In response to the growing demand for the global energy supply chain, wind power has become an important research subject among studies in the advancement of renewable energy sources. The major concern is the stochastic volatility of weather conditions that hinder the development of wind power forecasting approaches. To address this issue, the current study proposes a weather prediction method divided into two models for wind speed and atmospheric system forecasting. First, the data-based model incorporated with wavelet transform and recurrent neural networks is employed to predict the wind speed. Second, the physics-informed echo state network was used to learn the chaotic behavior of the atmospheric system. The findings were validated with a case study conducted on wind speed data from Turkmenistan. The results suggest the outperformance of physics-informed model for accurate and reliable forecasting analysis, which indicates the potential for implementation in wind energy analysis.