DeepTRNet: Time-resolved reconstruction of flow around a circular cylinder via spatiotemporal deep neural networks

We propose spatiotemporal deep neural networks for the time-resolved reconstruction of the velocity field around a circular cylinder (DeepTRNet) based only on two flow data types: the non-time-resolved wake velocity field and sparse time-resolved velocity measurements at specific discrete points. The DeepTRNet consists of two operations, i.e., compact spatial representations extraction and sequential learning. We use the convolutional autoencoder (CAE) in DeepTRNet to extract compact spatial representations embedded in the non-time-resolved velocity field. The nonlinear CAE modes and corresponding CAE coefficients are thus obtained. Based on the nonlinear correlation analysis of the velocity field, we use the bidirectional recurrent neural networks (RNN) with the gated recurrent unit for mapping the sparse time-resolved velocity measurements to the CAE coefficients via sequential learning. The early stopping technique is used to train the DeepTRNet to avoid overfitting. With the well-trained DeepTRNet, we can reconstruct the time-resolved velocity field around the circular cylinder. The DeepTRNet is verified on the simulated datasets at two representative Reynolds numbers, 200 and 500, and the experimental dataset at Reynolds number 3.3 × 104 with the steady jet at the rear stagnation point of the cylinder. We systematically compare the DeepTRNet method and the RNN-proper orthogonal decomposition (POD) approach. The DeepTRNet can obtain the accurate time-resolved velocity field depending on the two data types mentioned above. The DeepTRNet method outperforms the RNN-POD method in the reconstruction accuracy, especially for the reconstruction of small-scale flow structures. In addition, we get the reliable velocity field even for the high-frequency components.