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 fields are characterized by extreme events that are statistically intermittent and carry a significant amount of energy and physical importance. To emulate these flows, we introduce the extreme variational Autoencoder (xVAE), which embeds a max-infinitely divisible process with heavy-tailed distributions into a standard VAE framework, enabling accurate modeling of extreme events. xVAEs are neural network models that reduce system dimensionality by learning non-linear latent representations of data. We demonstrate the effectiveness of xVAE in large-eddy simulation data of wildland fire plumes, where intense heat release and complex plume-atmosphere interactions generate extreme turbulence. Comparisons with the commonly used Proper Orthogonal Decomposition (POD) modes show that xVAE is more robust in capturing extreme values and provides a powerful uncertainty quantification framework using variational Bayes. Additionally, xVAE enables analysis of the so-called copulas of fields to assess risks associated with rare events while rigorously accounting for uncertainty, such as simultaneous exceedances of high thresholds across multiple locations. The proposed approach provides a new direction for studying realistic turbulent flows, such as high-speed aerodynamics, space propulsion, and atmospheric and oceanic systems that are characterized by extreme events.
physics.flu-dyn
A novel strategy is proposed to improve the accuracy of state estimation and reconstruction from low-fidelity models and sparse data from sensors. This strategy combines ensemble Data Assimilation (DA) and Machine Learning (ML) tools, exploiting their complementary features. ML techniques rely on the data produced by DA methods during analysis phases to train physics-informed corrective algorithms, which are then coupled with the low-fidelity models when data from sensors is unavailable. The methodology is validated via the analysis of the turbulent plane channel flow test case for . Here, the low-fidelity model consists of coarse-grained simulations coupled with the Immersed Boundary Method (IBM), while observation is sampled by a highly refined body-fitted calculation. The analysis demonstrates the capabilities of the algorithm based on DA and ML to accurately predict the flow features with significantly reduced computational costs. This approach exhibits potential for future synergistic applications of DA and ML, leveraging the robustness and efficiency of ML models alongside the physical interpretability ensured by DA algorithms.
physics.flu-dyn
The high dimensionality and complex dynamics of turbulent flows in urban street canyons present significant challenges for wind and environmental engineering, particularly in addressing air quality, pollutant dispersion, and extreme wind events. This study introduces a deep learning framework to predict spatio-temporal flow behavior in street canyons with varying geometric configurations and upstream roughness conditions. A convolutional encoder-decoder transformer model, trained on particle image velocimetry (PIV) data from wind tunnel experiments, is employed with autoregressive training to predict flow characteristics. The training dataset contains diverse flow regimes, with a focus on the wall-parallel plane near the canyon roof, a critical region for pollutant exchange between the outer flow and the canyon interior. The model accurately reproduces key flow features, including mean turbulent statistics, two-point correlations, quadrant analysis, and dominant flow structures, while demonstrating strong agreement with experimental data in capturing the temporal evolution of flow dynamics. These findings demonstrate the potential of deep learning models to enhance predictive capabilities for urban canyon flows, offering a pathway toward improved urban design, sustainable environmental management, and more effective pollutant dispersion modeling.
physics.flu-dyn
Long-term prediction of three-dimensional (3D) turbulent flows is one of the most challenging problems for machine learning approaches. Although some existing machine learning approaches such as implicit U-net enhanced Fourier neural operator (IUFNO) have been proven to be capable of achieving stable long-term predictions for turbulent flows, their computational costs are usually high. In this paper, we use the adaptive Fourier neural operator (AFNO) as the backbone to construct a model that can predict 3D turbulence. Furthermore, we employ the implicit iteration to our constructed AFNO and propose the implicit adaptive Fourier neural operator (IAFNO). IAFNO is systematically tested in three types of 3D turbulence, including forced homogeneous isotropic turbulence (HIT), temporally evolving turbulent mixing layer and turbulent channel flow. The numerical results demonstrate that IAFNO is more accurate than IUFNO and the traditional large-eddy simulation using dynamic Smagorinsky model (DSM), while exhibiting greater stability compared to IUFNO. Meanwhile, the AFNO model exhibits instability in numerical simulations. Moreover, the training efficiency of IAFNO is 4 times higher than that of IUFNO, and the number of parameters and GPU memory occupation of IAFNO are only 1/80 and 1/3 of IUFNO, respectively in HIT. In other tests, the improvements are slightly lower but still considerable. These improvements mainly come from patching and self-attention in 3D space. Besides, the well-trained IAFNO is significantly faster than the DSM. The code (and datasets) of the current work can be accessed at https://github.com/yuchi-richard-jiang/IAFNO.
physics.flu-dyn
Models for the transport of high energy charged particles through strong magnetic turbulence play a key role in space and astrophysical studies, such as describing the propagation of solar energetic particles and high energy cosmic rays. Inspired by the recent advances in high-performance machine learning techniques, we investigate the application of generative diffusion models to synthesizing test particle trajectories obtained from a turbulent magnetohydrodynamics simulation. We consider velocity increment, spatial transport and curvature statistics, and find excellent agreement with the baseline trajectories for fixed particle energies. Additionally, we consider two synthetic turbulence models for comparison. Finally, challenges towards an application-ready transport model based on our approach are discussed.
physics.flu-dyn
With increasing computational demand, Neural-Network (NN) based models are being developed as pre-trained surrogates for different thermohydraulics phenomena. An area where this approach has shown promise is in developing higher-fidelity turbulence closures for computational fluid dynamics (CFD) simulations. The primary bottleneck to the widespread adaptation of these NN-based closures for nuclear-engineering applications is the uncertainties associated with them. The current paper illustrates three commonly used methods that can be used to quantify model uncertainty in NN-based turbulence closures. The NN model used for the current study is trained on data from an algebraic turbulence closure model. The uncertainty quantification (UQ) methods explored are Deep Ensembles, Monte-Carlo Dropout, and Stochastic Variational Inference (SVI). The paper ends with a discussion on the relative performance of the three methods for quantifying epistemic uncertainties of NN-based turbulence closures, and potentially how they could be further extended to quantify out-of-training uncertainties. For accuracy in turbulence modeling, paper finds Deep Ensembles have the best prediction accuracy with an RMSE of on the testing inputs followed by Monte-Carlo Dropout and Stochastic Variational Inference. For uncertainty quantification, this paper finds each method produces unique Epistemic uncertainty estimates with Deep Ensembles being overconfident in regions, MC-Dropout being under-confident, and SVI producing principled uncertainty at the cost of function diversity.
physics.flu-dyn
This article describes some common issues encountered in the use of Direct Numerical Simulation (DNS) turbulent flow data for machine learning. We focus on two specific issues; 1) the requirements for a fair validation set, and 2) the pitfalls in downsampling DNS data before training. We attempt to shed light on the impact these issues can have on machine learning and computer vision for turbulence. Further, we include statistical and spectral analysis for the homogenous isotropic turbulence from the John Hopkins Turbulence Database, a Kolmogorov flow, and a Rayleigh-Bénard Convection Cell using data generated by the authors, to concretely demonstrate these issues.
physics.flu-dyn
A deep-learning-based closure model to address energy loss in low-dimensional surrogate models based on proper-orthogonal-decomposition (POD) modes is introduced. Using a transformer-encoder block with easy-attention mechanism, the model predicts the spatial probability density function of fluctuations not captured by the truncated POD modes. The methodology is demonstrated on the wake of the Windsor body at yaw angles of [2.5,5,7.5,10,12.5], with 7.5 as a test case. Key coherent modes are identified by clustering them based on dominant frequency dynamics using Hotelling T2 on the spectral properties of temporal coefficients. These coherent modes account for nearly 60% of the total energy while comprising less than 10% of all modes. A common POD basis is created by concatenating coherent modes from training angles and orthonormalizing the set, reducing the basis vectors from 142 to 90 without losing information. Transformers with different size on the attention layer, (64, 128 and 256), are trained to model the missing fluctuations. Larger attention sizes always improve predictions for the training set, but the transformer with an attention layer of size 256 overshoots the fluctuations predictions in the test set because they have lower intensity than in the training cases. Adding the predicted fluctuations closes the energy gap between the reconstruction and the original flow field, improving predictions for energy, root-mean-square velocity fluctuations, and instantaneous flow fields. The deepest architecture reduces mean energy error from 37% to 12% and decreases the Kullback–Leibler divergence of velocity distributions from KL=0.2 to below KL=0.026.
physics.flu-dyn
Accurate simulation of turbulent flows remains a challenge due to the high computational cost of direct numerical simulations (DNS) and the limitations of traditional turbulence models. This paper explores a novel approach to augmenting standard models for Reynolds-Averaged Navier-Stokes (RANS) simulations using a Non-Linear Super-Stencil (NLSS). The proposed method introduces a fully connected neural network that learns a mapping from the local mean flow field to a corrective force term, which is added to a standard RANS solver in order to align its solution with high-fidelity data. A procedure is devised to extract training data from reference DNS and large eddy simulations (LES). To reduce the complexity of the non-linear mapping, the dimensionless local flow data is aligned with the local mean velocity, and the local support domain is scaled by the turbulent integral length scale. After being trained on a single periodic hill case, the NLSS-corrected RANS solver is shown to generalize to different periodic hill geometries and different Reynolds numbers, producing significantly more accurate solutions than the uncorrected RANS simulations.
physics.flu-dyn
Numerical simulations of turbulent flows present significant challenges in fluid dynamics due to their complexity and high computational cost. High resolution techniques such as Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are generally not computationally affordable, particularly for technologically relevant problems. Recent advances in machine learning, specifically in generative probabilistic models, offer promising alternatives as surrogates for turbulence. This paper investigates the application of three generative models - Variational Autoencoders (VAE), Deep Convolutional Generative Adversarial Networks (DCGAN), and Denoising Diffusion Probabilistic Models (DDPM) - in simulating a von Kármán vortex street around a fixed cylinder projected into 2D, as well as a real-world experimental dataset of the wake flow of a cylinder array. Training data was obtained by means of LES in the simulated case and Particle Image Velocimetry (PIV) in the experimental case. We evaluate each model's ability to capture the statistical properties and spatial structures of the turbulent flow. Our results demonstrate that DDPM and DCGAN effectively replicate all flow distributions, highlighting their potential as efficient and accurate tools for turbulence surrogacy. We find a strong argument for DCGAN, as although they are more difficult to train (due to problems such as mode collapse), they show the fastest inference and training time, require less data to train compared to VAE and DDPM, and provide the results most closely aligned with the input stream. In contrast, VAE train quickly (and can generate samples quickly) but do not produce adequate results, and DDPM, whilst effective, are significantly slower at both, inference and training time.
physics.flu-dyn
We show that flocking of microswimmers in a turbulent flow can enhance the efficacy of reinforcement-learning-based path-planning of microswimmers in turbulent flows. In particular, we develop a machine-learning strategy that incorporates Vicsek-model-type flocking in microswimmer assemblies in a statistically homogeneous and isotropic turbulent flow in two dimensions (2D). We build on the adversarial-reinforcement-learning of Ref.~\cite{alageshan2020machine} for non-interacting microswimmers in turbulent flows. Such microswimmers aim to move optimally from an initial position to a target. We demonstrate that our flocking-aided version of the adversarial-reinforcement-learning strategy of Ref.~\cite{alageshan2020machine} can be superior to earlier microswimmer path-planning strategies.
physics.flu-dyn
Eddy-resolving turbulence simulations require stochastic inflow conditions that accurately replicate the complex, multi-scale structures of turbulence. Traditional recycling-based methods rely on computationally expensive precursor simulations, while existing synthetic inflow generators often fail to reproduce realistic coherent structures of turbulence. Recent advances in deep learning (DL) have opened new possibilities for inflow turbulence generation, yet many DL-based methods rely on deterministic, autoregressive frameworks prone to error accumulation, resulting in poor robustness for long-term predictions. In this work, we present CoNFiLD-inlet, a novel DL-based inflow turbulence generator that integrates diffusion models with a conditional neural field (CNF)-encoded latent space to produce realistic, stochastic inflow turbulence. By parameterizing inflow conditions using Reynolds numbers, CoNFiLD-inlet generalizes effectively across a wide range of Reynolds numbers ( between and ) without requiring retraining or parameter tuning. Comprehensive validation through a priori and a posteriori tests in Direct Numerical Simulation (DNS) and Wall-Modeled Large Eddy Simulation (WMLES) demonstrates its high fidelity, robustness, and scalability, positioning it as an efficient and versatile solution for inflow turbulence synthesis.
quant-ph
Quantum differential equation solvers aim to prepare solutions as -qubit quantum states over a fine grid of points, surpassing the linear scaling of classical solvers. However, unlike classically stored vectors of solutions, the readout of exact quantum states poses a bottleneck due to the complexity of tomography. Here, we show that the readout problem can be addressed with quantum learning tools where we focus on distilling the relevant features. Treating outputs of quantum differential equation solvers as quantum data, we demonstrate that low-dimensional output can be extracted using a measurement operator adapted to detect relevant features. We apply this quantum scientific machine learning approach to classify solutions for shock wave detection and turbulence modeling in scenarios where data samples come directly from quantum differential equation solvers. We show that the basis chosen for performing analysis greatly impacts classification accuracy. Our work opens up the area of research where quantum machine learning for quantum datasets is inherently required.
physics.ao-ph
For reasons of computational constraint, most global ocean circulation models used for Earth System Modeling still rely on parameterizations of sub-grid processes, and limitations in these parameterizations affect the modeled ocean circulation and impact on predictive skill. An increasingly popular approach is to leverage machine learning approaches for parameterizations, regressing for a map between the resolved state and missing feedbacks in a fluid system as a supervised learning task. However, the learning is often performed in an `offline' fashion, without involving the underlying fluid dynamical model during the training stage. Here, we explore the `online' approach that involves the fluid dynamical model during the training stage for the learning of baroclinic turbulence and its parameterization, with reference to ocean eddy parameterization. Two online approaches are considered: a full adjoint-based online approach, related to traditional adjoint optimization approaches that require a `differentiable' dynamical model, and an approximately online approach that approximates the adjoint calculation and does not require a differentiable dynamical model. The online approaches are found to be generally more skillful and numerically stable than offline approaches. Others details relating to online training, such as window size, machine learning model set up and designs of the loss functions are detailed to aid in further explorations of the online training methodology for Earth System Modeling.
physics.flu-dyn
This work studies an a posteriori data-driven approach (known as solver-in-the-loop) for sub-grid modeling of a shell model for turbulence. This approach takes advantage of the differentiable physics paradigm of deep learning, allowing a neural network model to interact with the differential equation solver over time during the training process. The closure model is, then, naturally exposed to equations-informed input distributions by accounting for prior corrections over the temporal evolution in training. Such a characteristic makes this approach depart from the conventional a priori instantaneous training paradigm and often leads to a more accurate and stable closure model. Our study demonstrates that the closure learned via this a posteriori approach is able to reproduce high-order statistical moments of interest also in closures of high Reynolds number turbulence. Moreover, we investigate the performance of the learned model by experimenting with the effect of unrolling in time, which has remained for the most part unexplored in the literature. Finally, we discuss potential extensions of this approach to Navier-Stokes equations.
physics.flu-dyn
This study constitutes the second phase of a research endeavor aimed at evaluating the feasibility of employing Long Short-Term Memory (LSTM) neural networks as a replacement for Reynolds-Averaged Navier-Stokes (RANS) turbulence models. In the initial phase of this investigation (titled Modeling Turbulent Flows with LSTM Neural Networks, arXiv:2307.13784v1 [physics.flu-dyn] 25 Jul 2023), the application of an LSTM-based recurrent neural network (RNN) as an alternative to traditional RANS models was demonstrated. LSTM models were used to predict shear Reynolds stresses in both developed and developing turbulent channel flows, and these predictions were propagated through RANS simulations to obtain mean flow fields of turbulent flows. A comparative analysis was conducted, juxtaposing the LSTM results from computational fluid dynamics (CFD) simulations with outcomes from the model and data from direct numerical simulations (DNS). These initial findings indicated promising performance of the LSTM approach. This second phase delves further into the challenges encountered and presents robust solutions. Additionally, new results are provided, demonstrating the efficacy of the LSTM model in predicting turbulent behavior in perturbed flows. While the overall study serves as a proof-of-concept for the application of LSTM networks in RANS turbulence modeling, this phase offers compelling evidence of its potential in handling more complex flow scenarios.
physics.flu-dyn
We propose a defiltering method of turbulent flow fields for Lagrangian particle tracking using machine learning techniques. Numerical simulation of Lagrangian particle tracking is commonly used in various fields. In general, practical applications require an affordable grid size due to the limitation of computational resources; for instance, a large-eddy simulation reduces the number of grid points with a filtering operator. However, low resolution flow fields usually underestimate the fluctuations of particle velocity. We thus present a novel approach to defilter the fluid velocity to improve the particle motion in coarse-grid (i.e., filtered) fields. The proposed method, which is based on the machine learning techniques, intends to reconstruct the fluid velocity at a particle location. We assess this method in a priori manner using a turbulent channel flow at the friction Reynolds number . The investigation is conducted for the filter size, , of , , and . In the case of , the proposed method can perfectly reconstruct the fluid velocity fluctuations. The results of and also exhibit substantial improvements in the fluctuation statistics although with some underestimations. Subsequently, the particle motion computed using the present method is analyzed. The trajectories, the velocity fluctuations, and the deposition velocity of particles are reconstructed accurately. Moreover, the generalizability of the present method is also demonstrated using the fields whose computational domain is larger than that used for the training. The present findings suggest that machine learning-based velocity reconstruction will enable us precise particle tracking in coarse-grid flow fields.
physics.flu-dyn
The accurate and fast prediction of long-term dynamics of turbulence presents a significant challenge for both traditional numerical simulations and machine learning methods. In recent years, the emergence of neural operators has provided a promising approach to address this issue. The implicit U-Net enhanced Fourier neural operator (IU-FNO) has successfully demonstrated long-term stable predictions for three-dimensional incompressible turbulence. In this study, we extend this method to the three-dimensional chemically reacting compressible turbulence. Numerical results show that the IU-FNO model predicts flow dynamics significantly faster than the traditional dynamic Smagorinsky model (DSM) used in large eddy simulation (LES). In terms of prediction accuracy, the IU-FNO framework outperforms the traditional DSM in predicting the energy spectra of velocity, temperature, and density, the probability density functions (PDFs) of vorticity and velocity increments, and instantaneous spatial structures of temperature. Therefore, the IU-FNO represents a highly promising approach for predicting chemically reacting compressible turbulence.
physics.flu-dyn
We present a stochastic method for reconstructing missing spatial and velocity data along the trajectories of small objects passively advected by turbulent flows with a wide range of temporal or spatial scales, such as small balloons in the atmosphere or drifters in the ocean. Our approach makes use of conditional generative diffusion models, a recently proposed data-driven machine learning technique. We solve the problem for two paradigmatic open problems, the case of 3D tracers in homogeneous and isotropic turbulence, and 2D trajectories from the NOAA-funded Global Drifter Program. We show that for both cases, our method is able to reconstruct velocity signals retaining non-trivial scale-by-scale properties that are highly non-Gaussian and intermittent. A key feature of our method is its flexibility in dealing with the location and shape of data gaps, as well as its ability to naturally exploit correlations between different components, leading to superior accuracy, with respect to Gaussian process regressions, for both pointwise reconstruction and statistical expressivity. Our method shows promising applications also to a wide range of other Lagrangian problems, including multi-particle dispersion in turbulence, dynamics of charged particles in astrophysics and plasma physics, and pedestrian dynamics.
physics.flu-dyn
For the last 140 years, the mechanisms of transport and dissipation of energy in a turbulent flow have not been completely understood. Previous research has focused on analyzing the so-called coherent structures, organized flow patterns characterized by their spatial coherence, lifespan and significant contribution to momentum and energy transfer. However, the connection between these structures and the flow development is still uncertain. Here, we show a data-driven methodology for objectively identifying high-importance regions. A deep-learning model is trained to predict a future state of the flow and the gradient-SHAP explainability algorithm is used to calculate the importance of each grid point. Finally, high-importance regions are computed using the SHAP data and are compared to the other coherent structures. The SHAP analysis provides an objective way to identify the regions of higher importance, which exhibit different levels of agreement with the classical structures without being completely related to any particular one.