Generative Adversarial Networks (GANs) have been widely used for generating photo-realistic images. A variant of GANs called super-resolution GAN (SRGAN) has already been used successfully for image super-resolution where low resolution images can be upsampled to a $4\times$ larger image that is perceptually more realistic. However, when such generative models are used for data describing physical processes, there are additional known constraints that models must satisfy including governing equations and boundary conditions. In general, these constraints may not be obeyed by the generated data. In this work, we develop physics-based methods for generative enrichment of turbulence. We incorporate a physics-informed learning approach by a modification to the loss function to minimize the residuals of the governing equations for the generated data. We have analyzed two trained physics-informed models: a supervised model based on convolutional neural networks (CNN) and a generative model based on SRGAN: Turbulence Enrichment GAN (TEGAN), and show that they both outperform simple bicubic interpolation in turbulence enrichment. We have also shown that using the physics-informed learning can also significantly improve the model's ability in generating data that satisfies the physical governing equations. Finally, we compare the enriched data from TEGAN to show that it is able to recover statistical metrics of the flow field including energy metrics and well as inter-scale energy dynamics and flow morphology.
National Renewable Energy Laboratory（国家可再生能源实验室）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
We describe tests validating progress made toward acceleration and automation of hydrodynamic codes in the regime of developed turbulence by three Deep Learning (DL) Neural Network (NN) schemes trained on Direct Numerical Simulations of turbulence. Even the bare DL solutions, which do not take into account any physics of turbulence explicitly, are impressively good overall when it comes to qualitative description of important features of turbulence. However, the early tests have also uncovered some caveats of the DL approaches. We observe that the static DL scheme, implementing Convolutional G…
Turbulence is still one of the main challenges for accurately predicting reactive flows. Therefore, the development of new turbulence closures which can be applied to combustion problems is essential. Data-driven modeling has become very popular in many fields over the last years as large, often extensively labeled, datasets became available and training of large neural networks became possible on GPUs speeding up the learning process tremendously. However, the successful application of deep neural networks in fluid dynamics, for example for subgrid modeling in the context of large-eddy simula…
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Georgia Institute of Technology（佐治亚理工学院）；Center for Nonlinear Studies（非线性研究中心）
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 em…
Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH（于利希研究中心于利希超级计算中心）；RWTH Aachen University（亚琛工业大学）
Models for finite-rate-chemistry in underresolved flows still pose one of the main challenges for predictive simulations of complex configurations. The problem gets even more challenging if turbulence is involved. This work advances the recently developed PIESRGAN modeling approach to turbulent premixed combustion. For that, the physical information processed by the network and considered in the loss function are adjusted, the training process is smoothed, and especially effects from density changes are considered. The resulting model provides good results for a priori and a posteriori tests o…
Turbulence plays an important role in astrophysical phenomena, including core-collapse supernovae (CCSN), but current simulations must rely on subgrid models since direct numerical simulation (DNS) is too expensive. Unfortunately, existing subgrid models are not sufficiently accurate. Recently, Machine Learning (ML) has shown an impressive predictive capability for calculating turbulence closure. We have developed a physics-informed convolutional neural network (CNN) to preserve the realizability condition of Reynolds stress that is necessary for accurate turbulent pressure prediction. The app…
Simulating Three-dimensional Turbulence with Physics-informed Neural Networks
Institution for Foundation of Data Science, Yale University（数据科学基础研究所，耶鲁大学）；Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania（机械工程与应用力学系，宾夕法尼亚大学）；Sibley School of Mechanical and Aerospace Engineering, Cornell University（机械与航空航天工程学院，康奈尔大学）；Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory（先进计算、数学和数据部门，太平洋西北国家实验室）
Turbulence remains a problem that is yet to be fully understood, with experimental and numerical studies aiming to fully characterise the statistical properties of turbulent flows. Such studies require huge amount of resources to capture, simulate, store and analyse the data. In this work, we present physics-informed neural network (PINN) based methods to predict flow quantities and features of two-dimensional turbulence with the help of sparse data in a rectangular domain with periodic boundaries. While the PINN model can reproduce all the statistics at large scales, the small scale propertie…
High Reynolds Homogeneous Isotropic Turbulence is fully described within the Navier-Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as Large Eddy Simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about effects of sub-grid scales on the resolved scales. Here, we …
Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks
Brown University（布朗大学）；Technische Universität Ilmenau（伊尔默瑙工业大学）
Resolving Turbulent Magnetohydrodynamics: A Hybrid Operator-Diffusion Framework
National Center for Supercomputing Applications, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校国家超级计算中心）；Department of Physics, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校物理系）；Data Science and Learning Division, Argonne National Laboratory（阿贡国家实验室数据科学与学习部门）；Department of Computer Science, The University of Chicago（芝加哥大学计算机科学系）；Department of Astronomy, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校天文学系）；Department of Physics and Astronomy, University of British Columbia（不列颠哥伦比亚大学物理与天文学系）
Istituto Italiano di Tecnologia（意大利理工学院）；Johns Hopkins University（约翰斯·霍普金斯大学）
We study the applicability of tools developed by the computer vision community for features learning and semantic image inpainting to perform data reconstruction of fluid turbulence configurations. The aim is twofold. First, we explore on a quantitative basis, the capability of Convolutional Neural Networks embedded in a Deep Generative Adversarial Model (Deep-GAN) to generate missing data in turbulence, a paradigmatic high dimensional chaotic system. In particular, we investigate their use in reconstructing two-dimensional damaged snapshots extracted from a large database of numerical configu…
University of Tehran（德黑兰大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）
Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations (PDEs). We employ PINNs for solving the Reynolds-averaged Navier$\unicode{x2013}$Stokes (RANS) equations for incompressible turbulent flows without any specific model or assumption for turbulence, and by taking only the data on the domain boundaries. We first show the applicability of PINNs for solving the Navier$\unicode{x2013}$Stokes equations for laminar flows by solving the Falkner$\unicode{x2013}$Skan boundary layer. We then apply PINNs for…
Brown University（布朗大学）；Sandia National Laboratories（桑迪亚国家实验室）
Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integral equations with sparse, noisy, unstructured, and multi-fidelity data. PINNs incorporate all available information into a loss function, thus recasting the original problem into an optimization problem. In this paper, we extend PINNs to parameter and function inference for integral equations such as nonlocal Poisson and nonlocal turbulence models, and we refer to them as nonlocal PINNs (nPINNs). The contribution of the paper is three-fold. First, we propose a unified nonlocal ope…
Based on recent developments in physics-informed deep learning and deep hidden physics models, we put forth a framework for discovering turbulence models from scattered and potentially noisy spatio-temporal measurements of the probability density function (PDF). The models are for the conditional expected diffusion and the conditional expected dissipation of a Fickian scalar described by its transported single-point PDF equation. The discovered model are appraised against exact solution derived by the amplitude mapping closure (AMC)/ Johnsohn-Edgeworth translation (JET) model of binary scalar …
Despite their well-known limitations, RANS models remain the most commonly employed tool for modeling turbulent flows in engineering practice. RANS models are predicated on the solution of the RANS equations, but these equations involve an unclosed term, the Reynolds stress tensor, which must be modeled. The Reynolds stress tensor is often modeled as an algebraic function of mean flow field variables and turbulence variables. This introduces a discrepancy between the Reynolds stress tensor predicted by the model and the exact Reynolds stress tensor. This discrepancy can result in inaccurate me…
Northeastern University（东北大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Lawrence Berkeley Lab（劳伦斯伯克利实验室）
While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim to predict turbulent flow by learning its highly nonlinear dynamics from spatiotemporal velocity fields of large-scale fluid flow simulations of relevance to turbulence modeling and climate modeling. We adopt a hybrid approach by marrying two well-established turbulent flow simulation techniques with deep learning. Specifically, we introduce trainable spect…
Technische Universität Dresden（德累斯顿工业大学）；Max Planck Institute of Molecular Cell Biology and Genetics（马克斯·普朗克分子细胞生物学与遗传学研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Flatiron Institute（弗拉蒂伦研究所）；Helmholtz Zentrum München（亥姆霍兹慕尼黑中心）；Center for Scalable Data Analytics and Artificial Intelligence ScaDS.AI（可扩展数据分析与人工智能中心（ScaDS.AI））；Helmholtz-Zentrum Dresden-Rossendorf（亥姆霍兹德累斯顿罗森多夫研究中心）；Center for Advanced Systems Understanding (CASUS)（高级系统理解中心（CASUS））
We characterize and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks, such as Physics Informed Neural Networks (PINNs). PINNs are popular machine-learning templates that allow for seamless integration of physical equation models with data. Their training amounts to solving an optimization problem over a weighted sum of data-fidelity and equation-fidelity objectives. Conflicts between objectives can arise from scale imbalances, heteroscedasticity in the data, stiffness of the physical equation, or from catastrophic inte…
This work presents a formalism to improve the predictive accuracy of physical models by learning generalizable augmentations from sparse data. Building on recent advances in data-driven turbulence modeling, the present approach, referred to as Learning and Inference assisted by Feature-space Engineering (LIFE), is based on the hypothesis that robustness and generalizability demand a meticulously-designed feature space that is informed by the underlying physics, and a carefully constructed features-to-augmentation map. The critical components of this approach are: (1) Maintaining consistency ac…
Hierarchical Multi-Fidelity Learning for Predicting Three-Dimensional Flame Wrinkling and Turbulent Burning Velocity
Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115, USA（机械与工业工程系，东北大学，波士顿，马萨诸塞州，02115，美国）；School of Mechanical Engineering, University of Leeds, Leeds, UK（机械工程学院，利兹大学，利兹，英国）
LaPON: A Lagrange's-mean-value-theorem-inspired operator network for solving PDEs and its application on NSE
Ocean College, Zhejiang University（浙江大学海洋学院）；Ocean Research Center of Zhoushan, Zhejiang University（浙江大学舟山海洋研究中心）；Hangzhou International Innovation Institute, Beihang University（北京航空航天大学杭州国际创新研究院）
