building data-driven ROMs for turbulence, the superior representational capacity of deep neural networks has demonstrated considerable success in learning ROMs. Nevertheless, these strategies are typically devoid of physical foundations and often lack interpretability. Conversely, the Proper Orthogonal Decomposition (POD) based Galerkin projection (GP) approach for ROM has been popular in many problems owing to its theoretically consistent and explainable physical foundations. However, a key limitation is that the ordinary differential equations (ODEs) arising from GP ROMs are highly susceptible to instabilities due to truncation of POD modes and lead to deterioration in temporal predictions. In this work, we propose a \textit{differentiable programming} approach that blends the strengths of both these strategies, by embedding neural networks explicitly into the GP ODE structure, termed Neural Galerkin projection. We demonstrate this approach on the isentropic Navier-Stokes equations for compressible flow over a cavity at a moderate Mach number. When provided the structure of the projected equations, we show that the Neural Galerkin approach implicitly learns stable ODE coefficients from POD coefficients and demonstrates significantly longer and accurate time horizon predictions, when compared to the classical POD-GP assisted by calibration. We observe that the key benefits of this differentiable programming-based approach include increased flexibility in physics-based learning, very low computational costs, and a significant increase in interpretability, when compared to purely data-driven neural networks.
physics.flu-dyn
Modelling the near-wall region of wall-bounded turbulent flows is a widespread practice to reduce the computational cost of large-eddy simulations (LESs) at high Reynolds number. As a first step towards a data-driven wall-model, a neural-network-based approach to predict the near-wall behaviour in a turbulent open channel flow is investigated. The fully-convolutional network (FCN) proposed by Guastoni et al. [preprint, arXiv:2006.12483] is trained to predict the two-dimensional velocity-fluctuation fields at , using the sampled fluctuations in wall-parallel planes located farther from the wall, at . The data for training and testing is obtained from a direct numerical simulation (DNS) at friction Reynolds numbers and . The turbulent velocity-fluctuation fields are sampled at various wall-normal locations, i.e. . At , the FCN can take advantage of the self-similarity in the logarithmic region of the flow and predict the velocity-fluctuation fields at using the velocity-fluctuation fields at as input with less than 20% error in prediction of streamwise-fluctuations intensity. These results are an encouraging starting point to develop a neural-network based approach for modelling turbulence at the wall in numerical simulations.
physics.flu-dyn
Autoencoders and generative neural network models have recently gained popularity in fluid mechanics due to their spontaneity and low processing time instead of high fidelity CFD simulations. Auto encoders are used as model order reduction tools in applications of fluid mechanics by compressing input high-dimensional data using an encoder to map the input space into a lower-dimensional latent space. Whereas, generative models such as Variational Auto-encoders (VAEs) and Generative Adversarial Networks (GANs) are proving to be effective in generating solutions to chaotic models with high 'randomness' such as turbulent flows. In this study, forced isotropic turbulence flow is generated by parameterizing into some basic statistical characteristics. The models trained on pre-simulated data from dependencies on these characteristics and the flow generation is then affected by varying these parameters. The latent vectors pushed along the generator models like the decoders and generators contain independent entries which can be used to create different outputs with similar properties. The use of neural network-based architecture removes the need for dependency on the classical mesh-based Navier-Stoke equation estimation which is prominent in many CFD softwares.
physics.flu-dyn
Super-resolution is an innovative technique that upscales the resolution of an image or a video and thus enables us to reconstruct high-fidelity images from low-resolution data. This study performs super-resolution analysis on turbulent flow fields spatially and temporally using various state-of-the-art machine learning techniques like ESPCN, ESRGAN and TecoGAN to reconstruct high-resolution flow fields from low-resolution flow field data, especially keeping in mind the need for low resource consumption and rapid results production/verification. The dataset used for this study is extracted from the 'isotropic 1024 coarse' dataset which is a part of Johns Hopkins Turbulence Databases (JHTDB). We have utilized pre-trained models and fine tuned them to our needs, so as to minimize the computational resources and the time required for the implementation of the super-resolution models. The advantages presented by this method far exceed the expectations and the outcomes of regular single structure models. The results obtained through these models are then compared using MSE, PSNR, SAM, VIF and SCC metrics in order to evaluate the upscaled results, find the balance between computational power and output quality, and then identify the most accurate and efficient model for spatial and temporal super-resolution of turbulent flow fields.
physics.ao-ph
Ensemble forecast based on physics-informed models is one of the most widely used forecast algorithms for complex turbulent systems. A major difficulty in such a method is the model error that is ubiquitous in practice. Data-driven machine learning (ML) forecasts can reduce the model error but they often suffer from the partial and noisy observations. In this paper, a simple but effective Bayesian machine learning advanced forecast ensemble (BAMCAFE) method is developed, which combines an available imperfect physics-informed model with data assimilation (DA) to facilitate the ML ensemble forecast. In the BAMCAFE framework, a Bayesian ensemble DA is applied to create the training data of the ML model, which reduces the intrinsic error in the imperfect physics-informed model simulations and provides the training data of the unobserved variables. Then a generalized DA is employed for the initialization of the ML ensemble forecast. In addition to forecasting the optimal point-wise value, the BAMCAFE also provides an effective approach of quantifying the forecast uncertainty utilizing a non-Gaussian probability density function that characterizes the intermittency and extreme events. It is shown using a two-layer Lorenz 96 model that the BAMCAFE method can significant improve the forecasting skill compared to the typical reduced-order imperfect models with bare truncation or stochastic parameterization for both the observed and unobserved large-scale variables. It is also shown via a nonlinear conceptual model that the BAMCAFE leads to a comparable non-Gaussian forecast uncertainty as the perfect model while the associated imperfect physics-informed model suffers from large forecast biases.
physics.flu-dyn
The Reynolds-averaged Navier-Stokes (RANS) equations are widely used in turbulence applications. They require accurately modeling the anisotropic Reynolds stress tensor, for which traditional Reynolds stress closure models only yield reliable results in some flow configurations. In the last few years, there has been a surge of work aiming at using data-driven approaches to tackle this problem. The majority of previous work has focused on the development of fully-connected networks for modeling the anisotropic Reynolds stress tensor. In this paper, we expand upon recent work for turbulent channel flow and develop new convolutional neural network (CNN) models that are able to accurately predict the normalized anisotropic Reynolds stress tensor. We apply the new CNN model to a number of one-dimensional turbulent flows. Additionally, we present interpretability techniques that help drive the model design and provide guidance on the model behavior in relation to the underlying physics.
physics.flu-dyn
The predictive capabilities of turbulent flow simulations, critical for aerodynamic design and weather prediction, hinge on the choice of turbulence models. The abundance of data from experiments and simulations and the advent of machine learning have provided a boost to turbulence modeling efforts. However, simulations of turbulent flows remain hindered by the inability of heuristics and supervised learning to model the near-wall dynamics. We address this challenge by introducing scientific multi-agent reinforcement learning (SciMARL) for the discovery of wall models for large-eddy simulations (LES). In SciMARL, discretization points act also as cooperating agents that learn to supply the LES closure model. The agents self-learn using limited data and generalize to extreme Reynolds numbers and previously unseen geometries. The present simulations reduce by several orders of magnitude the computational cost over fully-resolved simulations while reproducing key flow quantities. We believe that SciMARL creates unprecedented capabilities for the simulation of turbulent flows.
physics.flu-dyn
In recent years, there has been an explosion of machine learning techniques for turbulence closure modeling, though many rely on augmenting existing models. While this has proven successful in single-phase flows, it breaks down for multiphase flows, particularly when the system dynamics are controlled by two-way coupling between the phases. In this work, we propose an approach that blends sparse regression and gene expression programming (GEP) to generate closed-form algebraic models from simulation data. Sparse regression is used to determine a minimum set of functional groups required to capture the physics and GEP is used to automate the formulation of the coefficients and dependencies on operating conditions. The framework is demonstrated on a canonical gas–solid flow in which two-way coupling generates and sustains fluid-phase turbulence.
physics.flu-dyn
We propose a supervised-machine-learning-based wall model for coarse-grid wall-resolved large-eddy simulation (LES). Our consideration is made on LES of turbulent channel flows with a first grid point set relatively far from the wall ( 10 wall units), while still resolving the near-wall region, to present a new path to save the computational cost. Convolutional neural network (CNN) is utilized to estimate a virtual wall-surface velocity from sectional fields near the wall, whose training data are generated by a direct numerical simulation (DNS) at . The virtual wall-surface velocity is prepared with the extrapolation of the DNS data near the wall. This idea enables us to give a proper wall condition to correct a velocity gradient near the wall. The estimation ability of the model from near wall information is first investigated as a priori test. The estimated velocity fields by the present CNN model are in statistical agreement with the reference DNS data. The model trained in a priori test is then combined with the LES as a posteriori test. We find that the LES can successfully be augmented using the present model at both the friction Reynolds number used for training and the unseen Reynolds number even when the first grid point is located at 5 wall units off the wall. We also investigate the robustness of the present model for the choice of sub-grid scale model and the possibility of transfer learning in a local domain. The observations through the paper suggest that the present model is a promising tool for recovering the accuracy of LES with a coarse grid near the wall.
astro-ph.GA
Magnetohydrodynamic (MHD) turbulence is a crucial component of the current paradigms of star formation, dynamo theory, particle transport, magnetic reconnection and evolution of structure in the interstellar medium (ISM) of galaxies. Despite the importance of turbulence to astrophysical fluids, a full theoretical framework based on solutions to the Navier-Stokes equations remains intractable. Observations provide only limited line-of-sight information on densities, temperatures, velocities and magnetic field strengths and therefore directly measuring turbulence in the ISM is challenging. A statistical approach has been of great utility in allowing comparisons of observations, simulations and analytic predictions. In this review article we address the growing importance of MHD turbulence in many fields of astrophysics and review statistical diagnostics for studying interstellar and interplanetary turbulence. In particular, we will review statistical diagnostics and machine learning algorithms that have been developed for observational data sets in order to obtain information about the turbulence cascade, fluid compressibility (sonic Mach number), and magnetization of fluid (Alfvénic Mach number). These techniques have often been tested on numerical simulations of MHD turbulence, which may include the creation of synthetic observations, and are often formulated on theoretical expectations for compressible magnetized turbulence. We stress the use of multiple techniques, as this can provide a more accurate indication of the turbulence parameters of interest. We conclude by describing several open-source tools for the astrophysical community to use when dealing with turbulence.
physics.flu-dyn
The application machine learning (ML) algorithms to turbulence modeling has shown promise over the last few years, but their application has been restricted to eddy viscosity based closure approaches. In this article we discuss rationale for the application of machine learning with high-fidelity turbulence data to develop models at the level of Reynolds stress transport modeling. Based on these rationale we compare different machine learning algorithms to determine their efficacy and robustness at modeling the different transport processes in the Reynolds Stress Transport Equations. Those data driven algorithms include Random forests, gradient boosted trees and neural networks. The direct numerical simulation (DNS) data for flow in channels is used both as training and testing of the ML models. The optimal hyper-parameters of the ML algorithms are determined using Bayesian optimization. The efficacy of above mentioned algorithms is assessed in the modeling and prediction of the terms in the Reynolds stress transport equations. It was observed that all the three algorithms predict the turbulence parameters with acceptable level of accuracy. These ML models are then applied for prediction of the pressure strain correlation of flow cases that are different from the flows used for training, to assess their robustness and generalizability. This explores the assertion that ML based data driven turbulence models can overcome the modeling limitations associated with the traditional turbulence models and ML models trained with large amounts data with different classes of flows can predict flow field with reasonable accuracy for unknown flows with similar flow physics. In addition to this verification we carry out validation for the final ML models by assessing the importance of different input features for prediction.
physics.flu-dyn
The weights of a deep neural network model are optimized in conjunction with the governing flow equations to provide a model for sub-grid-scale stresses in a temporally developing plane turbulent jet at Reynolds number . The objective function for training is first based on the instantaneous filtered velocity fields from a corresponding direct numerical simulation, and the training is by a stochastic gradient descent method, which uses the adjoint Navier–Stokes equations to provide the end-to-end sensitivities of the model weights to the velocity fields. In-sample and out-of-sample testing on multiple dual-jet configurations show that its required mesh density in each coordinate direction for prediction of mean flow, Reynolds stresses, and spectra is half that needed by the dynamic Smagorinsky model for comparable accuracy. The same neural-network model trained directly to match filtered sub-grid-scale stresses – without the constraint of being embedded within the flow equations during the training – fails to provide a qualitatively correct prediction. The coupled formulation is generalized to train based only on mean-flow and Reynolds stresses, which are more readily available in experiments. The mean-flow training provides a robust model, which is important, though a somewhat less accurate prediction for the same coarse meshes, as might be anticipated due to the reduced information available for training in this case. The anticipated advantage of the formulation is that the inclusion of resolved physics in the training increases its capacity to extrapolate. This is assessed for the case of passive scalar transport, for which it outperforms established models due to improved mixing predictions.
physics.flu-dyn
RANS simulations with the Spalart-Allmaras turbulence model are improved for cases with flow separation using the Field Inversion and Machine Learning approach. A compensatory discrepancy term is introduced into the turbulence model and optimized using high-fidelity reference data from experiments. Influences on the optimization results with respect to regularization, grid resolution and areas in which the optimization is active are investigated. Finally, a neural network is trained and used to augment simulations on a test case.
physics.flu-dyn
Machine learning is used to develop closure terms for coarse grained model of two-dimensional turbulent flow directly from the coarse grained data by adding a source term to the Navier-Stokes equations to ensure that the coarse-grained flow evolves in the correct way. The source term is related to the average flow using a Neural Network with a relatively simple structure and smoothed slightly to prevent instabilities in a posteriori test. The time dependent coarse grained flow field is generated by filtering fully resolved results and the predicted coarse field evolution agrees well with the filtered results, both for the flow used to learn the closure terms and for flows not used for the learning.
physics.flu-dyn
Training data-driven turbulence models with high fidelity Reynolds stress can be impractical and recently such models have been trained with velocity and pressure measurements. For gradient-based optimization, such as training deep learning models, this requires evaluating the sensitivities of the RANS equations. This paper explores the use of an ensemble approximation of the sensitivities of the RANS equations in training data-driven turbulence models with indirect observations. A deep neural network representing the turbulence model is trained using the network's gradients obtained by backpropagation and the ensemble approximation of the RANS sensitivities. Different ensemble approximations are explored and a method based on explicit projection onto the sample space is presented. As validation, the gradient approximations from the different methods are compared to that from the continuous adjoint equations. The ensemble approximation is then used to learn different turbulence models from velocity observations. In all cases, the learned model predicts improved velocities. However, it was observed that once the sensitivity of the velocity to the underlying model becomes small, the approximate nature of the ensemble gradient hinders further optimization of the underlying model. The benefits and limitations of the ensemble gradient approximation are discussed, in particular as compared to the adjoint equations.
physics.flu-dyn
The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations. This paper demonstrates the viability of this approach and presents an end-to-end differentiable framework for training deep neural networks to learn eddy viscosity models from indirect observations derived from the velocity and pressure fields. The framework consists of a Reynolds-averaged Navier-Stokes (RANS) solver and a neural-network-represented turbulence model, each accompanied by its derivative computations. For computing the sensitivities of the indirect observations to the Reynolds stress field, we use the continuous adjoint equations for the RANS equations, while the gradient of the neural network is obtained via its built-in automatic differentiation capability. We demonstrate the ability of this approach to learn the true underlying turbulence closure when one exists by training models using synthetic velocity data from linear and nonlinear closures. We also train a linear eddy viscosity model using synthetic velocity measurements from direct numerical simulations of the Navier-Stokes equations for which no true underlying linear closure exists. The trained deep-neural-network turbulence model showed predictive capability on similar flows.
physics.flu-dyn
Over the past few years, deep learning methods have proved to be of great interest for the computational fluid dynamics community, especially when used as surrogate models, either for flow reconstruction, turbulence modeling, or for the prediction of aerodynamic coefficients. Overall, exceptional levels of accuracy have been obtained, but the robustness and reliability of the proposed approaches remain to be explored, particularly outside of the confidence region defined by the training dataset. In this contribution, we present a twin auto-encoder network for incompressible laminar flow reconstruction with uncertainty estimation around 2D obstacles. The proposed architecture is trained over a dataset composed of numerically-computed laminar flows around 12,000 random shapes, and naturally enforces a quasi-linear relation between a geometric reconstruction branch and the flow prediction decoder. Based on this feature, two uncertainty estimation processes are proposed, allowing either a binary decision (accept or reject prediction), or proposing a confidence interval along with the flow quantities prediction (u,v,p). Results over dataset samples as well as unseen shapes show a strong positive correlation of this reconstruction score to the mean-squared error of the flow prediction. Such approaches offer the possibility to warn the user of trained models when the provided input shows too large deviation from the training data, making the produced surrogate model conservative for fast and reliable flow prediction.
physics.flu-dyn
The behaviour of the turbulent Prandtl number () for buoyancy-affected flows near a vertical surface is investigated as an extension study of {Gibson & Leslie, \emph{Int. Comm. Heat Mass Transfer}, Vol. 11, pp. 73-84 (1984)}. By analysing the location of mean velocity maxima in a differentially heated vertical planar channel, we {identify an} {infinity anomaly} for the eddy viscosity and the turbulent Prandtl number , as both terms are divided by the mean velocity gradient according to the standard definition, in vertical buoyant flow. To predict the quantities of interest, e.g. the Nusselt number, a machine learning framework via symbolic regression is used with various cost functions, e.g. the mean velocity gradient, with the aid of the latest direct numerical simulation (DNS) dataset for vertical natural and mixed convection. The study has yielded two key outcomes: the new machine learnt algebraic models, as the reciprocal of , successfully handle the infinity issue for both vertical natural and mixed convection; and the proposed models with embedded coordinate frame invariance can be conveniently implemented in the Reynolds-averaged scalar equation and are proven to be robust and accurate in the current parameter space, where the Rayleigh number spans from to for vertical natural convection and the bulk Richardson number is in the range of and for vertical mixed convection.
physics.flu-dyn
There exists continuous demand of improved turbulence models for the closure of Reynolds Averaged Navier-Stokes (RANS) simulations. Machine Learning (ML) offers effective tools for establishing advanced empirical Reynolds stress closures on the basis of high fidelity simulation data. This paper presents a turbulence model based on the Deep Neural Network(DNN) which takes into account the non-linear relationship between the Reynolds stress anisotropy tensor and the local mean velocity gradient as well as the near-wall effect. The construction and the tuning of the DNN-turbulence model are detailed. We show that the DNN-turbulence model trained on data from direct numerical simulations yields an accurate prediction of the Reynolds stresses for plane channel flow. In particular, we propose including the local turbulence Reynolds number in the model input.
physics.flu-dyn
Accurate prediction of laminar-turbulent transition is a critical element of computational fluid dynamics simulations for aerodynamic design across multiple flow regimes. Traditional methods of transition prediction cannot be easily extended to flow configurations where the transition process depends on a large set of parameters. In comparison, neural network methods allow higher dimensional input features to be considered without compromising the efficiency and accuracy of the traditional data driven models. Neural network methods proposed earlier follow a cumbersome methodology of predicting instability growth rates over a broad range of frequencies, which are then processed to obtain the N-factor envelope, and then, the transition location based on the correlating N-factor. This paper presents an end-to-end transition model based on a recurrent neural network, which sequentially processes the mean boundary-layer profiles along the surface of the aerodynamic body to directly predict the N-factor envelope and the transition locations over a two-dimensional airfoil. The proposed transition model has been developed and assessed using a large database of 53 airfoils over a wide range of chord Reynolds numbers and angles of attack. The sequence-to-sequence transduction model proposed herein provides a more direct approach for accurate predictions of the transition location than the earlier neural network methods, which predict the local amplification rate of a single instability mode at a fixed location along the airfoil. The large universe of airfoils encountered in various applications causes additional difficulties. As such, we provide further insights on selecting training datasets from large amounts of available data.