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The reduced-order model can accurately and efficiently predict unsteady problems in many aerospace engineering applications. The traditional reduced-order model based on proper orthogonal decomposition (POD) and Galerkin projection has poor robustness and large error in predicting complex problems. In this paper, a reduced-order model combining POD and deep learning is proposed to predict cavity flow oscillations under different flow conditions. Firstly, POD modes and corresponding coefficients are obtained by POD. Then, two deep learning frameworks, including multilayer perceptron (MLP) and long short-term memory (LSTM) neural networks, are used to predict the future POD coefficients, respectively. Finally, the cavity flow oscillations across multi-Mach numbers are predicted by the POD modes and the future coefficients. The results show that both of these frameworks can accurately predict cavity flow oscillations when the flow conditions change, and the time cost is reduced by order of magnitude. In addition, due to the performance of LSTM is better than that of MLP, its calculation speed is faster.