This study introduces a nonlinear reduced order model (ROM) for fluid dynamics, which combines proper orthogonal decomposition (POD) with deep learning error correction. Our approach merges the interpretability and physical adherence of classical POD Galerkin ROMs with the predictive capabilities of deep learning. The hybrid model addresses errors within and outside the POD subspace. Firstly, POD generates part of the reduced state, complemented by an autoencoder compressing only the unretained POD modes. Thus, the most energetic modes are computed interpretably, while the least energetic are handled with a superior reduction method. Secondly, the time integration employs a hybrid neural Ordinary Differential Equation (neural ODE). A POD ROM estimates part of the dynamics, and a deep learning model corrects its error. Using Neural ODE aligns the model with underlying physics for enhanced stability and accuracy. The proposed method differs from current hybrid methods operating solely in the POD subspace and using Mori-Zwanzig time dependency, posing potential initialisation issues. Our model is applied to the viscous Burgers’ equation, the parametric circular cylinder flow, and the fluidic pinball test case. Accuracy and numerical complexity are compared to classical POD Galerkin ROMs, fully data-driven models, and concurrent hybrid methods.