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Weather forecasting is the analysis of past and present weather observations, as well as the use of modern science and technology, to predict the state of the Earth atmosphere in the future. It is one of the most important applications of scientific computing and plays a crucial role in key sectors such as transportation, logistics, agriculture, and energy production. Traditionally, atmospheric scientists have relied on Numerical Weather Prediction (NWP) methods, which utilize mathematical models of the atmosphere and oceans to forecast the weather states based on current weather conditions. While modern meteorological forecasting systems have achieved satisfactory results using NWP methods, these methods largely rely on parametric numerical models, which can introduce errors in the parameterization of complex, unresolved processes. Additionally, NWP methods face challenges in meeting the diverse needs of weather forecasting due to its high computational cost, the difficulty of solving nonlinear physical processes, and model deviations. Code is available at https://anonymous.4open.science/r/EWMoE-6C21/.