This study proposes a novel hybrid intelligent model, POD–CAE–LSTM, to enhance the accuracy and stability of spatiotemporal predictions of unsteady turbulent flows. This model is based on the concept of a triple decomposition of the flow field, in which the flow field is separated into a time-averaged velocity, a coherent component, and a stochastic turbulent component. Proper orthogonal decomposition (POD) is employed to accurately capture the dominant large-scale coherent component of the flow field. Meanwhile, a convolutional autoencoder (CAE) is utilized to achieve efficient nonlinear dimensionality reduction of the stochastic turbulent component. Subsequently, a long short-term memory (LSTM) network with a coupled self-attention mechanism is introduced to perform temporal predictions using the reduced low-dimensional vectors. Finally, the predicted results are reconstructed through the POD modes and the CAE decoder to obtain the future evolution of the flow field. The predictive performance of the proposed model is evaluated using two representative cases: the quasi-periodic flow field of a cylinder wake at a Reynolds number of 1 × 104, and a highly nonlinear single-vortex tornado flow field. The results demonstrate that the proposed model outperforms the widely used POD–LSTM and CAE–LSTM models in terms of both dimensionality-reduction reconstruction accuracy and spatiotemporal prediction capability. These encouraging findings indicate that the proposed POD–CAE–LSTM model successfully integrates the advantages of physical interpretability and deep learning, thereby providing a reliable and efficient solution for the spatiotemporal prediction of complex turbulent flows.
Zhang et al. (Thu,) studied this question.