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
cs.CE
A probabilistic machine learning model is introduced to augment the turbulence model in order to improve the modelling of separated flows and the generalisability of learnt corrections. Increasingly, machine learning methods have been used to leverage experimental and high-fidelity data, improving the accuracy of the Reynolds Averaged Navier Stokes (RANS) turbulence models widely used in industry. A significant challenge for such methods is their ability to generalise to unseen geometries and flow conditions. Furthermore, heterogeneous datasets containing a mix of experimental and simulation data must be efficiently handled. In this work, field inversion and an ensemble of Gaussian Process Emulators (GPEs) is employed to address both of these challenges. The ensemble model is applied to a range of benchmark test cases, demonstrating improved turbulence modelling for cases with separated flows with adverse pressure gradients, where RANS simulations are understood to be unreliable. Perhaps more significantly, the simulation reverted to the uncorrected model in regions of the flow exhibiting physics outside of the training data.
physics.flu-dyn
This work introduces a novel data-driven framework to formulate explicit algebraic Reynolds-averaged Navier-Stokes (RANS) turbulence closures. Recent years have witnessed a blossom in applying machine learning (ML) methods to revolutionize the paradigm of turbulence modeling. However, due to the black-box essence of most ML methods, it is currently hard to extract interpretable information and knowledge from data-driven models. To address this critical limitation, this work leverages deep learning with symbolic regression methods to discover hidden governing equations of Reynolds stress models. Specifically, the Reynolds stress tensor is decomposed into linear and non-linear parts. While the linear part is taken as the regular linear eddy viscosity model, a long short-term memory neural network is employed to generate symbolic terms on which tractable mathematical expressions for the non-linear counterpart are built. A novel reinforcement learning algorithm is employed to train the neural network to produce best-fitted symbolic expressions. Within the proposed framework, the Reynolds stress closure is explicitly expressed in algebraic forms, thus allowing for direct functional inference. On the other hand, the Galilean and rotational invariance are craftily respected by constructing the training feature space with independent invariants and tensor basis functions. The performance of the present methodology is validated through numerical simulations of three different canonical flows that deviate in geometrical configurations. The results demonstrate promising accuracy improvements over traditional RANS models, showing the generalization ability of the proposed method. Moreover, with the given explicit model equations, it can be easier to interpret the influence of input features on generated models.
physics.flu-dyn
Inference problems for two-dimensional snapshots of rotating turbulent flows are studied. We perform a systematic quantitative benchmark of point-wise and statistical reconstruction capabilities of the linear Extended Proper Orthogonal Decomposition (EPOD) method, a non-linear Convolutional Neural Network (CNN) and a Generative Adversarial Network (GAN). We attack the important task of inferring one velocity component out of the measurement of a second one, and two cases are studied: (I) both components lay in the plane orthogonal to the rotation axis and (II) one of the two is parallel to the rotation axis. We show that EPOD method works well only for the former case where both components are strongly correlated, while CNN and GAN always outperform EPOD both concerning point-wise and statistical reconstructions. For case (II), when the input and output data are weakly correlated, all methods fail to reconstruct faithfully the point-wise information. In this case, only GAN is able to reconstruct the field in a statistical sense. The analysis is performed using both standard validation tools based on spatial distance between the prediction and the ground truth and more sophisticated multi-scale analysis using wavelet decomposition. Statistical validation is based on standard Jensen-Shannon divergence between the probability density functions, spectral properties and multi-scale flatness.
physics.comp-ph
Data-driven methods are widely used to develop physical models, but there still exist limitations that affect their performance, generalizability and robustness. By combining gene expression programming (GEP) with artificial neural network (ANN), we propose a novel method for symbolic regression called the gene expression programming neural network (GEPNN). In this method, candidate expressions generated by evolutionary algorithms are transformed between the GEP and ANN structures during training iterations, and efficient and robust convergence to accurate models is achieved by combining the GEP's global searching and the ANN's gradient optimization capabilities. In addition, sparsity-enhancing strategies have been introduced to GEPNN to improve the interpretability of the trained models. The GEPNN method has been tested for finding different physical laws, showing improved convergence to models with precise coefficients. Furthermore, for large-eddy simulation of turbulence, the subgrid-scale stress model trained by GEPNN significantly improves the prediction of turbulence statistics and flow structures over traditional models, showing advantages compared to the existing GEP and ANN methods in both a priori and a posteriori tests.
physics.flu-dyn
Because the Navier-Stokes equations are dissipative, the long-time dynamics of a flow in state space are expected to collapse onto a manifold whose dimension may be much lower than the dimension required for a resolved simulation. On this manifold, the state of the system can be exactly described in a coordinate system parameterizing the manifold. Describing the system in this low-dimensional coordinate system allows for much faster simulations and analysis. We show, for turbulent Couette flow, that this description of the dynamics is possible using a data-driven manifold dynamics modeling method. This approach consists of an autoencoder to find a low-dimensional manifold coordinate system and a set of ordinary differential equations defined by a neural network. Specifically, we apply this method to minimal flow unit turbulent plane Couette flow at , where a fully resolved solutions requires degrees of freedom. Using only data from this simulation we build models with fewer than degrees of freedom that quantitatively capture key characteristics of the flow, including the streak breakdown and regeneration cycle. At short-times, the models track the true trajectory for multiple Lyapunov times, and, at long-times, the models capture the Reynolds stress and the energy balance. For comparison, we show that the models outperform POD-Galerkin models with 2000 degrees of freedom. Finally, we compute unstable periodic orbits from the models. Many of these closely resemble previously computed orbits for the full system; additionally, we find nine orbits that correspond to previously unknown solutions in the full system.
physics.flu-dyn
Direct numerical simulation (DNS) is very accurate however, the computational cost increases significantly with the increase in Reynolds number. On the other hand, we have the Reynolds Averaged Navier Stokes (RANS) method for simulating turbulent flows, which needs less computational power. Turbulence models based on linear eddy viscosity models (LEVM) in the RANS method, which use a linear stress-strain rate relationship for modelling the Reynolds stress tensor do not perform well for complex flows \cite{shih1995new} . In this work, we intend to study the performance of non linear eddy viscosity model (NLEVM) hypothesis for turbulent forced plumes in a linearly stratified environment and modify the standard RANS model coefficients obtained from machine learning. The general eddy viscosity hypothesis supported by the closure coefficients generated from the tensor basis neural network (TBNN) is used to develop TBNN based K- model. The aforementioned model is used to evaluate the plume's mean velocity profile, and maximum height reached. The comparison between standard LEVM, NLEVM and the experimental results indicates a significant improvement in the maximum height achieved, and a good improvement in the mean velocity profile.
physics.comp-ph
Generative Adversarial Networks (GANs) have received wide acclaim among the machine learning (ML) community for their ability to generate realistic 2D images. ML is being applied more often to complex problems beyond those of computer vision. However, current frameworks often serve as black boxes and lack physics embeddings, leading to poor ability in enforcing constraints and unreliable models. In this work, we develop physics embeddings that can be stringently imposed, referred to as hard constraints, in the neural network architecture. We demonstrate their capability for 3D turbulence by embedding them in GANs, particularly to enforce the mass conservation constraint in incompressible fluid turbulence. In doing so, we also explore and contrast the effects of other methods of imposing physics constraints within the GANs framework, especially penalty-based physics constraints popular in literature. By using physics-informed diagnostics and statistics, we evaluate the strengths and weaknesses of our approach and demonstrate its feasibility.
cs.LG
Chaos and turbulence are complex physical phenomena, yet a precise definition of the complexity measure that quantifies them is still lacking. In this work we consider the relative complexity of chaos and turbulence from the perspective of deep neural networks. We analyze a set of classification problems, where the network has to distinguish images of fluid profiles in the turbulent regime from other classes of images such as fluid profiles in the chaotic regime, various constructions of noise and real world images. We analyze incompressible as well as weakly compressible fluid flows. We quantify the complexity of the computation performed by the network via the intrinsic dimensionality of the internal feature representations, and calculate the effective number of independent features which the network uses in order to distinguish between classes. In addition to providing a numerical estimate of the complexity of the computation, the measure also characterizes the neural network processing at intermediate and final stages. We construct adversarial examples and use them to identify the two point correlation spectra for the chaotic and turbulent vorticity as the feature used by the network for classification.
eess.SP
We define and study a fully-convolutional neural network stochastic model, NN-Turb, which generates a 1-dimensional field with some turbulent velocity statistics. In particular, the generated process satisfies the Kolmogorov 2/3 law for second order structure function. It also presents negative skewness across scales (i.e. Kolmogorov 4/5 law) and exhibits intermittency as characterized by skewness and flatness. Furthermore, our model is never in contact with turbulent data and only needs the desired statistical behavior of the structure functions across scales for training.
physics.flu-dyn
Reynolds-averaged Navier-Stokes (RANS)-based transition modeling is widely used in aerospace applications but suffers inaccuracies due to the Boussinesq turbulent viscosity hypothesis. The eigenspace perturbation method can estimate the accuracy of a RANS model by injecting perturbations to its predicted Reynolds stresses. However, there lacks a reliable method for choosing the strength of the injected perturbation, while existing machine learning models are often complex and data craving. We examined two light-weighted machine learning models to help select the strength of the injected perturbation for estimating the RANS uncertainty of flows undergoing the transition to turbulence over a Selig-Donovan 7003 airfoil. On the one hand, we examined polynomial regression to construct a marker function augmented with eigenvalue perturbations to estimate the uncertainty bound for the predicted skin friction coefficient. On the other hand, we trained a convolutional neural network (CNN) to predict high-fidelity turbulence kinetic energy. The trained CNN acts as a marker function that can be integrated into the eigenspace perturbation method to quantify the RANS uncertainty. Our findings suggest that the light-weighted machine learning models are effective in constructing an appropriate marker function that is promising to enrich the existing eigenspace perturbation method to quantify the RANS uncertainty more precisely.
physics.flu-dyn
In recent years, machine learning methods represented by deep neural networks (DNN) have been a new paradigm of turbulence modeling. However, in the scenario of high Reynolds numbers, there are still some bottlenecks, including the lack of high-fidelity data and the convergence and stability problem in the coupling process of turbulence models and the RANS solvers. In this paper, we propose an improved ensemble kalman inversion method as a unified approach of data assimilation and turbulence modeling for separated flows at high Reynolds numbers. The trainable parameters of the DNN are optimized according to the given experimental surface pressure coefficients in the framework of mutual coupling between the RANS equations and DNN eddy-viscosity models. In this way, data assimilation and model training are combined into one step to get the high-fidelity turbulence models agree well with experiments efficiently. The effectiveness of the method is verified by cases of separated flows around airfoils(S809) at high Reynolds numbers. The results show that through joint assimilation of vary few experimental states, we can get turbulence models generalizing well to both attached and separated flows at different angles of attack. The errors of lift coefficients at high angles of attack are significantly reduced by more than three times compared with the traditional SA model. The models obtained also perform well in stability and robustness.
physics.flu-dyn
In this paper, deep learning (DL) methods are evaluated in the context of turbulent flows. Various generative adversarial networks (GANs) are discussed with respect to their suitability for understanding and modeling turbulence. Wasserstein GANs (WGANs) are then chosen to generate small-scale turbulence. Highly resolved direct numerical simulation (DNS) turbulent data is used for training the WGANs and the effect of network parameters, such as learning rate and loss function, is studied. Qualitatively good agreement between DNS input data and generated turbulent structures is shown. A quantitative statistical assessment of the predicted turbulent fields is performed.
physics.flu-dyn
This paper presents a machine learning methodology to improve the predictions of traditional RANS turbulence models in channel flows subject to strong variations in their thermophysical properties. The developed formulation contains several improvements over the existing Field Inversion Machine Learning (FIML) frameworks described in the literature, as well as the derivation of a new modelling technique. We first showcase the use of efficient optimization routines to automatize the process of field inversion in the context of CFD, combined with the use of symbolic algebra solvers to generate sparse-efficient algebraic formulas to comply with the discrete adjoint method. The proposed neural network architecture is characterized by the use of an initial layer of logarithmic neurons followed by hyperbolic tangent neurons, which proves numerically stable. The machine learning predictions are then corrected using a novel weighted relaxation factor methodology, that recovers valuable information from otherwise spurious predictions. The study uses the K-fold cross-validation technique, which is beneficial for small datasets. The results show that the machine learning model acts as an excellent non-linear interpolator for DNS cases well-represented in the training set, and that moderate improvement margins are obtained for sparser DNS cases. It is concluded that the developed machine learning methodology corresponds to a valid alternative to improve RANS turbulence models in flows with strong variations in their thermophysical properties without introducing prior modeling assumptions into the system.
physics.flu-dyn
White paper: The aim of this work is to apply and analyze machine learning methods for uncertainty quantification of turbulence models. In this work we investigate the classical and data-driven variants of the eigenspace perturbation method. This methodology is designed to estimate the uncertainties related to the shape of the modeled Reynolds stress tensor in the Navier-Stokes equations for Computational Fluid Dynamics (CFD). The underlying methodology is extended by adding a data-driven, physics-constrained machine learning approach in order to predict local perturbations of the Reynolds stress tensor. Using separated two-dimensional flows, we investigate the generalization properties of the machine learning models and shed a light on impacts of applying a data-driven extension.
stat.ML
Physical parameterizations are used as representations of unresolved subgrid processes within weather and global climate models or coarse-scale turbulent models, whose resolutions are too coarse to resolve small-scale processes. These parameterizations are typically grounded on physically-based, yet empirical, representations of the underlying small-scale processes. Machine learning-based parameterizations have recently been proposed as an alternative and have shown great promises to reduce uncertainties associated with small-scale processes. Yet, those approaches still show some important mismatches that are often attributed to stochasticity in the considered process. This stochasticity can be due to noisy data, unresolved variables or simply to the inherent chaotic nature of the process. To address these issues, we develop a new type of parameterization (closure) which is based on a Bayesian formalism for neural networks, to account for uncertainty quantification, and includes memory, to account for the non-instantaneous response of the closure. To overcome the curse of dimensionality of Bayesian techniques in high-dimensional spaces, the Bayesian strategy is based on a Hamiltonian Monte Carlo Markov Chain sampling strategy that takes advantage of the likelihood function and kinetic energy's gradients with respect to the parameters to accelerate the sampling process. We apply the proposed Bayesian history-based parameterization to the Lorenz '96 model in the presence of noisy and sparse data, similar to satellite observations, and show its capacity to predict skillful forecasts of the resolved variables while returning trustworthy uncertainty quantifications for different sources of error. This approach paves the way for the use of Bayesian approaches for closure problems.
physics.flu-dyn
The state of turbulent, minimal-channel flow is estimated from spatio-temporal sparse observations of the velocity, using both a physics-informed neural network (PINN) and adjoint-variational data assimilation (4DVar). The performance of PINN is assessed against the benchmark results from 4DVar. The PINN is efficient to implement, takes advantage of automatic differentiation to evaluate the governing equations, and does not require the development of an adjoint model. In addition, the flow evolution is expressed in terms of the network parameters which have a far smaller dimension than the predicted trajectory in state space or even just the initial condition of the flow. Provided adequate observations, network architecture and training, the PINN can yield satisfactory estimates of the the flow field, both for the missing velocity data and the entirely unobserved pressure field. However, accuracy depends on the network architecture, and the dependence is not known a priori. In comparison to 4DVar estimation which becomes progressively more accurate over the observation horizon, the PINN predictions are generally less accurate and maintain the same level of errors throughout the assimilation time window. Another notable distinction is the capacity to accurately forecast the flow evolution: while the 4DVar prediction depart from the true flow state gradually and according to the Lyapunov exponent, the PINN is entirely inaccurate immediately beyond the training time horizon unless re-trained. Most importantly, while 4DVar satisfies the discrete form of the governing equations point-wise to machine precision, in PINN the equations are only satisfied in an sense.
physics.flu-dyn
Modeling three-dimensional (3D) turbulence by neural networks is difficult because 3D turbulence is highly-nonlinear with high degrees of freedom and the corresponding simulation is memory-intensive. Recently, the attention mechanism has been shown as a promising approach to boost the performance of neural networks on turbulence simulation. However, the standard self-attention mechanism uses time and space with respect to input dimension , and such quadratic complexity has become the main bottleneck for attention to be applied on 3D turbulence simulation. In this work, we resolve this issue with the concept of linear attention network. The linear attention approximates the standard attention by adding two linear projections, reducing the overall self-attention complexity from to in both time and space. The linear attention coupled Fourier neural operator (LAFNO) is developed for the simulation of 3D turbulence. Numerical simulations show that the linear attention mechanism provides 40% error reduction at the same level of computational cost, and LAFNO can accurately reconstruct a variety of statistics and instantaneous spatial structures of 3D turbulence. The linear attention method would be helpful for the improvement of neural network models of 3D nonlinear problems involving high-dimensional data in other scientific domains.
astro-ph.EP
We investigate the utility of deep learning for modeling the clustering of particles that are aerodynamically coupled to turbulent fluids. Using a Lagrangian particle module within the Athena++ hydrodynamics code, we simulate the dynamics of particles in the Epstein drag regime within a periodic domain of isotropic forced hydrodynamic turbulence. This setup is an idealized model relevant to the collisional growth of micron to mm-sized dust particles in early stage planet formation. The simulation data are used to train a U-Net deep learning model to predict gridded three-dimensional representations of the particle density and velocity fields, given as input the corresponding fluid fields. The trained model qualitatively captures the filamentary structure of clustered particles in a highly non-linear regime. We assess model fidelity by calculating metrics of the density field (the radial distribution function) and of the velocity field (the relative velocity and the relative radial velocity between particles). Although trained only on the spatial fields, the model predicts these statistical quantities with errors that are typically <10%. Our results suggest that, given appropriately expanded training data, deep learning could complement direct numerical simulations in predicting particle clustering within turbulent flows.
cs.CE
In order to achieve a virtual certification process and robust designs for turbomachinery, the uncertainty bounds for Computational Fluid Dynamics have to be known. The formulation of turbulence closure models implies a major source of the overall uncertainty of Reynolds-averaged Navier-Stokes simulations. We discuss the common practice of applying a physics constrained eigenspace perturbation of the Reynolds stress tensor in order to account for the model form uncertainty of turbulence models. Since the basic methodology often leads to overly generous uncertainty estimates, we extend a recent approach of adding a machine learning strategy. The application of a data-driven method is motivated by striving for the detection of flow regions, which are prone to suffer from a lack of turbulence model prediction accuracy. In this way any user input related to choosing the degree of uncertainty is supposed to become obsolete. This work especially investigates an approach, which tries to determine an a priori estimation of prediction confidence, when there is no accurate data available to judge the prediction. The flow around the NACA 4412 airfoil at near-stall conditions demonstrates the successful application of the data-driven eigenspace perturbation framework. Furthermore, we especially highlight the objectives and limitations of the underlying methodology.
physics.flu-dyn
Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with machine learning to develop closure models for Burgers' turbulence. We consider the 1D Burgers system as a prototypical test problem for modeling the unresolved terms in advection-dominated turbulence problems. We train a series of models that incorporate varying degrees of physical assumptions on an a posteriori loss function to test the efficacy of models across a range of system parameters, including viscosity, time, and grid resolution. We find that constraining models with inductive biases in the form of partial differential equations that contain known physics or existing closure approaches produces highly data-efficient, accurate, and generalizable models, outperforming state-of-the-art baselines. Addition of structure in the form of physics information also brings a level of interpretability to the models, potentially offering a stepping stone to the future of closure modeling.