In this article, we propose an unsteady data-driven reduced order model (ROM) (surrogate model) for predicting the velocity field around an airfoil. The network model applies a convolutional neural network (CNN) as the encoder and a deconvolutional neural network (DCNN) as the decoder. The model constructs a mapping function between temporal evolution of the pressure signal on the airfoil surface and the surrounding velocity field. For improving the model performance, the input matrix is designed to further incorporate the information of the Reynolds number, the geometry of the airfoil, and the angle of attack. The DCNN works as the decoder for better reconstructing the spatial and temporal information of the features extracted by the CNN encoder. The training and testing datasets of flow fields under different conditions are obtained by solving the Navier–Stokes equations using the computational fluid dynamics method. After model training, the neural network based ROM shows accurate and dramatically fast predictions on the flow field of the testing dataset with extended angles of attack and Reynolds numbers. According to the current study, the neural network-based ROM has exhibited attractive potentials on ROM of the unsteady fluid dynamic problem, and the model can potentially serve on investigating flow control or optimization problems in the future.

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In this paper, we propose a neural network based reduced-order model for predicting the unsteady flow field over single/multiple cylinders. The neural network model constructs a mapping function between the temporal evolution of the pressure signal on the cylinder surface and the surrounding velocity field, where Convolutional Neural Network (CNN) layers are used as the encoder and deconvolutional neural network layers are used as the decoder. Compared with the network model with a fully connected (FC) decoder, the model with the deconvolution connected (DC) decoder is good for capturing and reconstructing the spatial relationships of low-rank feature spaces, such as edge intersections, parallelism, and symmetry, while the fluid flow, which is described by Navier–Stokes equations containing convection and diffusion terms, displays outstanding features of locality. In this article, the performance of the network models with the FC decoder and the DC decoder is evaluated by studying the problem of flow over a single cylinder first, and then the complexity of the flow structure of the studied problems is enhanced by increasing the number of cylinders and the Reynolds number. The results indicate that both the CNN-FC decoder model and CNN-DC decoder model achieve fast and accurate prediction on the velocity field, and the CNN-DC decoder model gives more robust and precise performance for all studied problems.

We develop a deep neural network-based reduced-order model (ROM) for rapid prediction of the steady-state velocity field with arbitrary geometry and various boundary conditions. The input matrix of the network is composed of the nearest wall signed distance function (NWSDF), which contains more physical information than the signed distance function (SDF) and binary map; the boundary conditions are represented by specifically designed values and fused with NWSDF. The network architecture comprises convolutional and transpose-convolutional layers, and convolutional layers are employed to encode and extract the physical information from NWSDF. The highly encoded information is decoded by transpose-convolutional layers to estimate the velocity fields. Furthermore, we introduce a pooling layer to innovatively emphasize/preserve information of boundary conditions, which are gradually flooded by other features during the convolutional operation. The network model is trained using several simple geometries and tested with more complex cases. The proposed network model shows excellent adaptability to arbitrary complex geometry and variable boundary conditions. The average prediction error of the network model on the testing dataset is less than 6%, and the prediction speed is two orders faster than that of the numerical simulation. In contrast to the current model, the average error of the network model with the input matrix of the binary map, traditional SDF, and model without pooling layers is around 12%, 11%, and 11%, respectively. The outstanding performance of the proposed network model indicates the potential of the deep neural network-based ROM for real-time control and rapid optimization, while encouraging further investigation to achieve practical application.

In the interdisciplinary field of data-driven models and computational fluid mechanics, the reduced-order model for flow field prediction is mainly constructed by a convolutional neural network (CNN) in recent years. However, the standard CNN is only applicable to data with Euclidean spatial structure, while data with non-Euclidean properties can only be convolved after pixelization, which usually leads to decreased data accuracy. In this work, a novel data-driven framework based on graph convolution network (GCN) is proposed to allow the convolution operator to predict fluid dynamics on non-uniform structured or unstructured mesh data. This is achieved by the fact that the graph data inherit the spatial characteristics of the mesh and by the message passing mechanism of GCN. The conversion method from the form of mesh data to graph data and the operation mechanism of GCN are clarified. Moreover, additional relevance features and weight loss function of the dataset are also investigated to improve the model performance. The model learns an end-to-end mapping between the mesh spatial features and the physical flow field. Through our studies of various cases of internal flow, it is shown that the proposed GCN-based model offers excellent adaptability to non-uniformly distributed mesh data, while also achieving a high accuracy and three-order speedup compared with numerical simulation. Our framework generalizes the graph convolution network to flow field prediction and opens the door to further extending GCN to most existing data-driven architectures of fluid dynamics in the future.