Geometry and boundary condition adaptive data-driven model of fluid flow based on deep convolutional neural networks

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.