In this paper, Physics Informed Neural Network (PINN) is explored in order to obtain flow predictions near the wall region accurately with measurements (or sampling points) away from the wall. Often, in fluid mechanics experiments, it is difficult to perform velocity measurements near the wall accurately. Therefore, the present study reveals a new and elegant approach to recover the flow solutions near the wall. Laminar boundary layer flow over a flat plate case is considered for this study in order to explore the ability of PINN to accurately predict the flow field. All the required sampling data for this study is obtained from CFD simulations. A wide range of Reynolds number cases from Re=500 to 100000 has been investigated. First, using PINN, the boundary layer solution is obtained with three different types of boundary conditions. Further, the influence of the location of the sampling points on the accuracy is analysed. From the velocity profiles and the skin friction coefficient distribution, it is clear that PINN results are reasonably accurate near the wall with only a few sampling points away from the wall. This approach has potential application in experiments to obtain the near wall solutions accurately with measurements away from the wall.
Brown University（布朗大学）；Xiamen University（厦门大学）；Dalian University of Technology（大连理工大学）
Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier-Stokes equations (NSE), we still cannot incorporate seamlessly noisy data into existing algorithms, mesh-generation is complex, and we cannot tackle high-dimensional problems governed by parametrized NSE. Moreover, solving inverse flow problems is often prohibitively expensive and requires complex and expensive formulations and new computer codes. Here, we review flow physics-informed learning, integrating seamlessly data and mathematical models, and implementing the…
Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training a reliable model. This can be achieved by incorporating the residual of physics equations into the loss function. Through minimizing the loss function, the network could approximate the solution. In this paper, we propose a mixed-variable scheme of physics-informed neural network (PINN) for fluid dynamics and apply it to simulate steady and transient lamina…
Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in scenarios of reconstructing the physics field and solving the inverse problem. Considering the advantages of parameter sharing, spatial feature extraction and low inference cost, convolutional neural networks (CNN) are increasingly used in PINN. However, some challenges still remain as follows. To adapt convolutional PINN to solve different PDEs, considerable effo…
Solving Euler equations with Multiple Discontinuities via Separation-Transfer Physics-Informed Neural Networks
Graduate School, China Academy of Engineering Physics（中国工程物理研究院研究生院）；China Academy of Engineering Physics（中国工程物理研究院）；Zhejiang Institute of Modern Physics（浙江现代物理研究所）；School of Physics, Zhejiang University（浙江大学物理学院）；Beijing Computational Science Research Center（北京计算科学研究院）
We consider the approximation of a class of dynamic partial differential equations (PDE) of second order in time by the physics-informed neural network (PINN) approach, and provide an error analysis of PINN for the wave equation, the Sine-Gordon equation and the linear elastodynamic equation. Our analyses show that, with feed-forward neural networks having two hidden layers and the $\tanh$ activation function, the PINN approximation errors for the solution field, its time derivative and its gradient field can be effectively bounded by the training loss and the number of training data points (q…
LSTM-PINN: An Hybrid Method for Prediction of Steady-State Electrohydrodynamic Flow
Nanophotonics and Biophotonics Key Laboratory of Jilin Province, School of Physics, Changchun University of Science and Technology（吉林省纳米光子学与生物光子学重点实验室，长春理工大学物理学院）
Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局（A*STAR））；Nanyang Technological University（南洋理工大学）
In this study, novel physics-informed neural network (PINN) methods for coupling neighboring support points and their derivative terms which are obtained by automatic differentiation (AD), are proposed to allow efficient training with improved accuracy. The computation of differential operators required for PINNs loss evaluation at collocation points are conventionally obtained via AD. Although AD has the advantage of being able to compute the exact gradients at any point, such PINNs can only achieve high accuracies with large numbers of collocation points, otherwise they are prone to optimizi…
PT-PINNs: A Parametric Engineering Turbulence Solver based on Physics-Informed Neural Networks
Zhejiang University（浙江大学）；Shanghai Institute for Advanced Study of Zhejiang University（浙江大学上海高等研究院）；State Key Laboratory of Clean Energy Utilization（清洁能源利用国家重点实验室）
Though PINNs (physics-informed neural networks) are now deemed as a complement to traditional CFD (computational fluid dynamics) solvers rather than a replacement, their ability to solve the Navier-Stokes equations without given data is still of great interest. This report presents our not-so-successful experiments of solving the Navier-Stokes equations with PINN as a replacement for traditional solvers. We aim to, with our experiments, prepare readers for the challenges they may face if they are interested in data-free PINN. In this work, we used two standard flow problems: 2D Taylor-Green vo…
While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this work we attribute this shortcoming to the inability of existing PINNs formulations to respect the spatio-temporal causal structure that is inherent to the evolution of physical systems. We argue that this is a fundamental limitation and a key source of error that can ultimately steer PINN models to converge towards erroneous solutions. We address this pathology…
Universidad de San Andrés（圣安德烈斯大学）；Institute of Science and Technology Austria（奥地利科学技术研究所）
We investigate the capabilities of Physics-Informed Neural Networks (PINNs) to reconstruct turbulent Rayleigh-Benard flows using only temperature information. We perform a quantitative analysis of the quality of the reconstructions at various amounts of low-passed-filtered information and turbulent intensities. We compare our results with those obtained via nudging, a classical equation-informed data assimilation technique. At low Rayleigh numbers, PINNs are able to reconstruct with high precision, comparable to the one achieved with nudging. At high Rayleigh numbers, PINNs outperform nudging …
