2017 Preprint**Abstract:** We present an efficient deep learning technique for the model reduction of the Navier-Stokes equations for unsteady flow problems. The proposed technique relies on the Convolutional Neural Network (CNN) and the stochastic gradient descent method. Of particular interest is to predict the unsteady fluid forces for different bluff body shapes at low Reynolds number. The discrete convolution process with a nonlinear rectification is employed to approximate the mapping between the bluff-body shape and the fluid for…

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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.…”

confidence: 99%

“…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.…”

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.…”

confidence: 99%

“…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.…”

confidence: 99%

“…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.…”

confidence: 99%