In an Atmospheric General Circulation Model (AGCM), the representation of subgrid-scale physical phenomena, also referred to as physical parameterizations, requires computational time which constrains model numerical efficiency. However, the development of emulators based on Machine Learning offers a promising alternative to traditional approaches. We have developed offline emulators of the physics parameterizations of an AGCM, ICOLMDZ, in an idealized aquaplanet configuration. The emulators reproduce the profiles of the tendencies of the state variables for each independent atmospheric column. In particular, we compare Dense Neural Network (DNN) and U-Net models. The U-Net provides better predictions in terms of mean and variance. For the DNN, while it consistently delivers good performances in predicting the mean tendencies, the variability is not well captured, posing challenges for our application. We then investigate why the DNN's predictions are poorer compared to those of the U-Net, in terms of physical processes. We find that turbulence is not well emulated by the DNN. Leveraging a priori knowledge of how turbulence is parameterized in the phyLMDZ model, we show that incorporating physical knowledge through latent variables as predictors into the learning process leads to a significant improvement of the variability emulated with the DNN model. This improvement brought by the addition of these new predictors is not limited to the DNN, as the U-Net has also shown enhanced results. This study hence emphasizes the importance of adding physical knowledge in Neural Network (NN) models to improve predictions and to ensure better interpretability. It opens perspectives on a deeper understanding of the emulator, as well as exploring the contribution of new physical predictors, aiming to make climate simulations and projections.