This paper introduces the Multi-Scale Physics-Constrained Neural Network (MSPCNN), a novel method for incorporating data with different levels of fidelity into a unified latent space through a customized multi-fidelity autoencoder. The approach enables the training of predictive models by mapping latent representations of inputs into various fidelity physical spaces, allowing physical constraints to be evaluated within low-fidelity spaces. This reduces training complexity and improves accuracy. The MSPCNN is tested on two fluid dynamics problems: the two-dimensional Burgers' system and the shallow water system. Results show that incorporating physical constraints in low-fidelity fields significantly enhances prediction accuracy and noise robustness. Additionally, the training complexity is reduced by computing physical constraint loss in the low-fidelity field rather than the high-fidelity one. The MSPCNN demonstrates robust performance in the presence of noisy data and achieves a significant reduction in MSE compared to conventional physics-constrained neural networks. It also exhibits a remarkable reduction in training time, ranging from half to a quarter of the original computation time. The method leverages multi-fidelity data to train high-fidelity models, ensuring a balance between computational efficiency and physical accuracy. The study highlights the effectiveness of using physical constraints in low-fidelity fields for model training and prediction.This paper introduces the Multi-Scale Physics-Constrained Neural Network (MSPCNN), a novel method for incorporating data with different levels of fidelity into a unified latent space through a customized multi-fidelity autoencoder. The approach enables the training of predictive models by mapping latent representations of inputs into various fidelity physical spaces, allowing physical constraints to be evaluated within low-fidelity spaces. This reduces training complexity and improves accuracy. The MSPCNN is tested on two fluid dynamics problems: the two-dimensional Burgers' system and the shallow water system. Results show that incorporating physical constraints in low-fidelity fields significantly enhances prediction accuracy and noise robustness. Additionally, the training complexity is reduced by computing physical constraint loss in the low-fidelity field rather than the high-fidelity one. The MSPCNN demonstrates robust performance in the presence of noisy data and achieves a significant reduction in MSE compared to conventional physics-constrained neural networks. It also exhibits a remarkable reduction in training time, ranging from half to a quarter of the original computation time. The method leverages multi-fidelity data to train high-fidelity models, ensuring a balance between computational efficiency and physical accuracy. The study highlights the effectiveness of using physical constraints in low-fidelity fields for model training and prediction.