Machine learning is a promising technology to improve the computation time, accuracy, and stability of physical simulations. However, it is still an open problem to obtain more general and reliable machine learning models because of the data-driven nature of the scheme. In particular, machine learning on mesh-structured data is inevitable to realize accurate prediction because the mesh is a common data structure used in various methods for computational fluid dynamics (CFD). For machine learning models that learn mesh-based CFD, we put three requirements: 1. Ability to deal with mesh-structured data as an input and an output. 2. Fulfillment of constraints coming from physical laws. 3. Lightweight model to make the computation faster. In this study, we propose a graph neural network that can reflect physical symmetry and perform prediction efficiently. Graph neural networks can deal with arbitrary meshes without any modifications in the models. Physical symmetries, such as translation and rotation, are considered through the concept of equivariance. Furthermore, we implemented differential operators in the model, which are critical to expressing spatial relationships in physical simulations. Since most physical laws are described using differential equations, it is possible to construct an efficient machine learning model corresponding to a given governing equation, which reduces computation time. We demonstrate that the proposed model learns mesh-based physical simulations with high accuracy and computational efficiency. We expect our model to be key to realizing more general and reliable machine learning models for physical simulations.