An Efficient Deep Learning Technique for the Navier-Stokes Equations: Application to Unsteady Wake Flow Dynamics

Miyanawala, Tharindu P.; Jaiman, Rajeev K.

doi:10.48550/arxiv.1710.09099

Cited by 19 publications

(21 citation statements)

References 29 publications

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“…al 56 also employed physics-informed machine learning to model the reconstruction of inconsistencies in the Reynolds stresses. As the second category of neural architectural designs, convolutional neural networks are utilized for the prediction of steady laminar flows 18 and the bulk quantities of interest 38 for bluff bodies. Similarly, Lee et.…”

Section: B Review Of Physics-based Deep Leaningmentioning

confidence: 99%

“…They are utilized to extract relevant features from the 3D unsteady flow data to construct the reduced-order state. The application of 2D CNNs as a reduced-order model has been explored by Miyanawala and Jaiman 38 to predict bluff body forces. For the sake of explanation, we briefly describe the feature extraction process of a 3D CNN that is useful for constructing the encoder network of the convolutional autoencoder.…”

Section: A 3d Convolutional Neural Networkmentioning

confidence: 99%

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Three-dimensional deep learning-based reduced order model for unsteady flow dynamics with variable Reynolds number

Gupta,

Jaiman

2021

Preprint

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In this article, we present a deep learning-based reduced order model (DL-ROM) for predicting the fluid forces and unsteady vortex shedding patterns. We consider the flow past a sphere to examine the accuracy of our DL-ROM predictions. The proposed DL-ROM methodology relies on a three-dimensional convolutional recurrent autoencoder network (3D CRAN) to extract the low-dimensional flow features from the full-order snapshots in an unsupervised manner. The low-dimensional features are evolved in time using a long short-term memory-based recurrent neural network (LSTM-RNN) and reconstructed back to the full-order as flow voxels. These flow voxels are introduced as static and uniform query probes in the point cloud domain to reduce the unstructured mesh complexity while providing convenience in the 3D CRAN training. We analyze a novel procedure to recover the interface description and the instantaneous force quantities from these 3D flow voxels. The 3D CRAN-based DL-ROM methodology is first applied to an external flow past a static sphere at single Reynolds number (Re) of Re = 300 to test the 3D flow reconstruction and inference. We provide an assessment of the computing requirements in terms of the memory usage, training costs and testing times associated with the 3D CRAN framework. Subsequently, variable Re-based flow information is infused in one 3D CRAN to learn a complicated symmetry-breaking flow regime (280 ≤ Re ≤ 460) for the flow past a sphere. Effects of transfer learning are analyzed for training this complicated 3D flow regime on a relatively smaller time series dataset. The 3D CRAN framework learns the complicated flow regime nearly 20 times faster than the parallel full-order model and predicts this flow regime in time with an excellent to good accuracy. Based on the predicted flow fields, the network demonstrates an R 2 accuracy of 98.58% for the drag and 76.43% for the lift over the sphere in this flow regime. The proposed framework aligns with the development of a digital twin for 3D unsteady flow field and instantaneous force predictions with variable Re effects.

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Section: B Review Of Physics-based Deep Leaningmentioning

confidence: 99%

Section: A 3d Convolutional Neural Networkmentioning

confidence: 99%

Three-dimensional deep learning-based reduced order model for unsteady flow dynamics with variable Reynolds number

Gupta,

Jaiman

2021

Preprint

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“…Guo et al (2016) employed a convolutional neural network (CNN) to predict steady flow fields around bluff objects and reported reasonable prediction of steady flow fields with significantly reduced computational cost than that required for numerical simulations. Similarly, Miyanawala & Jaiman (2017) employed a CNN to predict aerodynamic force coefficients of bluff bodies, also with notably reduced computational costs. Those previous studies showed high potential of deep learning techniques for enhancing simulation accuracy and reducing computational cost.…”

Section: Introductionmentioning

confidence: 99%

Data-driven prediction of unsteady flow over a circular cylinder using deep learning

2019

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Unsteady flow fields over a circular cylinder are trained and predicted using four different deep learning networks: generative adversarial networks with and without consideration of conservation laws and convolutional neural networks with and without consideration of conservation laws. Flow fields at future occasions are predicted based on information of flow fields at previous occasions. Predictions of deep learning networks are conducted on flow fields at Reynolds numbers that were not informed during training. Physical loss functions are proposed to explicitly impose information of conservation of mass and momentum to deep learning networks. An adversarial training is applied to extract features of flow dynamics in an unsupervised manner. Effects of the proposed physical loss functions and adversarial training on predicted results are analyzed. Captured and missed flow physics from predictions are also analyzed. Predicted flow fields using deep learning networks are in favorable agreement with flow fields computed by numerical simulations.

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“…Consequently, the recent developments in CNN architectures have yielded new methods to approximate flow at states such as geometries or Reynolds numbers that were not utilized during training [32][33][34][35][36]. For instance, Lee and You [35] developed a generative adversarial network (GAN), which is composed of multiple CNNs, to predict flow over a circular cylinder on two-dimensional slices at Reynolds numbers that were not utilized during training.…”

Section: Introductionmentioning

confidence: 99%

Mechanisms of a Convolutional Neural Network for Learning Three-dimensional Unsteady Wake Flow

Lee,

You

2019

Preprint

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In the present study, a convolutional neural network (CNN) system which consists of multiple multi-resolution CNNs to predict future three-dimensional unsteady wake flow using flow fields in the past occasions is developed. Mechanisms of the developed CNN system for prediction of wake flow behind a circular cylinder are investigated in two flow regimes: the three-dimensional wake transition regime and the shear-layer transition regime. Understanding of mechanisms of CNNs for learning fluid dynamics is highly necessary to design the network system or to reduce trial-and-errors during the network optimization. Feature maps in the CNN system are visualized to compare flow structures which are extracted by the CNN system from flow in the two flow regimes. In both flow regimes, feature maps are found to extract similar sets of flow structures such as braid shear-layers and shedding vortices. A Fourier analysis is conducted to investigate mechanisms of the CNN system for predicting wake flow in flow regimes with different wavenumber characteristics. It is found that a convolution layer in the CNN system integrates and transports wavenumber information from flow to predict the dynamics.Characteristics of the CNN system for transporting input information including time histories of flow variables are analyzed by assessing contributions of each flow variable and time history to feature maps in the CNN system. Structural similarities among feature maps in the CNN system are calculated to reveal the number of feature maps that contain similar flow structures.By reducing feature maps which contain similar flow structures, it is also able to successfully reduce the number of weights to learn in the CNN system without affecting prediction performance.

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An Efficient Deep Learning Technique for the Navier-Stokes Equations: Application to Unsteady Wake Flow Dynamics

Cited by 19 publications

References 29 publications

Three-dimensional deep learning-based reduced order model for unsteady flow dynamics with variable Reynolds number

Three-dimensional deep learning-based reduced order model for unsteady flow dynamics with variable Reynolds number

Data-driven prediction of unsteady flow over a circular cylinder using deep learning

Mechanisms of a Convolutional Neural Network for Learning Three-dimensional Unsteady Wake Flow

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