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
Building efficient, accurate and generalizable reduced order models of developed turbulence remains a major challenge. This manuscript approaches this problem by developing a hierarchy of parameterized reduced Lagrangian models for turbulent flows, and investigates the effects of enforcing physical structure through Smoothed Particle Hydrodynamics (SPH) versus relying on neural networks (NN)s as universal function approximators. Starting from Neural Network (NN) parameterizations of a Lagrangian acceleration operator, this hierarchy of models gradually incorporates a weakly compressible and parameterized SPH framework, which enforces physical symmetries, such as Galilean, rotational and translational invariances. Within this hierarchy, two new parameterized smoothing kernels are developed in order to increase the flexibility of the learn-able SPH simulators. For each model we experiment with different loss functions which are minimized using gradient based optimization, where efficient computations of gradients are obtained by using Automatic Differentiation (AD) and Sensitivity Analysis (SA). Each model within the hierarchy is trained on two data sets associated with weekly compressible Homogeneous Isotropic Turbulence (HIT): (1) a validation set using weakly compressible SPH; and (2) a high fidelity set from Direct Numerical Simulations (DNS). Numerical evidence shows that encoding more SPH structure improves generalizability to different turbulent Mach numbers and time shifts, and that including the novel parameterized smoothing kernels improves the accuracy of SPH at the resolved scales.
physics.flu-dyn
In fluid physics, data-driven models to enhance or accelerate solution methods are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In the context of reduced order models of high-dimensional time-dependent fluid systems, machine learning methods grant the benefit of automated learning from data, but the burden of a model lies on its reduced-order representation of both the fluid state and physical dynamics. In this work, we build a physics-constrained, data-driven reduced order model for the Navier-Stokes equations to approximate spatio-temporal turbulent fluid dynamics. The model design choices mimic numerical and physical constraints by, for example, implicitly enforcing the incompressibility constraint and utilizing continuous Neural Ordinary Differential Equations for tracking the evolution of the differential equation. We demonstrate this technique on three-dimensional, moderate Reynolds number turbulent fluid flow. In assessing the statistical quality and characteristics of the machine-learned model through rigorous diagnostic tests, we find that our model is capable of reconstructing the dynamics of the flow over large integral timescales, favoring accuracy at the larger length scales. More significantly, comprehensive diagnostics suggest that physically-interpretable model parameters, corresponding to the representations of the fluid state and dynamics, have attributable and quantifiable impact on the quality of the model predictions and computational complexity.
physics.flu-dyn
Reynolds-averaged Navier-Stokes simulations are still the main method to study complex flows in engineering. However, traditional turbulence models cannot accurately predict flow fields with separations. In such situation, machine learning methods provide an effective way to build new data-driven turbulence closure models. Nevertheless, a bottleneck that the data-driven turbulence models encounter is how to ensure the stability and convergence of the RANS equations in posterior iterations. This paper studies the effects of different coupling modes on the convergence and stability between the RANS equations and turbulence models. Numerical results demonstrate that the frozen coupling mode, commonly used in machine learning turbulence models, may lead to divergence and instability in posterior iterations; while the mutual coupling mode can maintain good convergence and stability in the process of iterations. This research can provide a new perspective to the coupling mode for machine learning turbulence models with RANS equations in posterior iterations.
physics.flu-dyn
This study presents a deep learning-based framework to reconstruct high-resolution turbulent velocity fields from extremely low-resolution data at various Reynolds numbers using the concept of generative adversarial networks (GANs). A multiscale enhanced super-resolution generative adversarial network (MS-ESRGAN) is applied as a model to reconstruct the high-resolution velocity fields, and direct numerical simulation (DNS) data of turbulent channel flow with large longitudinal ribs at various Reynolds numbers are used to evaluate the performance of the model. The model is found to have the capacity to accurately reproduce high-resolution velocity fields from data at two different low-resolution levels in terms of the quantities of velocity fields and turbulent statistics. The results further reveal that the model is able to reconstruct velocity fields at Reynolds numbers that are not used in the training process.
physics.flu-dyn
Deep neural network models have shown a great potential in accelerating the simulation of fluid dynamic systems. Once trained, these models can make inference within seconds, thus can be extremely efficient. However, they suffer from a generalization problem when the flow becomes chaotic and turbulent. One of the most important reasons is that, existing models lack the mechanism to handle the unique characteristic of turbulent flow: multi-scale flow structures are non-uniformly distributed and strongly nonequilibrium. In this work, we address this issue with the concept of visual attention: intuitively, we expect the attention module to capture the nonequilibrium of turbulence by automatically adjusting weights on different regions. We benchmark the performance improvement with a state of the art neural network model, the Fourier Neural Operator (FNO), on two-dimensional (2D) turbulence prediction task. Numerical experiments show that the attention-enhanced neural network model can generalize well on higher Reynolds numbers flow, and can accurately reconstruct a variety of statistics and instantaneous spatial structures of turbulence. The attention mechanism provides 40% error reduction with 1% increase of parameters, at the same level of computational cost.
physics.flu-dyn
Modelling the sudden depressurisation of superheated liquids through nozzles is a challenge because the pressure drop causes rapid flash boiling of the liquid. The resulting jet usually demonstrates a wide range of structures, including ligaments and droplets, due to both mechanical and thermodynamic effects. As the simulation comprises increasingly numerous phenomena, the computational cost begins to increase. One way to moderate the additional cost is to use machine learning surrogacy for specific elements of the calculations. The present study presents a machine learning-assisted computational fluid dynamics approach for simulating the atomisation of flashing liquids accounting for distinct stages, from primary atomisation to secondary break-up to small droplets using the -Y model coupled with the homogeneous relaxation model. Notably, the model for the thermodynamic non-equilibrium (HRM) and -Y are coupled, for the first time, with a deep neural network that simulates the turbulence quantities, which are then used in the prediction of superheated liquid jet atomisation. The data-driven component of the method is used for turbulence modelling, avoiding the solution of the two-equation turbulence model typically used for Reynolds-averaged Navier-Stokes simulations for these problems. Both the accuracy and speed of the hybrid approach are evaluated, demonstrating adequate accuracy and at least 25% faster computational fluid dynamics simulations than the traditional approach. This acceleration suggests that perhaps additional components of the calculation could be replaced for even further benefit.
q-bio.NC
Tracking a turbulent plume to locate its source is a complex control problem because it requires multi-sensory integration and must be robust to intermittent odors, changing wind direction, and variable plume statistics. This task is routinely performed by flying insects, often over long distances, in pursuit of food or mates. Several aspects of this remarkable behavior have been studied in detail in many experimental studies. Here, we take a complementary in silico approach, using artificial agents trained with reinforcement learning to develop an integrated understanding of the behaviors and neural computations that support plume tracking. Specifically, we use deep reinforcement learning (DRL) to train recurrent neural network (RNN) agents to locate the source of simulated turbulent plumes. Interestingly, the agents' emergent behaviors resemble those of flying insects, and the RNNs learn to represent task-relevant variables, such as head direction and time since last odor encounter. Our analyses suggest an intriguing experimentally testable hypothesis for tracking plumes in changing wind direction – that agents follow local plume shape rather than the current wind direction. While reflexive short-memory behaviors are sufficient for tracking plumes in constant wind, longer timescales of memory are essential for tracking plumes that switch direction. At the level of neural dynamics, the RNNs' population activity is low-dimensional and organized into distinct dynamical structures, with some correspondence to behavioral modules. Our in silico approach provides key intuitions for turbulent plume tracking strategies and motivates future targeted experimental and theoretical developments.
physics.flu-dyn
This study presents an artificial neural network and proper orthogonal decomposition (POD)-based reduced-order model (ROM) of turbulent flow around a finite wall-mounted square cylinder. The proposed model is suitable for turbulent wake control applications because it can predict the dynamics of the main features of the flow field without computing Navier-Stokes equations. Long short-term memory neural network (LSTM NN) and bidirectional long short-term memory neural network (BLSTM NN) are used to predict the temporal evolution of the POD time coefficients at different planes along the height of the obstacle. The improved delayed detached-eddy simulation (IDDES) is performed to generate the training datasets. Transfer learning (TL) approach is utilized in the training process by using the weights of the LSTM/BLSTM NN that are used to predict the POD time coefficients of the planes at lower elevations to initialize the weights of the networks at higher elevations along the height of the obstacle. The use of TL results in a remarkable improvement in the capability of the LSTM/BLSTM NN prediction compared with the one when the network is initialized with random weights. BLSTM NN shows better results compared with LSTM NN in terms of training and prediction error, indicating that the BLSTM-POD model is more suitable to be used as a ROM for predicting the turbulent wake. Furthermore, the temporal behavior of the time coefficients is carefully examined using the phase space plots and Poincar sections. The results of using different lengths of the prediction time window showed that the prediction error of the POD time coefficients increases as the prediction time window increases and the error increasing rate decreases with the ranking of the POD time coefficients.
physics.flu-dyn
Accurate simulation of turbulent flow with separation is an important but challenging problem. In this paper, a data-driven Reynolds-averaged turbulence modeling approach, field inversion and machine learning is implemented to modify the Spalart-Allmaras model separately on three cases, namely, the S809 airfoil, a periodic hill and the GLC305 airfoil with ice shape 944. Field inversion based on a discrete adjoint method is used to quantify the model-form uncertainty with limited experimental data. An artificial neural network is trained to predict the model corrections with local flow features to extract generalized modeling knowledge. Physical knowledge of the nonequilibrium turbulence in the separating shear layer is considered when setting the prior model uncertainty. The results show that the model corrections from the field inversion demonstrate strong consistency with the underlying physical mechanism of nonequilibrium turbulence. The quantity of interest from the observation data can be reproduced with relatively high accuracy by the augmented model. In addition, the validation in similar flow conditions shows a certain extent of generalization ability.
physics.flu-dyn
Advanced nuclear reactors often exhibit complex thermal-fluid phenomena during transients. To accurately capture such phenomena, a coarse-mesh three-dimensional (3-D) modeling capability is desired for modern nuclear-system code. In the coarse-mesh 3-D modeling of advanced-reactor transients that involve flow and heat transfer, accurately predicting the turbulent viscosity is a challenging task that requires an accurate and computationally efficient model to capture the unresolved fine-scale turbulence. In this paper, we propose a data-driven coarse-mesh turbulence model based on local flow features for the transient analysis of thermal mixing and stratification in a sodium-cooled fast reactor. The model has a coarse-mesh setup to ensure computational efficiency, while it is trained by fine-mesh computational fluid dynamics (CFD) data to ensure accuracy. A novel neural network architecture, combining a densely connected convolutional network and a long-short-term-memory network, is developed that can efficiently learn from the spatial-temporal CFD transient simulation results. The neural network model was trained and optimized on a loss-of-flow transient and demonstrated high accuracy in predicting the turbulent viscosity field during the whole transient. The trained model's generalization capability was also investigated on two other transients with different inlet conditions. The study demonstrates the potential of applying the proposed data-driven approach to support the coarse-mesh multi-dimensional modeling of advanced reactors.
physics.flu-dyn
In this study, a deep learning-based approach is applied with the aim of reconstructing high-resolution turbulent flow fields using minimal flow fields data. A multi-scale enhanced super-resolution generative adversarial network with a physics-based loss function is introduced as a model to reconstruct the high-resolution flow fields. The model capability to reconstruct high-resolution laminar flows is examined using data of laminar flow around a square cylinder. The results reveal that the model can accurately reproduce the high-resolution flow fields even when limited spatial information is provided. The case of turbulent channel flow is used to assess the ability of the model to reconstruct the high-resolution wall-bounded turbulent flow fields. The instantaneous and statistical results obtained from the model agree well with the ground truth data, indicating that the model can successfully learn to map the coarse flow fields to the high-resolution once. Furthermore, the computational cost of the proposed model, which is examined carefully, is found to be effectively low. This demonstrates that using high-fidelity training data with physics-guided generative adversarial network-based models can be practically efficient in reconstructing high-resolution turbulent flow fields from extremely coarse data.
physics.flu-dyn
The present study investigates the accurate inference of Reynolds-averaged Navier-Stokes solutions for the compressible flow over aerofoils in two dimensions with a deep neural network. Our approach yields networks that learn to generate precise flow fields for varying body-fitted, structured grids by providing them with an encoding of the corresponding mapping to a canonical space for the solutions. We apply the deep neural network model to a benchmark case of incompressible flow at randomly given angles of attack and Reynolds numbers and achieve an improvement of more than an order of magnitude compared to previous work. Further, for transonic flow cases, the deep neural network model accurately predicts complex flow behaviour at high Reynolds numbers, such as shock wave/boundary layer interaction, and quantitative distributions like pressure coefficient, skin friction coefficient as well as wake total pressure profiles downstream of aerofoils. The proposed deep learning method significantly speeds up the predictions of flow fields and shows promise for enabling fast aerodynamic designs.
physics.flu-dyn
We propose a deep probabilistic-neural-network architecture for learning a minimal and near-orthogonal set of non-linear modes from high-fidelity turbulent-flow-field data useful for flow analysis, reduced-order modeling, and flow control. Our approach is based on -variational autoencoders (-VAEs) and convolutional neural networks (CNNs), which allow us to extract non-linear modes from multi-scale turbulent flows while encouraging the learning of independent latent variables and penalizing the size of the latent vector. Moreover, we introduce an algorithm for ordering VAE-based modes with respect to their contribution to the reconstruction. We apply this method for non-linear mode decomposition of the turbulent flow through a simplified urban environment, where the flow-field data is obtained based on well-resolved large-eddy simulations (LESs). We demonstrate that by constraining the shape of the latent space, it is possible to motivate the orthogonality and extract a set of parsimonious modes sufficient for high-quality reconstruction. Our results show the excellent performance of the method in the reconstruction against linear-theory-based decompositions. Moreover, we compare our method with available AE-based models. We show the ability of our approach in the extraction of near-orthogonal modes that may lead to interpretability.
cs.CV
Computer vision and machine learning tools offer an exciting new way for automatically analyzing and categorizing information from complex computer simulations. Here we design an ensemble machine learning framework that can independently and robustly categorize and dissect simulation data output contents of turbulent flow patterns into distinct structure catalogues. The segmentation is performed using an unsupervised clustering algorithm, which segments physical structures by grouping together similar pixels in simulation images. The accuracy and robustness of the resulting segment region boundaries are enhanced by combining information from multiple simultaneously-evaluated clustering operations. The stacking of object segmentation evaluations is performed using image mask combination operations. This statistically-combined ensemble (SCE) of different cluster masks allows us to construct cluster reliability metrics for each pixel and for the associated segments without any prior user input. By comparing the similarity of different cluster occurrences in the ensemble, we can also assess the optimal number of clusters needed to describe the data. Furthermore, by relying on ensemble-averaged spatial segment region boundaries, the SCE method enables reconstruction of more accurate and robust region of interest (ROI) boundaries for the different image data clusters. We apply the SCE algorithm to 2-dimensional simulation data snapshots of magnetically-dominated fully-kinetic turbulent plasma flows where accurate ROI boundaries are needed for geometrical measurements of intermittent flow structures known as current sheets.
physics.comp-ph
We propose a Machine Learning (ML) non-Markovian closure modeling framework for accurate predictions of statistical responses of turbulent dynamical systems subjected to external forcings. One of the difficulties in this statistical closure problem is the lack of training data, which is a configuration that is not desirable in supervised learning with neural network models. In this study with the 40-dimensional Lorenz-96 model, the shortage of data (in temporal) is due to the stationarity of the statistics beyond the decorrelation time, thus, the only informative content in the training data is on short-time transient statistics. We adopted a unified closure framework on various truncation regimes, including and excluding the detailed dynamical equations for the variances. The closure frameworks employ a Long-Short-Term-Memory architecture to represent the higher-order unresolved statistical feedbacks with careful consideration to account for the intrinsic instability yet producing stable long-time predictions. We found that this unified agnostic ML approach performs well under various truncation scenarios. Numerically, the ML closure model can accurately predict the long-time statistical responses subjected to various time-dependent external forces that are not (and maximum forcing amplitudes that are relatively larger than those) in the training dataset.
physics.flu-dyn
Deep Learning (DL) algorithms are emerging as a key alternative to computationally expensive CFD simulations. However, state-of-the-art DL approaches require large and high-resolution training data to learn accurate models. The size and availability of such datasets are a major limitation for the development of next-generation data-driven surrogate models for turbulent flows. This paper introduces SURFNet, a transfer learning-based super-resolution flow network. SURFNet primarily trains the DL model on low-resolution datasets and transfer learns the model on a handful of high-resolution flow problems - accelerating the traditional numerical solver independent of the input size. We propose two approaches to transfer learning for the task of super-resolution, namely one-shot and incremental learning. Both approaches entail transfer learning on only one geometry to account for fine-grid flow fields requiring 15x less training data on high-resolution inputs compared to the tiny resolution (64x256) of the coarse model, significantly reducing the time for both data collection and training. We empirically evaluate SURFNet's performance by solving the Navier-Stokes equations in the turbulent regime on input resolutions up to 256x larger than the coarse model. On four test geometries and eight flow configurations unseen during training, we observe a consistent 2-2.1x speedup over the OpenFOAM physics solver independent of the test geometry and the resolution size (up to 2048x2048), demonstrating both resolution-invariance and generalization capabilities. Our approach addresses the challenge of reconstructing high-resolution solutions from coarse grid models trained using low-resolution inputs (super-resolution) without loss of accuracy and requiring limited computational resources.
physics.flu-dyn
This work studies the effectiveness of several machine learning techniques for predicting extreme events occurring in the flow around an airfoil at low Reynolds. For certain Reynolds numbers the aerodynamic forces exhibit intermittent fluctuations caused by changes in the behavior of vortices in the airfoil wake. Such events are prototypical of the unsteady behavior observed in airfoils at low Reynolds and their prediction is extremely challenging due to their intermittency and the chaotic nature of the flow. We seek to forecast these fluctuations in advance of their occurrence by a specified length of time. We assume knowledge only of the pressure at a discrete set of points on the surface of the airfoil, as well as offline knowledge of the state of the flow. Methods include direct prediction from historical pressure measurements, flow reconstruction followed by forward integration using a full order solver, and data-driven dynamic models in various low dimensional quantities. Methods are compared using several criteria tailored for extreme event prediction. We show that methods using data-driven models of low order dynamic variables outperform those without dynamic models and that unlike previous works, low dimensional initializations do not accurately predict observables with extreme events such as drag.
physics.flu-dyn
From the simplest models to complex deep neural networks, modeling turbulence with machine learning techniques still offers multiple challenges. In this context, the present contribution proposes a robust strategy using patch-based training to learn turbulent viscosity from flow velocities, and demonstrates its efficient use on the Spallart-Allmaras turbulence model. Training datasets are generated for flow past two-dimensional (2D) obstacles at high Reynolds numbers and used to train an auto-encoder type convolutional neural network with local patch inputs. Compared to a standard training technique, patch-based learning not only yields increased accuracy but also reduces the computational cost required for training.
physics.flu-dyn
We develop a novel data-driven approach to modeling the atmospheric boundary layer. This approach leads to a nonlocal, anisotropic synthetic turbulence model which we refer to as the deep rapid distortion (DRD) model. Our approach relies on an operator regression problem which characterizes the best fitting candidate in a general family of nonlocal covariance kernels parameterized in part by a neural network. This family of covariance kernels is expressed in Fourier space and is obtained from approximate solutions to the Navier–Stokes equations at very high Reynolds numbers. Each member of the family incorporates important physical properties such as mass conservation and a realistic energy cascade. The DRD model can be calibrated with noisy data from field experiments. After calibration, the model can be used to generate synthetic turbulent velocity fields. To this end, we provide a new numerical method based on domain decomposition which delivers scalable, memory-efficient turbulence generation with the DRD model as well as others. We demonstrate the robustness of our approach with both filtered and noisy data coming from the 1968 Air Force Cambridge Research Laboratory Kansas experiments. Using this data, we witness exceptional accuracy with the DRD model, especially when compared to the International Electrotechnical Commission standard.
physics.plasm-ph
A key uncertainty in the design and development of magnetic confinement fusion energy reactors is predicting edge plasma turbulence. An essential step in overcoming this uncertainty is the validation in accuracy of reduced turbulent transport models. Drift-reduced Braginskii two-fluid theory is one such set of reduced equations that has for decades simulated boundary plasmas in experiment, but significant questions exist regarding its predictive ability. To this end, using a novel physics-informed deep learning framework, we demonstrate the first ever direct quantitative comparisons of turbulent field fluctuations between electrostatic two-fluid theory and electromagnetic gyrokinetic modelling with good overall agreement found in magnetized helical plasmas at low normalized pressure. This framework is readily adaptable to experimental and astrophysical environments, and presents a new technique for the numerical validation and discovery of reduced global plasma turbulence models.