This paper introduces the Multi-Scale Physics-Constrained Neural Network (MSPCNN), a novel methodology for incorporating multi-fidelity data into a unified latent space through a customized multi-fidelity autoencoder (AE). The MSPCNN aims to address the computational challenges of physics-constrained neural networks (PCNNs) by leveraging low-fidelity data to evaluate physical constraints, thereby reducing training complexity and improving prediction accuracy. The proposed model consists of two separate AEs, one trained on high-fidelity data and the other on low-fidelity data, both mapping to a shared latent space. An LSTM model is then trained to predict the evolution of the physical system within this latent space, incorporating physical constraints such as energy conservation and flow operator. The effectiveness of MSPCNN is demonstrated through numerical experiments on the 2D Burgers' system and a shallow water system, showing significant improvements in prediction accuracy and robustness compared to conventional PCNNs. The results highlight that MSPCNN can achieve up to 50% reduction in mean squared error (MSE) and a substantial decrease in training time, making it a promising approach for high-dimensional dynamical systems.This paper introduces the Multi-Scale Physics-Constrained Neural Network (MSPCNN), a novel methodology for incorporating multi-fidelity data into a unified latent space through a customized multi-fidelity autoencoder (AE). The MSPCNN aims to address the computational challenges of physics-constrained neural networks (PCNNs) by leveraging low-fidelity data to evaluate physical constraints, thereby reducing training complexity and improving prediction accuracy. The proposed model consists of two separate AEs, one trained on high-fidelity data and the other on low-fidelity data, both mapping to a shared latent space. An LSTM model is then trained to predict the evolution of the physical system within this latent space, incorporating physical constraints such as energy conservation and flow operator. The effectiveness of MSPCNN is demonstrated through numerical experiments on the 2D Burgers' system and a shallow water system, showing significant improvements in prediction accuracy and robustness compared to conventional PCNNs. The results highlight that MSPCNN can achieve up to 50% reduction in mean squared error (MSE) and a substantial decrease in training time, making it a promising approach for high-dimensional dynamical systems.